Eroshkin (2008)
y2 + xy = x3 - 3969894586069811345797915011354270x + 96060267726898136055233656334812211512766915208900 Torsion points: O, [42608376638232540, 2064919764454782297078930], [42608376638232540, -2064919807063158935311470], [102000243167270700, -27428919904947941620316670], [102000243167270700, 27428919802947698453045970], [37773199222238940, -18886599611119470] Independent points of infinite order: P1 = [19009234576838940, 5240669432779505183920530] P2 = [37871089128607740, 177444177960827044499730] P3 = [37969586449003500, 255667665375551443275330] P4 = [39249365168545680, 841765753894805349859890] P5 = [40358796111683340, 1256111928005948324372130] P6 = [34516084242736860, 395140905689330572017810] P7 = [38420722546570140, 498871396814474291589330] P8 = [528262098613980, 9693465339791103915219090]
Dujella - Eroshkin (2008)
y2 + xy = x3 - 684648272485680709402900211994868050x + 78106637528224228839785060686283103205949536929802500 Torsion points: O, [1102021082445716100, -813609135503177007756478050], [1102021082445716100, 813609134401155925310761950], [-537011663296475700, 539357490149052705460413750], [-537011663296475700, -539357489612041042163938050], [116385524298476100, -58192762149238050] Independent points of infinite order: P1 = [97315168809936360, 111362352308790161728571550] P2 = [100266286616126100, 102310837586325137753761950] P3 = [65918771706660540, 182378453106162486365435910] P4 = [26186020984556100, 245349504681668391482761950] P5 = [2080373091888524100, 2767225702968301958261161950] P6 = [113959322895490740, 39554299596194279632619550] P7 = [-427795713199021500, -541022822031147788173558050] P8 = [32154420277084490052, 182271049773796813890991310046]
Dujella - Eroshkin (2008)
y2 + xy = x3 - 475580051023836530278979780324370x + 3991178865068293690072267520912681524547928912900 Torsion points: O, [13518316590105540, -180389476580872603967970], [13518316590105540, 180389463062556013862430], [11684356686817860, -171840809940319288581090], [11684356686817860, 171840798255962601763230], [-25180945414732860, 12590472707366430] Independent points of infinite order: P1 = [12414160757549190, 20376334565212544774130] P2 = [-2913636650512200, -2313463129634505564898530] P3 = [-8796678909081774, -2737517691286172125747428] P4 = [12159120155571140, 78735685592736995110430] P5 = [-5126598523468860, -2508894081763080979161570] P6 = [-18577968488402460, -2532680992738305321897570] P7 = [1772678827009290180, 2360002023751301613880680990] P8 = [23747617109637060, 2467739518676845265287710]
Elkies (2008)
y2 = x3 + x2 - 196348925423783757393146158660311426285x
+ 1051757327090520025478687684152067952012419669968483731900
Torsion points:
O, [7537968017313745980, 0],
[10132363338719401605, -10124998556114464265515325625],
[10132363338719401605, 10124998556114464265515325625],
[-2439709524759448545, -38939312707414052613432763725],
[-2439709524759448545, 38939312707414052613432763725]
Independent points of infinite order:
P1 = [6023881995371818689, 9357569440591044907223158455]
P2 = [7270559978599909245, 2918915446078886619276240615]
P3 = [3629951324598415980, 19668515653655328302780242500]
P4 = [5221270916602449105, 12996420964925856481700015625]
P5 = [-12379625066269681395, 39815104178698903249192193625]
P6 = [-6788411736470472855, 45517331456067424746735963735]
P7 = [8967887941144144365, 3485218083173721934181508135]
P8 = [-1643227814742177267, 37013055843255638108712796761]
Elkies (2008)
y2 + xy + y = x3 - 913217994232980248076710723083809326628x
+ 11134659509213630442423739721043373303068542539029002813998
Torsion points:
O, [-35080242650405792251, 17540121325202896125],
[10457916253930998974, 52230869394111038538388255350],
[10457916253930998974, -52230869404568954792319254325],
[25937864929179419519, 69985894996077621947272533495],
[25937864929179419519, -69985895022015486876451953015]
Independent points of infinite order:
P1 = [-649578426066748876, -108294007800484741498750710375]
P2 = [6720075382423660274, 72809617547796961950943751775]
P3 = [-12979543526370783241, -144226097960871109655672768265]
P4 = [13227370736142192374, 37006640679945108356282215875]
P5 = [15179996327376133699, 27748423439323339154524885325]
P6 = [-3105396365976348817, -118070387910224620788423175497]
P7 = [8377788197190378269, 63811654127849456017897604745]
P8 = [15677080881840697349, 25904379534934585054470613725]
Elkies (2008)
y2 = x3 + x2 - 2988953265941486315671511392675613660213547766700x
+ 1988561710795654748570775576651431494771732919207799253936953545372685348
Torsion points:
O, [1009717521070207317070191, 0],
[1073282221112051638300816, 130086018425624273993885089962026250],
[1073282221112051638300816, -130086018425624273993885089962026250],
[2105217870810973618012516, 2241956283721027904726941711993376850],
[2105217870810973618012516, -2241956283721027904726941711993376850]
Independent points of infinite order:
P1 = [-604068163732154016647549, 1890415231517780160670737258638609970]
P2 = [2857576690277708440973316, 4096539977629565042954566540469868750]
P3 = [-563231808943581685114004, 1869053557044598493055541403937978390]
P4 = [3013566251458771097202316, 4510997749515905302688211682319565750]
P5 = [-12342722470026536474684, 1423183632251359984976720720715995250]
P6 = [879646162190920779802636, 199976838486383464625330430583774410]
P7 = [1349260407411465907296492, 641886985312754258304009460566854550]
P8 = [20528665690170346229179576, 92692746035914225383396312639611897970]
Dujella (2008)
y2 + xy = x3 - 7215616324653838384913625350620220143981486228910x + 7312288533664556036160260732587179429322821986829787336941560686885443972 Torsion points: O, [5475588829411348697262111/4, -5475588829411348697262111/8], [2121120609105544610860684, 1245127071749416083147406497213054658], [2121120609105544610860684, -1245127071751537203756512041823915342], [-750124386557461278266516, -3507536652081801573285227520396800942], [-750124386557461278266516, 3507536652082551697671784981675067458] Independent points of infinite order: P1 = [219358968239218978506724, 2395836717017909381572859545984513378] P2 = [-3091229166689958930955316, -280286541269987268033484163341331342] P3 = [-2239228398261706467323936, -3498840991672330941909886905283845662] P4 = [-1018176442660332951335316, -3688296708824472065498352578784711342] P5 = [-855772402164816811361156, -3586152814267631298233544662798353982] P6 = [818923650391563376777253524, 23434882858174236476471778528071875889698] P7 = [981195552157289045494942, 1084895717891006504444506347310740220] P8 = [1539660764869579845477917076266194444/667735756801, 934583054231014825389260075072386122889330284513311438/545640941405693951]
Dujella (2008)
y2 + xy + y = x3 - 360225153137805377563861499671657822554529441873x
+ 83216446291933254309928055003080883290004599027629309383724863943212006
Torsion points:
O, [1386073885849902527145255/4, -1386073885849902527145259/8],
[346518562747739275398970, -93100933945378027529949880423],
[346518562747739275398970, 93100587426815279790674481452],
[347134849579162392965920, 628636750636938998383579509354077],
[347134849579162392965920, -628636750984073847962741902319998]
Independent points of infinite order:
P1 = [-201350765871070825072280, -384167759776924072704852498720199798]
P2 = [3465453741425681714259167951170/13184161, 3916020594579611161495588016200914654954857132/47871688591]
P3 = [-1530891906851027420988621020/2209, -375226532559615842514877321739813505254/103823]
P4 = [208329125332353622742620998117865/635846656, -305793216111890946837183045973963735496750650933/16033509277696]
P5 = [143700762204124840536068555097557883894670/414695968638028561,
623123690513904427915920801326096141042018288195689409168/267051314637489154718295559]
P6 = [38665199748292222396169549408788065050829520/111581923925922542521,
21859453055797108234579056052243102483020191167988153101063/1178666032742375478596523332819]
P7 = [2595865259686900521076205534620, 4182377403483061900627454349269280339739736702]
P8 = [134167494836388112037821368497653010676658625761570/387187137927973517540875681,
7175269377858450105973312787736488735603282558693036044163524585292/7618708948796969539862652307413564038671]
Dujella (2008)
y2 + xy = x3 - 164709440877242365084184292915926531855737195x + 813625350097041580941646921583190206129348507310784165707920095025 Torsion points: O, [-59277305281049993422321/4, 59277305281049993422321/8], [7547598942322316688230, -20565870659408465943020870326135], [7547598942322316688230, 20565870651860867000698553637905], [7272572815673036201750, 20312990487148414788069681298745], [7272572815673036201750, -20312990494420987603742717500495] Independent points of infinite order: P1 = [7204921519339507272476, -30342594986928428224771428237583] P2 = [553028774526498558335227670/78961, 1329781793949257140660840569253346992225/22188041] P3 = [7823258661841924440650, 62214405062270243908610496702845] P4 = [7304081951789605918670, 15621853339457769804240056773025] P5 = [25406528236662964478578622/3481, 3375388464199383880408878427323611923/205379] P6 = [19892700252670441957070, -2325734222986633537381401327065695] P7 = [50684735214742788000780155/7396, -52115209593338433659753650190151348695/636056] P8 = [68112130364806350968358710/7921, -128294785685905133481525886871050467335/704969]
Dujella - Peral (2012)
y2 + xy + y = x3 - 1335985556213327566393188804097819664x + 594359932384372250781816622950011820594941728829430686 Torsion points: O, [666411001163892393, -333205500581946197], [381052561931994273, 374977929121253630729947603], [679288450334257194, -16921733012834847802357562], [679288450334257194, 16921732333546397468100367], [381052561931994273, -374977929502306192661941877] Independent points of infinite order: P1 = [-140507948167530447, -882781142581362400909478117] P2 = [970750778144885553, 460700310200518512519240883] P3 = [655818982441251378, 16187331635074900618288183] P4 = [663790984763164161, 4830472387434653237227987] P5 = [653009534357684748, 20146964675065541058778498] P6 = [816035821190266398, 218077775456715021304543123] P7 = [694665952143846729, 38920446123657493602545947] P8 = [-510779650064624895, -1069342730510619994725877973]
Dujella - Peral - Tadic (2014)
y2 + xy = x3 - 6425764677860152725987889739367599975652685x
+ 6269378239936665797804421444079658936297007509538479980249111697
Torsion points:
O, [1517955063240217792634, -3606855504159781197488412843817],
[1517955063240217792634, 3606855502641826134248195051183],
[2554304868262237681034, -80755868564113968693239261885617],
[2554304868262237681034, 80755868561559663824977024204583],
[5878015362945634044911/4, -5878015362945634044911/8]
Independent points of infinite order:
P1 = [1479198619437225203114, 961674873976968940724553185423]
P2 = [983878248659722617554, 29993639837709698275453651811903]
P3 = [-195270002998284904246, -86698855872338945168351261518897]
P4 = [1905768976745927479129172/1369, 236977986013326425218546342851879443/50653]
P5 = [-6311475309396756863458144/2809, -14406515547556997158113573289642138709/148877]
P6 = [247988092428272416664, 68491721471136821252796551194823]
P7 = [-9690047463126775012507114/4489, -30199010299318291598491430799264039151/300763]
P8 = [64598145397069207714673134373185088874536/212324772722617129,
16417803290702261388641963692832568226039135864150739507379661/97836521164483623902429867]
Dujella - Peral - Tadic (2014)
y2 + xy + y = x3 - 196088112850250619096616465973482541791329679334818x
+ 1056769769874550553807438390237468946455487112972817882032821970832478722306
Torsion points:
O, [8568770960311046386464160, 2384884601829486253161022032872853857],
[8568770960311046386464160, -2384884601838055024121333079259318018],
[32606185327713118408341015/4, -32606185327713118408341019/8],
[15953123067909853191678910, 44594347893083770521585821338568986982],
[15953123067909853191678910, -44594347893099723644653731191760665893]
Independent points of infinite order:
P1 = [1057973462598959467952560, 29163297964171432456943011018660933457]
P2 = [6390444722296280203020060, 8040592243914015726243050965950513982]
P3 = [10382194565777549006869345384/1369, 122534813782624874765286026024762963502662/50653]
P4 = [270353769673133729567976642040/26569, 46453901406064491867231675645914400643500554/4330747]
P5 = [43203697102467548760345377151565/1507984, 254953468763255199423326052551783700114691703789/1851804352]
P6 = [4871309206909977593031642361996240/779689, 339991027601031870439903062701394163947516029697659/688465387]
P7 = [-12563289877496241311102966112331660427615/950665009116736,
-1073052947602698733419285331654325649505466143175326000545413/29311717330335008278016]
P8 = [-175623332716620572051126606963232368719550/15374892203954089,
-81021788245304035137144982461959794292535587758641904563056146/1906417953646831973084437]
Dujella - Peral - Tadic (2014)
y2 + xy = x3 - 1601825625756180889302684290822230x + 24675947726759132681554784670325851665637575876900 Torsion points: O, [-46214398621289140, 23107199310644570], [22563957778149260, 143035619776855373588570], [22563957778149260, -143035642340813151737830], [23654765830935140, 145304129651912056789370], [23654765830935140, -145304153306677887724510] Independent points of infinite order: P1 = [22311083413962860, 208788897012877753988570] P2 = [21662349223926860, 376641377102266218260570] P3 = [-18959179128730940, -6944808179987330872541630] P4 = [-18026270162169940, -6906034839364874838747430] P5 = [23277178428047720, 46598373994440978778970] P6 = [22597546137330830, 134296855095359975095070] P7 = [-19676169383912140, -6969654126829489724751430] P8 = [24054284208284660, 251384777499127214019770]
Dujella - Peral - Tadic (2014)
y2 + xy = x3 - 40261759047198447746757434668761470x + 3060380746085656600349631533426865337350014313816900 Torsion points: O, [103749338665821340, -51874669332910670], [155127013688094940, 23403660202067945040817330], [155127013688094940, -23403660357194958728912270], [-51376077635273900, -70663036833673849226285870], [-51376077635273900, 70663036885049926861559770] Independent points of infinite order: P1 = [57915247207650940, 30378758041630841142337330] P2 = [55925258489949340, 31363118982496469145553330] P3 = [43427614290454522, 37333781548767800284291312] P4 = [128656237705564060, 3166599180935284108069810] P5 = [-31117058267646860, -65445232762546245363178670] P6 = [143976949354409740, 15753278881617607486963330] P7 = [69595528562908840, 24401452861042487623969330] P8 = [603422305010816860, 445514027200451219573049010]
Dujella - Peral - Tadic (2015)
y2 + xy = x3 - 18131452558471483129875821564394494454484900x + 27258515593219545269929733144764982359147216805507430448480010000 Torsion points: O, [-4871082049418599238200, 2435541024709299619100], [1130860723404503757560, 90556969481739681683345838981740], [3967867345142114803400, 133361563224381251999394767721500], [3967867345142114803400, -133361563228349119344536882524900], [1130860723404503757560, -90556969482870542406750342739300] Independent points of infinite order: P1 = [3677101340806938192380, 101516931635836622115160987431500] P2 = [456697255017527735299328/49, 280320687988858352967786568660804868/343] P3 = [1105017658807656237512, 92586379385650335920764736151836] P4 = [37285131903192444003873230/10201, 102079480195952015031266992878925028770/1030301] P5 = [-21153632112275493108374430700/4661281, -1276111158392901590687686440495353546165600/10063705679] P6 = [-1031610275069089952242196650792/2047291009, -17641041671674171027159334240799001843934703772/92633776284223] P7 = [22425927162893873857854908102140/49857721, 106195524618376134691950508628230065359986624760/352045367981] P8 = [20567114201971284897580030787843900/13451531822689, 2751437681922221518913081493704773640024112414126200/49335282013444325137]
Dujella - Peral - Tadic (2015)
y2 + xy = x3 - x2 - 51900732008393603998885951715125368699x + 46417971051490003806207921373628830870755520996382489505 Torsion points: O, [9705823536209070331, 21377474622103797304470834122], [9705823536209070331, -21377474631809620840679904453], [-30462022090411145901/4, 30462022090411145901/8], [-567141007878794379, 8698884079181711280939722937], [-567141007878794379, -8698884078614570273060928558] Independent points of infinite order: P1 = [-6154572799863548636, -11520294242319441803593622511] P2 = [7220627323148293479, 6937383364814481651691155279] P3 = [455126116795783006069341/44944, 225331925195437391204566751648308041/9528128] P4 = [2041470057744234449240730/69169, 2831337416979550828604821387230408105/18191447] P5 = [5043342585840457843441936/57121, 11288647158812882569260229688399437663/13651919] P6 = [48860035682311664588755/56169, 18488986295180666844578659313339090/13312053] P7 = [2716009269149768367840805/394384, 978461322828567779158262455968895125/247673152] P8 = [254967578145149321436294966592101/10741114788496, 3886625915284820478563009806677673568390692044693/35202542927684404544]
Dujella - Peral - Tadic (2015)
y2 + xy = x3 - 40181448765949668810483386349055533876x + 87685454975186288849638211899417160265576039917893134480 Torsion points: O, [-7232264724957374232, 3616132362478687116], [6115606257695808744, 8407087653678098186834947980], [6115606257695808744, -8407087659793704444530756724], [1513362989106346248, 5508388483134534423945289836], [1513362989106346248, -5508388484647897413051636084] Independent points of infinite order: P1 = [5767574207154876648, 6913307257513139305206397836] P2 = [-4392687999111426144, -13395148314120232071888737196] P3 = [-508299732196550424, -10391262960665328649059773556] P4 = [-2013136420006718136, -12665603742771148123065580404] P5 = [873116869278439656, 7298490260347533004478059404] P6 = [1196221225405469826, 6428940824958120242378308230] P7 = [-4478026713934625982, -13335007517439310419079211784] P8 = [73818477197226261511336/729, 20017664665370240627142983822734628/19683]
Dujella - Peral - Tadic (2015)
y2 + xy = x3 - 13579205648744547106359624860424940534765x + 568609448618954655318256769174781341052119102179499627318225 Torsion points: O, [-534216794604535705105/4, 534216794604535705105/8], [105426657885843307730, 555691739321518888942958589935], [105426657885843307730, -555691739426945546828801897665], [33534357570174157490, 388523715989670962577616455935], [33534357570174157490, -388523716023205320147790613425] Independent points of infinite order: P1 = [-68125728946350153670, -1085137499657173204590021465265] P2 = [-2411792587660417630, -775464794409275143548509448865] P3 = [47257826968730065250, 180074171077330885332711899615] P4 = [37629831017824874930, 333031879544959852526337677135] P5 = [13592542643486836130, 621727301230890014364854211935] P6 = [13921403378216971430, 618276550882608461881691870435] P7 = [81597993707839884530, 62224846045143291519345883535] P8 = [46130304047697398630, 200903157606131590903799414435]
Dujella - Peral - Tadic (2015)
y2 + xy = x3 - 1161478661360056498450485718381297335x + 795675079452688771133200765624035786829237375610829225 Torsion points: O, [1445245886909047470, -1461434043893853937205491635], [-1327049612953350634, 663524806476675317], [159697872862442070, -783748842682768308063711435], [159697872862442070, 783748842523070435201269365], [1445245886909047470, 1461434042448608050296444165] Independent points of infinite order: P1 = [-431902785304108410, -1103065635140539084577485035] P2 = [2254549066884405462, 3104338604644785612099564981] P3 = [-4090237474027380, -894665152202297571183112635] P4 = [999870563737515990, 796215106755089875498414965] P5 = [77735311620644178472470/841, 21671961090277366062462349437791385/24389] P6 = [-928617289694051277086/729, -8982321052449310891079230302749/19683] P7 = [382333220754431321212710/573049, 244526314435395210191808302614541745/433798093] P8 = [16543676786475853768766520/1776889, 66870680148155482396445570969792440185/2368593037]
Dujella - Peral - Tadic (2015)
y2 + xy + y = x3 - x2 - 574566017499116627722160048766372482x + 183318463515904127413857838802960720074418403931454081 Torsion points: O, [-884241588715000959, 442120794357500479], [227571040211066641, 253671949238545255146888079], [227571040211066641, -253671949466116295357954721], [708727854212906421, 363453025212131634641373859], [708727854212906421, -363453025920859488854280281] Independent points of infinite order: P1 = [327016118214648825, 174347550963201094598668087] P2 = [524152945235151489, 161746218428062387756839871] P3 = [358148635689684019, 153226346116986737191013701] P4 = [429153480712042791, 125617740407867851514090479] P5 = [20357270873756856289, 91787340742738526836614344671] P6 = [-17116878043610652891/49, -200413324409213842532654013503/343] P7 = [171495550578045804822301/370881, 29018928146389652669842676566852151/225866529] P8 = [35316680003361131871639/39601, 4859197606767536054005218514568761/7880599]
Gandhikumar - Voznyy (2019)
y2 + xy = x3 - 988951765004387920861556578668438719509056534725x + 4431534526239166862771591096675025752199977904072746707532095151207939457 Torsion points: O, [-7369455181597954992773009/4, 7369455181597954992773009/8], [18429292760989840435654, -2100789162181417942471683081606249077], [18429292760989840435654, 2100789162181399513178922091765813423], [3098519399669179644226654, -5578134363164735412686928339908200577], [3098519399669179644226654, 5578134363161636893287259160263973923] Independent points of infinite order: P1 = [-414258825707396842320596, -2184061677425240635298379013050267827] P2 = [1130471105143790654971234, 2181342601810627012363717521746701903] P3 = [320028957153794432721004, 2036619311666125407808094752836182023] P4 = [-1261040317929041352914252, -1916587502851870430197369895283895529] P5 = [1540572205438528511873154, 2562092809534337156227832925822063423] P6 = [788731088319214158998876134961746/1849, 22151005183481378004888510960818021515619786822461/79507] P7 = [-49515282851232306970749904994/54289, -27055405849882722136206091169472780617099449/12649337] P8 = [-48437553648810943809894832487474/135094129, -3418574954569561268661287195734684883698467604619/1570199061367]
Dujella - Peral - Tadic (2019)
y2 + xy = x3 - 38330935927950988758564975538833073660x + 85931186193126044675921569605579658081947137757428867600 Torsion points: O, [2838418966030476920, -1419209483015238460], [5519209682359438520, 6519132450618668351367199940], [5519209682359438520, -6519132456137878033726638460], [-2444003552642819440, 12845766686469474736264826540], [-2444003552642819440, -12845766684025471183622007100] Independent points of infinite order: P1 = [-577411150927472680, -10386115011857245766747010460] P2 = [4553773156954668920, 2410748805436383920532473540] P3 = [2369215018971188920, 2900997586240158055009297540] P4 = [-1839418549739123080, -12256191111160798501401798460] P5 = [221553767030841981874324550/20675209, 2829218020599599644978930597039522564270/94010175323] P6 = [2297401290825999755384702940680/84845786089, 3397698156396974571201405268550870155742227580/24714135109362187] P7 = [31770180822230064430557745430/2716598641, 4980232254184243522673881097514165448272640/141591837767561] P8 = [479845529435359076201012461045962406648/17831493937336689, 10511196813572479275647556050259611015841944090814024074468/2381121713460076765663113]
Dujella - Peral - Tadic (2019)
y2 + xy = x3 - 351800107054876846907380158079364186x + 80277302459037686725168689689159569323645590756047716 Torsion points: O, [336435780064188244, -168217890032094122], [376507117442241940, 34565982489931017704538454], [376507117442241940, -34565982866438135146780394], [31155109811837308, 263338512007898032840898830], [31155109811837308, -263338512039053142652736138] Independent points of infinite order: P1 = [-254318153624678132, -391532548927561772381649218] P2 = [241856296970960496, 96641020204392836585524122] P3 = [-418370739024069392, -392722596302120509409302538] P4 = [253893640430180020, 85580251753625011482856054] P5 = [17339449182571915212/49, 3407963516277579678349447770/343] P6 = [627732015188462580, 326798611724275996285982166] P7 = [234354875957012380, 103452980626067202582661366] P8 = [10144819850624382484/25, 8235173538152164801055655038/125]
Dujella - Peral - Tadic (2019)
y2 + xy = x3 - 262504052726499199028600605821170774370x + 1636654058247187351529049657559922095478041054731129912900 Torsion points: O, [10078148675134552740, 3837640326999262624275956430], [10078148675134552740, -3837640337077411299410509170], [1690043109307441980, -34609797329844091248543001170], [1690043109307441980, 34609797328154048139235559190], [9240887879951959140, -4620443939975979570] Independent points of infinite order: P1 = [9469778089871945580, 131728254193348855958353830] P2 = [-2923414951897468938, -48775791011969362220468995224] P3 = [-5553826982149538820, -54067073049513869015079965010] P4 = [7267195298178249252, 10619881595931144962684885262] P5 = [9703217075980900290, 1761146371906935264751734780] P6 = [-18176829019283349660, -20064234501414505873566718770] P7 = [7621853814648978096660/841, 34480160895540607955565668694390/24389] P8 = [63585211592090995865240/6889, 153829183559690640955378663444570/571787]
Dujella - Peral - Tadic (2019)
y2 + xy + y = x3 - 19268651287520295734172617502244x + 32555553942033212710586516699879290958187545426 Torsion points: O, [2434546657346653, 8644293020444829455783], [2534338701081673, -1267169350540837], [2534672716881154, -28934744823072961798], [2534672716881154, 28932210150356080643], [2434546657346653, -8644295454991486802437] Independent points of infinite order: P1 = [2140883341156045, 33408148409468593971467] P2 = [2533820973458533, 45331337312131766243] P3 = [2540709721186549, 555563200532839538387] P4 = [2534229790601908, 9684394686284923493] P5 = [2534377191793933, 3158038739286397223] P6 = [2533846600502521, 43096907321293963667] P7 = [-506801237403755, -205403893647732916078153] P8 = [4318476084514441, 172860121954632936055307]
Dujella - Peral - Tadic (2019)
y2 + xy = x3 - 242101612082080883465208402167744401x + 43842467815131256256702280920634993360357741186747305 Torsion points: O, [-178210079582851222, -285180068131629023421096229], [234046202231251658, -117023101115625829], [422687931117102794, 130493732658450497947793051], [422687931117102794, -130493733081138429064895845], [-178210079582851222, 285180068309839103003947451] Independent points of infinite order: P1 = [30717756770685386, 190878584588007445622602139] P2 = [60241511964749578, 171687272347754923212039451] P3 = [-13857054040762702, -217243232647265695380535189] P4 = [337529039187789578, 24071284945326557666239451] P5 = [115639503008553674, 131880045257617185316824731] P6 = [223498627488115574, 29953497150152201347510631] P7 = [378488396512305866, 80184734129444227581857435] P8 = [920022405772931786, 774498840307411286234181275]
Dujella - Peral - Tadic (2019)
y2 = x3 + x2 - 453220454411081041475408053976625x + 3713747448382841638829425541194406169971714250000 Torsion points: O, [12291171619722000, 0], [12293949391944225, -528831745112701055025], [12293949391944225, 528831745112701055025], [11659350663210255, 120285953022903319356705], [11659350663210255, -120285953022903319356705] Independent points of infinite order: P1 = [7897185698712315, 791892431774850716925615] P2 = [-8585429915368875, 2640456633311322595662375] P3 = [12291329513849820, 25341040176735910770] P4 = [1757983318732800, 1709510604433197899787300] P5 = [12292093458085875, 172387650860123180625] P6 = [10443296941646145, 345836990554602929727345] P7 = [-10358652366744495, 2701295946670331624909295] P8 = [1355808910864875, 1761181248419137157468625]
Dujella - Peral - Tadic (2019)
y2 + xy = x3 - 2895282112695299617406105462760x + 1551478570292532622613954216675017870898049600 Torsion points: O, [1306988206791120, -653494103395560], [1786766413536720, -45635498543792443363560], [1786766413536720, 45635496757026029826840], [5953661136143280, 441981788960023433677080], [5953661136143280, -441981794913684569820360] Independent points of infinite order: P1 = [423466519365720, 20034000793195593882840] P2 = [152239878532560, 33380078321810438812440] P3 = [1452694866019920, 20277365658610124188440] P4 = [-169921905167448, -45150240120280712371584] P5 = [1307294853205320, 827040928799822932440] P6 = [96839725767120, 35665226726282437276440] P7 = [1419452549202870, 17370682407864884975940] P8 = [-1487468380734000, -50665597817761688849640]
Dujella - Peral - Tadic (2019)
y2 + xy = x3 - 2823100570650333061135120044365876x + 53722680317053770426036738014476974297901621850256 Torsion points: O, [-21897751424161352, 10249000491228052078378300], [23812609303061224, -11906304651530612], [48358017988086760, -5503476728348980079805044], [48358017988086760, 5503476679990962091718284], [-21897751424161352, -10249000469330300654216948] Independent points of infinite order: P1 = [37497502076189416, 766353942334195781084812] P2 = [-19121772923482584, -10035618618832957263979188] P3 = [14540875248609124, 3968224648100376962930848] P4 = [-2955112386341624, -7876512786755741025664628] P5 = [13798398225446656, 4170799843622529041881612] P6 = [11999087776084648, 4644960135738064461700300] P7 = [23746724655812560, 272453714449283191765156] P8 = [-50138484280898984, -8320285574296593695077988]
Dujella - Peral - Tadic (2019)
y2 + xy = x3 - 521898581151662383158650415466x + 139102677048540476550558210975450499388872100 Torsion points: O, [616639861102724, 7193973470858883240566], [616639861102724, -7193974087498744343290], [-257427387545992, 16012315573060968144326], [-257427387545992, -16012315315633580598334], [345678105543668, -172839052771834] Independent points of infinite order: P1 = [329822230580036, 1687565207858244545030] P2 = [339674215029686, 1009114376200243682234] P3 = [302154232422500, 2999106591792166425110] P4 = [-199734351443992, -15341955029071957267834] P5 = [29871458072000, 11114830612904501597990] P6 = [-580988662510316, -15691028220629492394074] P7 = [340328699602681364, 198539481505542503412693830] P8 = [97457855700918346/49, 28633912063299364148293828/343]
Dujella - Peral - Tadic (2019)
y2 + xy = x3 - 1872011578199241696858789714444730545072390x + 928514599239546628471182227392719371419100052181457961233600100 Torsion points: O, [940758436665362398380, -470379218332681199190], [1216856525812402558380, -21269531916958343580568223759190], [1216856525812402558380, 21269531915741487054755821200810], [3776952387485840245980, 218489443167738072692580024264810], [3776952387485840245980, -218489443171515025080065864510790] Independent points of infinite order: P1 = [1121514677097442438380, 15481016877856266374405561160810] P2 = [570050266422379025580, 6827583711687323953685587728810] P3 = [529499523834493438380, 9259643990614348310645036400810] P4 = [985377622445118485880, 6375536350852877850122235713310] P5 = [46496420373566847314220/49, 879073041413364602386809654834630/343] P6 = [628614770541693446220, 376433036229457502214345865770] P7 = [147166406708945947620, 25616492828230726064141616776010] P8 = [5610222622906578225212760/1369, 12620563529678888735290193561548474950/50653]
Voznyy (2019)
y2 + xy + y = x3 - 114366667228892131864239266348961991763x + 133933421605655657951410456339557051163582538807116292138 Torsion points: O, [14577364030645917204, 39553154882211361522886668585], [14577364030645917204, -39553154896788725553532585790], [-44950628272970786809/4, 44950628272970786805/8], [-992143771615187346, 15697929232922170575893975560], [-992143771615187346, -15697929231930026804278788215] Independent points of infinite order: P1 = [-5201913821219659371, -24250683745034050074716394890] P2 = [17190055908092829, 11487708965733715910031195460] P3 = [-7085909403404849046, -24259863126182288556553739540] P4 = [-2105089627867232796, -19114314202110710115332251415] P5 = [9379948455183834155794779, 28727688153665472543021433238095923910] P6 = [-767530074370798693, -14874848717802978456706530570] P7 = [354668234432888554122801/316969, 484306458711357149149397511468426620/178453547] P8 = [5406922898123461576857, 397579895906799178086735850458580]
Voznyy (2019)
y2 + xy = x3 + 559385891168349980722395673069449996015x - 38442351661794090503736559354538799936131699316186002775 Torsion points: O, [274887355699892655/4, -274887355699892655/8], [9362196745727186970, 77583772640116489058601408315], [9362196745727186970, -77583772649478685804328595285], [60261498475395098490, -502501243564436883501141287685], [60261498475395098490, 502501243504175385025746189195] Independent points of infinite order: P1 = [7417367095758243570, 67222108851389131466069879715] P2 = [286621257370554000, 11041425734639493393695813085] P3 = [2719308472391446830, 38766077241983254131897916755] P4 = [478033008252760800, 15135118322611949072662605165] P5 = [1068308713115260538355/4, 35054275101718448702651663266695/8] P6 = [58403548368228574350, 481502534308784726835432720735] P7 = [253592097843473905410, 4055867289315869233363646596875] P8 = [165052894227051733560/841, 206009983873206473497652764805625/24389]
Voznyy (2019)
y2 + xy = x3 - 6889860610334057189402959744342034583398891x + 9237609872689667373966543917188645330280958771089536835713667121 Torsion points: O, [531373260454119440830, 75674034012524254601103659366689], [531373260454119440830, -75674034013055627861557778807519], [-3136142971241712665154, 1568071485620856332577], [3030514834500218542366, 127240301896527958391203750659937], [3030514834500218542366, -127240301899558473225703969202303] Independent points of infinite order: P1 = [1018088815649178924010, 57257085372259627510426464720889] P2 = [193899238066374982366, 88932340366284765022273828617697] P3 = [370611202531744674458026/169, 150210707728538128585760858956011601/2197] P4 = [59202037661325348149134/25, 9843787366634584664319565718162717/125] P5 = [-338584844310799754974130/1369, -5294753213099670238824454407511983107/50653] P6 = [15993966009015413493140434/4225, 53112964070863662792187394446116732293/274625] P7 = [79481452217555363951365582/1089, 708146014453974348690348613679713496465/35937] P8 = [116694517538767100547016606/22801, 1131640228968912632958797001436970684647/3442951]
Voznyy (2019)
y2 + xy = x3 - 5735720609435000360396020614667808752375x + 150485353390295360395953965468084020388390614011037316510057 Torsion points: O, [127566650300506323791/4, -127566650300506323791/8], [72487052427534670754, 339990981153884973858901142273], [72487052427534670754, -339990981226372026286435813027], [-34236195631870546486, -553828291262734622988845224147], [-34236195631870546486, 553828291296970818620715770633] Independent points of infinite order: P1 = [307129101046759980674, 5230663430517545261011967274593] P2 = [2499269100780577772, 369006579072985798540766412965] P3 = [-62388070013310182456, -515261680304117184355425579557] P4 = [67063744313843965334, 259708903641139226966414453453] P5 = [27124708743663717014, 121912272215974727024584813853] P6 = [7491625573880096747411/4, 647908563044524826035180689211399/8] P7 = [-25186664740889745748, -528177441057045126355981681105] P8 = [31876973792589050954, 6281120384112931775566435373]
Voznyy (2019)
y2 + xy + y = x3 - 27789073528333919645896990986690198743049x + 1859857500012745921403724958577667925343184951959353727909116 Torsion points: O, [-193404925306860615997, 96702462653430307998], [58903093019802135764, 653730662197228261957079152323], [58903093019802135764, -653730662256131354976881288088], [141215125337804888183, -867001329449863658168912414682], [141215125337804888183, 867001329308648532831107526498] Independent points of infinite order: P1 = [-22247573546029669837, -1570695839364373760796044000442] P2 = [81769399275005539018, 366457422549468457006671738578] P3 = [85243092329695878083, 332325215719424312050941857598] P4 = [70647563210276525500016/625, 6307728360286192875705413340101739/15625] P5 = [5683060484921861130149/16, 388246668212343379600609280012343/64] P6 = [7104324080859695587865/64, 193579204630527022500921928807329/512] P7 = [96745901438343078659, 277304640375557873094609383022] P8 = [1725574804383906267589424/289, 2265860967673265506729707483453378108/4913]
Voznyy (2019)
y2 + xy = x3 - 10748559915580117411148840629957123150377245x + 51353186154970235088176813558981483453831048361767253377943481137 Torsion points: O, [6564230390421723432514, -513462829782218147204176897285457], [6564230390421723432514, 513462829775653916813755173852943], [-18658125014864893245713/4, 18658125014864893245713/8], [191302119821575718914, 222044961317019402060256253789743], [191302119821575718914, -222044961317210704180077829508657] Independent points of infinite order: P1 = [-861141448706983554686, -244889004658441704667113192335057] P2 = [-350228164692339729656, -234679943033078397896973684041567] P3 = [-2680449352248466396286, -246790681978380518833091264475857] P4 = [10935662262699592253794, 1114267606325364564241637892253423] P5 = [307749878141307053264914, 170715349619724697442311873525917343] P6 = [-55936618816569497586251/16, -13756424656496731457384488586221073/64] P7 = [15127985641024008299362, 1830540533502080819122360461761263] P8 = [-2475100484215989347924462/1849, -20010305998858386680307859781267358275/79507]
Voznyy (2019)
y2 + xy = x3 - 1175965898117969065391602759190738535941395215x + 13886508272221232916512908346768597122959550121293581577167667901817 Torsion points: O, [33073888572052058491974, 3342406027714325324219833529291613], [24836397282053381749574, -12418198641026690874787], [106727105021800821497334, 33227591450853310142056569761250573], [33073888572052058491974, -3342406027747399212791885587783587], [106727105021800821497334, -33227591450960037247078370582747907] Independent points of infinite order: P1 = [7808082730666491834774, 2276070745939073963677698626836413] P2 = [45758169723715042191174, 7475652404956927322354867125010013] P3 = [71910385275792117743174, 17354492018151902476948487904830813] P4 = [-6564360115659671404776, -4617695120570542858267232268982587] P5 = [-11816564857826838493626, -5111988300782958413188140625908387] P6 = [38383857523967338752665366/2809, 90420846793873120225085934062344159801/148877] P7 = [-2919198273281472279961310283/126736, -241930173000871141029943392498665326506657/45118016] P8 = [-411797845672008000610085818/16129, -10696358766565457359382358259443432617437/2048383]
Voznyy (2020)
y2 + xy = x3 - 2710804785482350140002262807627047854670x + 54317364067271902603276583693676832699580348548939354942212 Torsion points: O, [32012525220633195724, 18551281453092861872649483298], [32012525220633195724, -18551281485105387093282679022], [29778866334177098428, -14889433167088549214], [7187169212485265104, -187631573790623249403584105342], [7187169212485265104, 187631573783436080191098840238] Independent points of infinite order: P1 = [70294303658674845928, 459464588008208312500208520886] P2 = [-23825149742872497506, -324620762366182482659131073252] P3 = [-2130089561260599908, -245116209637139891513718651422] P4 = [29694299548538408962, 2214883952921482923063652888] P5 = [30774738860264045062, 6271718787944554766057854438] P6 = [30583058121520372828, 4208920156024563789827431906] P7 = [30720295536744824524, 5701392908593846160701553698] P8 = [119618523062081798994652/5041, 20726504139604956766590474893042510/357911]
Voznyy (2020)
y2 + xy = x3 - 9598448290837410416433175183014219186075x + 403046614881349832317788129293290798901662698812680574011857 Torsion points: O, [94211948569381291134, 578768613836503061706486147153], [-458127130711474491633/4, 458127130711474491633/8], [28007297473148682174, 395207776288192687330707872433], [28007297473148682174, -395207776316199984803856554607], [94211948569381291134, -578768613930715010275867438287] Independent points of infinite order: P1 = [16973188957109914014, 494995080586151732114071419633] P2 = [65106725217183578414, 232600610338358938518859292033] P3 = [-8615224029716407618, -696491175355170163332851651407] P4 = [134263480354819003674, 1238810165775559570599950219433] P5 = [-4226917128581034402, -665990194194949921193615434959] P6 = [-24128301658050565252, -787777873566545747104029185149] P7 = [53305120111107068139218/169, 11781144820616836453496615279755661/2197] P8 = [9647815222697221080441/64, 790172100040726504962454759069041/512]
Voznyy (2020)
y2 + xy = x3 - 28902434997566728221995372158795948632978030x
+ 59802932895295336101499213250419273077803080660758195348604896900
Torsion points:
O, [12495823204528597900319/4, -12495823204528597900319/8],
[5854005825705858773340, -302028284830550121463685258309310],
[3261266305093861857180, 15190804425789424340804620368450],
[3261266305093861857180, -15190804429050690645898482225630],
[5854005825705858773340, 302028284824696115637979399535970]
Independent points of infinite order:
P1 = [3049191492769402583100, 4893009863158143474974749658370]
P2 = [3181783968373106714940, 7294624427369697456585823571970]
P3 = [3078540185626787737320, 1487222737320594187689400034370]
P4 = [85567749543424947947454/25, 3903393141370837501446265707597948/125]
P5 = [149157227923677954301981500/12769, 1655306738327449232332855831243874360610/1442897]
P6 = [9955269270993424970070, 871040829606205416092169962594310]
P7 = [-27196370953766059737804120/4489, -33670409142113018163156794372438629770/300763]
P8 = [8530067587191741568304217456911439059083075020/2333689096616244202554889,
195064994919050930783729363968533937487227508414617907990324293259190/3565040727678839610667870787875797787]
Voznyy (2020)
y2 + xy = x3 - 47521204035926841956898925141731957068499123595x + 3982325303626844390018987506350285511096154267481713720529176140727537 Torsion points: O, [122210010406484126810878, -61105005203242063405439], [-5375481488790609865186, -65096999373258450931636826017402207], [143492556446254749673214, 10858835637365337766355883464958593], [143492556446254749673214, -10858835637508830322802138214631807], [-5375481488790609865186, 65096999373263826413125616627267393] Independent points of infinite order: P1 = [33490774325202355272854, 49278471025474468168924683909256913] P2 = [86214479614179016665164, 22937658532689497921563887292337393] P3 = [46764043792092309068414, 43154475924646151103094203366712193] P4 = [138784861547461446853954, 7763362770593220468445882781845333] P5 = [-62024500070941809883416953506/707281, -51428208952203139176605559997368678565928167/594823321] P6 = [106595647214395231027970477641949172734/1137815508973441, 720664537881769620608979121266726596281716953031122602433/38380247735063313533761] P7 = [413787866838688013162770494201972526/1550281480609, 196029315129689780302292864634221322140944782645002911/1930260122350707727] P8 = [6672534185195203783106227062741653961034/14290263703855881, 493910789613231770792103664200740387441072382911462767862303/1708285146047596006210971]
Orozgani - Voznyy (2020)
y2 + xy = x3 - 952728212693461467276534157906420051862114553060x
+ 357884838511562116559489813199629322271431639095878154384363495517243600
Torsion points:
O, [600480891004198246007100, 48057581351474454667269032456402940],
[600480891004198246007100, -48057581352074935558273230702410040],
[2275455423322677732642239/4, -2275455423322677732642239/8],
[1141025243476981597121940, -869679661051724257002026223078829860],
[1141025243476981597121940, 869679661050583231758549241481707920]
Independent points of infinite order:
P1 = [510390165592067687487960, 67656540350668526642185945266851700]
P2 = [85767094233972020915180, 526120718451133845118123726733909180]
P3 = [548462216442417635194116, 18242011391166772103526063019804572]
P4 = [21406816616407467624243469345878/39904489, 8631556366906560068683025700755761274175398058/252076657013]
P5 = [145397175745659222362241240/289, 377562237405083408255909833717578546420/4913]
P6 = [5305837138623802137859515257330/23049601, 42968993903665378428119688389737770542499140390/110661134401]
P7 = [32422345278453860952441459820127025/56994877696, 1067451847504911421572611576393160999162271396335/13606729121632256]
P8 = [30401301538310246708432879264185717350555422698144948814722688347041366771000/52439649976651617663113418509170761939796827846982849,
240124060306367236771164130199243642222989581414450113577877940047642418882385118156668794600923333737562392095580/12008525269964389937738941569528374341956611472536386837265643663424633415479007]
Orozgani - Voznyy (2020)
y2 + xy + y = x3 - 299060956210539783759852343001586293825163x + 62948439399794304891707376109467111082257061553106032413026406 Torsion points: O, [315086810627933895575, -157543405313966947788], [323109444869308400600, 227053486927460346109539839562], [323109444869308400600, -227053487250569790978848240163], [162785025612241254155, 4310386132113744229316387879112], [162785025612241254155, -4310386132276529254928629133268] Independent points of infinite order: P1 = [313102255757392685150, 78357537310948850905887169212] P2 = [-76879561037960993785, -9245848816356825735425429645028] P3 = [310461012222703152275, 160560876700034648233855256712] P4 = [308619044057369046935, 217196440839635750005575099252] P5 = [311390973157491894535, 131821221333679219296342214652] P6 = [62006241654205653395, 6681556215826836744982444345992] P7 = [319305775181299459031, 108376297143090073646321612964] P8 = [1626333499178589221229350/5929, 569180890945757186522716494936693396/456533]
Orozgani - Voznyy (2020)
y2 + xy + y = x3 - 728177856117250596635013323700992100749546784263413x
+ 7725511368374502384905062271934799362136250437256099440874528514783779254988
Torsion points:
O, [-124933619064699558386490009/4, 124933619064699558386490005/8],
[21265833906735617647516354, -43097228832631667306871828440562981790],
[10641466552297531532628904, -34375563478033084878116582221059424765],
[10641466552297531532628904, 34375563478022443411564284689526795860],
[21265833906735617647516354, 43097228832610401472965092822915465435]
Independent points of infinite order:
P1 = [17748996164989313381147029, 19811512033990913286644864631285473360]
P2 = [8870738659891183846814329, 44317878703392630117816440541168544010]
P3 = [61339810590192565389735634, 440289331793561183098250231365796281490]
P4 = [2689912634870006410616089, 76067337046100774552067772275948794570]
P5 = [12495717670305680867142229, 24031745881850919801748603142375558810]
P6 = [128748115820040187892117323/4, 1062330937057645222226866408046953830811/8]
P7 = [-5058486271161250839916632293471/249001, -14772033021635679932369950571387401103297142610/124251499]
P8 = [708642966801927957194910338367725204969804581613237979381641749/274609944098394175843364282887965681,
18863295719751676396370341775877849284037211725567391925151777817615914406114899589895707734560/143904504885892743720924199913022651007202872255854921]
Orozgani - Voznyy (2020)
y2 + xy = x3 - 1014496779500059672455281028048689531196403660x + 12395163886199166059057137251571878361480091007191998138642824467600 Torsion points: O, [54609132885636962407400, 10947483906593448607199596664472740], [54609132885636962407400, -10947483906648057740085233626880140], [77023418470518842421055/4, -77023418470518842421055/8], [22024113643678191285320, -857218131446595116348555426204860], [22024113643678191285320, 857218131424571002704877234919540] Independent points of infinite order: P1 = [195005745095835475146152, 85029952690814126110734363187872116] P2 = [42288692559302212336120, 6717120501174457493474226286267540] P3 = [1296667099219159562498320, 1476090244081284951783815214207724540] P4 = [50154896797634656907960, 9363680433449259096507926481827540] P5 = [1078305212333124690420004400/80089, 24587294500029084467860728364818220140380/22665187] P6 = [59952639494805281405409080/4489, 333329781295320083159315484610510530620/300763] P7 = [207627767346438243258046640/10609, 209046974809355027508699946042850281580/1092727] P8 = [1693173445281903546241721290/56169, 40389090373035635765303586824307482381120/13312053]
Klagsbrun (2020)
y2 + xy + y = x3 - 6731612366192377228520404x + 3182900810959595258205766071715171806 Torsion points: O, [3316255436574, -4162914109900494853], [3316255436574, 4162910793645058278], [2314376554853, -1157188277427], [11634269724703, -38725145186591031527], [11634269724703, 38725133552321306823] Independent points of infinite order: P1 = [71245230500, 1644283142159898882] P2 = [336545034178, 977510982171662398] P3 = [2321008034964, 249451111998060642] P4 = [53011446939, 1681129734303793317] P5 = [-1340852485347, -3130223106305263327] P6 = [5163116922911, 10298735949654325017] P7 = [-22717663328123/9, -54616556850967347829/27] P8 = [382252340914, 815830511061642718]
Orozgani - Voznyy (2020)
y2 = x3 + x2 - 60313024735007362096072931339173916555726439220x
+ 3303762732437764940265112114690488828303891527290367159038723810320068
Torsion points:
O, [-269400128398817960910169, 0],
[300089670417845929510856, -110583295610371871078393056235330550],
[300089670417845929510856, 110583295610371871078393056235330550],
[7016171131015298962676, -53674403695988069797742165160924990],
[7016171131015298962676, 53674403695988069797742165160924990]
Independent points of infinite order:
P1 = [58007198432078931397328, 598158999308297172916869894056862]
P2 = [-108427296385410370841188, 92566828570027620341222482486229910]
P3 = [52451721019265542950331, 16868463782605221745749715581783750]
P4 = [48474744907239528567656, 22226341190917530302419963504675350]
P5 = [1521645572343712794396956, 1853309164504557572407788096216777750]
P6 = [30089244387022819458738989/4, 164963185085547559044466862956833045285/8]
P7 = [50259473549510044315364816963047/529, 356309090633909063646983926957844863796356762164/12167]
P8 = [113831063522920379897284145226257947398828456481016916780261047795963721987399510364320402221/29449670507082505516270472158613670567276949157621507498050185046756,
1212063246704129141130804437790563043668945571059059107100341881468330749685406240598668920634435959409710427645414282477109131244196731605/159816148509775155573785427168946757980951358542618172990822150557920593554547558095722528257118995096]
Orozgani - Voznyy (2020)
y2 + xy = x3 - 2777246582103454442974884437155452336x + 1455564445936125191935204839747626363854260068301461760 Torsion points: O, [-1884091709305859232, 942045854652929616], [1751761215160858464, 1402164059812676993611870800], [1751761215160858464, -1402164061564438208772729264], [281055860923869888, 834987600329742754146234096], [281055860923869888, -834987600610798615070103984] Independent points of infinite order: P1 = [-312174334736176672, -1513977305594611360432623664] P2 = [-68426427546461856, -1282685122429272546839243184] P3 = [-209179257155126304, -1423851812187872543860758960] P4 = [-766483769423750592, -1770302707361759173601464464] P5 = [1504208621136972768, 825526599392365299673294416] P6 = [590411166144132768, 147158869068468512012340816] P7 = [597625472040405504, 96212222617721279502224976] P8 = [1289926173238662144, 139434019218357552839237040]
Dujella - Peral (2020)
y2 + xy = x3 + 12370764835409459885826379544x + 1795055346226263534415826963120427011109440 Torsion points: O, [287442952043156, 5394485288717244083624], [287442952043156, -5394485576160196126780], [6938304779744, 1371576277133924417816], [6938304779744, -1371576284072229197560], [-88697342525360, 44348671262680] Independent points of infinite order: P1 = [-56977005345494, -951439538990147868830] P2 = [-88177687531336, -136460691923638786600] P3 = [61269766750790, 1668237052561641052790] P4 = [57375133290296, 1641250460574949681904] P5 = [3414484775543894, 199630932637620976515140] P6 = [-47496752261296, -1048968183674705543080] P7 = [279283600210559/4, 13854482876787646623025/8] P8 = [-3211280688799924/49, -287556207376563099439660/343]
Dujella - Peral (2020)
y2 = x3 + x2 - 749176510115432376219665096358484445x + 243093364565008663402919785745371914691215587070812100 Torsion points: O, [702082710854756485, -251356703834519074472262525], [702082710854756485, 251356703834519074472262525], [2055796754818629535, 2718704316765145370088113775], [2055796754818629535, -2718704316765145370088113775], [564175470609389604, 0] Independent points of infinite order: P1 = [-172761691757401365, 606107264763204933307782375] P2 = [273730166715571135, 241932352881773187443811375] P3 = [568529102921119129, 30458634649807027233914355] P4 = [171351809055627955, 346051658770606463098444695] P5 = [255106745157894163, 261869415072508102377913641] P6 = [1657354948605617925, 1885180808392639171251234435] P7 = [281302292184716619085/36, 4690196381274145571859003361475/216] P8 = [451638372104180386221760/95481, 298748844159381494083422260007607450/29503629]
Dujella - Peral (2020)
y2 + xy = x3 - 724016704581073411076105781935x - 220753490559318324998944201709786454755631303 Torsion points: O, [-431760017754266, 3370562688248652389533], [-431760017754266, -3370562256488634635267], [1460931326182534, 42890595786631943091133], [1460931326182534, -42890597247563269273667], [-593182814314362, 296591407157181] Independent points of infinite order: P1 = [-394226023171526, -1845109664794335908447] P2 = [-405292302390506, -2472011746215283313507] P3 = [983835558752934, 4383998879741211236733] P4 = [-496375109089826, -4040963278237561638827] P5 = [1058161029785734, 14069405815261419929533] P6 = [696116936708208076/9, 580760291708194905583202621/27] P7 = [26824447802498614, 4391117855252108880847213] P8 = [14301405513797491/4, 1656885557501400892736399/8]
Dujella - Peral (2020)
y2 + xy = x3 + 10129358605546801850018730604093405x + 987295481956596247636872669057081383779119725697025 Torsion points: O, [246404201391361870, -135807402695846757292607895], [8305299377204910, 32741345731727567626088105], [8305299377204910, -32741345740032867003293015], [246404201391361870, 135807402449442555901246025], [-67332390755112274, 33666195377556137] Independent points of infinite order: P1 = [-48981654490862930, -19329403271011069972247895] P2 = [389914676431924360, 253410647643876402015412785] P3 = [-54898409999228674, -16301994562734309793608823] P4 = [8784389765984430, 32816970725504765241204905] P5 = [1040649713498247282, 1067006052547941327159169981] P6 = [10192063936521890590/9, 32677439078214071897727514835/27] P7 = [-58565119514886674, -13899548500840914349818903] P8 = [169201520817452516665950/51529, 69633199025947417848118381713222835/11697083]
Dujella - Peral (2020)
y2 + xy + y = x3 - x2 - 41478854711290905361075386062753768x + 6403249394898252963732849109959916162148122363168427 Torsion points: O, [24287968399663117, -73553653125693498316581383], [24287968399663117, 73553653101405529916918265], [301379428140772845, 145864788762488624775734713], [301379428140772845, -145864789063868052916507559], [-257564734993073139, 128782367496536569] Independent points of infinite order: P1 = [138049858029444237, 57515397077943543035286265] P2 = [59232189843554877, 64452923190714115199196265] P3 = [-100031414542615539, -97731751049127095403871751] P4 = [-251667047863008915, -30040804045712185496903207] P5 = [-21209744462642163, -85284606051883858459913735] P6 = [-33111028904276889, -87979292995759574126781281] P7 = [-5508430518114573471/25, -8701243988081958343443304543/125] P8 = [375085843663797261, 208843761433145992053326329]
Dujella - Peral (2020)
y2 + xy + y = x3 - 99634728422186774531580539738790094244x + 375457508444593787454386978108526003626550333098115853466 Torsion points: O, [-46005140473834622985/4, 46005140473834622981/8], [3852427728210910236, -6985453893468080387691978338], [7855853618867443434, -8806886095398705159843590573], [7855853618867443434, 8806886087542851540976147138], [3852427728210910236, 6985453889615652659481068101] Independent points of infinite order: P1 = [4243879065162177906, 5390194301816255678032453627] P2 = [1240869355561367010, 15929044671653913749851685362] P3 = [-10577311772274797526, -15682489738433771354833497278] P4 = [4218726526387914361056/361, 194856661165417943479275991361539/6859] P5 = [521814636845693181510605196/50623225, 7586616245015859294254322832074592652399/360184245875] P6 = [-2111560886178822016208938896/183683809, -3226692870874984951051081006937872041418/2489466663377] P7 = [251991243787981418955577869651/401956, 126496402677791622835396099257421400073102859/254840104] P8 = [-227437720524157488451081128864/126281440321, -1051525328907152931009339928292229829741449034/44875498913910881]
Dujella - Peral (2020)
y2 + xy = x3 - 11294541157720050543614442617749590666x + 14594228853098919253439575045715564198796435129317530660 Torsion points: O, [2199086281222517444, -625537092935831373332720154], [2199086281222517444, 625537090736745092110202710], [-43948037867844444, 3884651450672099358003873014], [-43948037867844444, -3884651450628151320136028570], [7551961523951506015/4, -7551961523951506015/8] Independent points of infinite order: P1 = [1168330198798584046, 1730098478237185575002201560] P2 = [704605569791117076, 2643075305818675846616762054] P3 = [864284449959151776, 2340543170943748494303380954] P4 = [2683863143195567636, 1900899281961392500660097574] P5 = [5520361376091106316, 10976061406969227466116058734] P6 = [-176325290705307896, -4071886546169981087930985710] P7 = [1104711969356435106, 1861502583362314513995009530] P8 = [562748451482453440943734/50625, 404744742447208727094333821966861402/11390625]
Dujella - Peral (2020)
y2 = x3 + x2 - 21810674198865395737062871633956077082660x + 1151582912834331488017675826216127056963052542628118246416900 Torsion points: O, [65951374575037388855, 0], [-61246880660064451620, 1502554682828900969671508591850], [134835360111316794480, -813705776452288425960003408750], [134835360111316794480, 813705776452288425960003408750], [-61246880660064451620, -1502554682828900969671508591850] Independent points of infinite order: P1 = [-16124648182294909945, 1224369177733938915707191092300] P2 = [7738682434434843520380/121, 179870387162569306543473487726050/1331] P3 = [2245075312189619640756045/4, 3363925401337597090349023468585183125/8] P4 = [699201704119207524810567/10609, 21686685475172599933428647469693312/1092727] P5 = [278489727834959001017697/64, 146881309544296708300479312606990927/512] P6 = [1466955820116456517398582480/90601, 56183338777607743204316654897770543683750/27270901] P7 = [3388345818518143739363541920/1760929, 196668106184991647978894429014447095378750/2336752783] P8 = [3288243978211158996972880/81, 5962703030366327150708042069397278750/729]
Dujella - Peral (2020)
y2 = x3 + x2 - 337623059472632292818061395642167180x + 243132517058363181473177057453027217617653118422244100 Torsion points: O, [40188402754650040, -479196091557935617673834650], [40188402754650040, 479196091557935617673834650], [1085279617117561340, -1074706466270641618886979650], [1085279617117561340, 1074706466270641618886979650], [-800777005254988881, 0] Independent points of infinite order: P1 = [-296235414730031185, 563162641327183550896828000] P2 = [2667440753438486845/4, 4486705982095404507959563645/8] P3 = [3461410913218914520, 6367645538701633239445737670] P4 = [3050932586643296295445/8836, 340156144329125890764610040099255/830584] P5 = [-484580054356719265005/14161, 850372182643113318123730897682070/1685159] P6 = [-13063347589466118975477765/630863689, 7924520915245649128091339226754488746850/15845403276613] P7 = [76607949702924338312944/22201, 20964428626802396733490473110282230/3307949] P8 = [2409496055962002296505271360/72812089, 118256175139512100074368052781694765810650/621305555437]
Dujella - Peral (2020)
y2 = x3 + x2 - 14056407680017271277544631905x + 1082872295776815338920297488812717727150600 Torsion points: O, [161079735169295, -1731517942873417789805], [161079735169295, 1731517942873417789805], [-146458586456760, 0], [17078577610465, 920755281526657623475], [17078577610465, -920755281526657623475] Independent points of infinite order: P1 = [59634286205865, 675797879291569588125] P2 = [-72491520392635, 1311830107876079631125] P3 = [-145856174368105, 173604289809758688595] P4 = [55369108120840, 688715271624167187400] P5 = [51366212060820, 704540274874545565170] P6 = [-32985584476331, 1229081443064564094005] P7 = [-7360495312085, 1089006726267725332925] P8 = [-142604450061560, 432862940841014483800]
Dujella - Peral (2020)
y2 + xy = x3 - 15526899693898468469916326724876x - 21604871823375940499049510857364653112584174960 Torsion points: O, [-1970250420590904, 36588522225426559390724], [6753639809717864, 426118172834657977032756], [6753639809717864, -426118179588297786750620], [-1970250420590904, -36588520255176138799820], [-11158741786780865/4, 11158741786780865/8] Independent points of infinite order: P1 = [-2203822366813366, -43704229335281318234624] P2 = [-2397808878658960, -42889323121979949995300] P3 = [-1889479983718526, -31419681975434359677890] P4 = [-2071336339751956, -40861073564018374531164] P5 = [1779272612893807704/25, 2369649056447672694762426532/125] P6 = [-2156139204446536, -43006179660146105359820] P7 = [-2112984278971336, -42063959821128151606220] P8 = [6109256573416351464/961, 11010826103711868658025174860/29791]
Dujella - Peral (2020)
y2 + xy = x3 + 11117292632236250245666794458636697124x + 121988636725290161362318441824000186384565986624370943760 Torsion points: O, [84107681033727304, 11087122323368843600573055316], [84107681033727304, -11087122323452951281606782620], [10773871181894535976, 38631024075483846390048536164], [10773871181894535976, -38631024086257717571943072140], [-16875178086556225985/4, 16875178086556225985/8] Independent points of infinite order: P1 = [570994433994895444, 11336785827549700039671231256] P2 = [-1261845428822079974, -10293257673621206872953694736] P3 = [91432609327863275280736/121, 27647505946888501629889842185353964/1331] P4 = [13255112613547790559747784, 48258646000474200404759691376599102820] P5 = [-126290644490474815825640/44521, -77251766842052619536543280717135380/9393931] P6 = [2492204621639405414464, 124415914455124769674555890915676] P7 = [39471005226155958789190/169, 7842664024119026728988973492154450/2197] P8 = [-1748130040559884221258585669/616330276, -125839024042391191207973393888466761372601/15301015431976]
Dujella - Peral (2020)
y2 + xy + y = x3 - 175219044424068117509041966499617841475424x + 28239604496925998457224868144701482152553911582356171886973022 Torsion points: O, [-483365240359059394959, 241682620179529697479], [262645526885075397901, -580600289019340458737426276341], [221325422860290839290, -548441953774784249601171221434], [221325422860290839290, 548441953553458826740880382143], [262645526885075397901, 580600288756694931852350878439] Independent points of infinite order: P1 = [105598670933902619530, 3303671508634469663626264681103] P2 = [38435766982817970050965, 7534903228706910911064635295998843] P3 = [-7818033882866061851111/25, -905295767298078374330551978648973/125] P4 = [11879028904116235631871948421/126736, 1294693850295564939902280357594075571166869/45118016] P5 = [11841793843559928298389573937/66049, 1288620575585003280994852676839503894755287/16974593] P6 = [394758612321259048779032024548/554084521, 212332652315309267647212836075765710692083363/13042595539819] P7 = [322989623916146803229307283465/1334294784, 4654285756112117813326730664443238359515757/48739119869952] P8 = [58936077519499244757210978233930692422380629/93852343284319260441025, 370265713488043237842323705717166228301352955525227705366489572943/28751974903787946897255236014398625]
Dujella - Peral (2020)
y2 = x3 + x2 - 93971455422934013299698478937937711342461641x + 241891322469438552698504208730495830849813441909007302990150413480 Torsion points: O, [-10788539834326987167320, 0], [829595513774363232839, -405590897436521512197789076130361], [11177663192336205944321, -766843536584648822098157380861839], [11177663192336205944321, 766843536584648822098157380861839], [829595513774363232839, 405590897436521512197789076130361] Independent points of infinite order: P1 = [-13205219258288468783323205/3249, 138175257059060983736835491118303310495/185193] P2 = [20733326731645706748816299129/19280881, 31912692493725043329639314080094732524179369/84662348471] P3 = [11632888920764005842776453345/2209, 1254673242700933533224438573222965653467295/103823] P4 = [30823918166291764144895903171444/159693769, 170919134658669692254632803836973939953199025162/2018050158853] P5 = [-2081673480526680804301745228431/192987664, 60219397480660533025282532196733884053673807/2680984628288] P6 = [79081241151386903656979831158049339/50850062831929, 114385240888672752163497980281531413608910298729731483/362607882599647640467] P7 = [169731025615339000619415110420729/20354443561, 566992158627416073061706507455133628838227479451/2903948108404309] P8 = [-2772006979001397235285843541383782991/271720244955721, 1668832501978352608797368071623235719662963818764066459/4479019942915162665019]
Dujella - Peral (2020)
y2 + xy = x3 - 447356321155692541021835770377275637640375x + 115130968927509369313052214651851701004675603492806696081862057 Torsion points: O, [380559769242873912854, -190279884621436956427], [53305636542527899574, 9562208058128840184481207597493], [419914832999752786454, -1149935998512027023880553346827], [419914832999752786454, 1149935998092112190880800560373], [53305636542527899574, -9562208058182145821023735497067] Independent points of infinite order: P1 = [786149629054783303219646/49, 696443945502538594193880624118318139/343] P2 = [269696925875193912854, 3754615346838637345173071843573] P3 = [232576136690372033174, 4864873399029276000069614095733] P4 = [5544794764828700649494, 410009701338822735853159812930293] P5 = [28372909466489891427777254/89401, 60488921450679802971210092474516305327/26730899] P6 = [328640051529469080451351334/436921, 4126916531832119827819106617062709768913/288804781] P7 = [4504266173261098763915677094/11015761, 27708063782214592597404747197776451632307/36561310759] P8 = [3757195138733221490309572421414/1069224601, 7159446283484185289883780973435446179651819167/34962575228099]
Dujella - Peral (2020)
y2 + xy + y = x3 - 255425110305106802414698911353x + 49687082457794764104885126714843336579491148 Torsion points: O, [292351214851124, 16589168932156835800], [292351214851124, -16589461283371686925], [337231414690599, -1378899338723337566350], [337231414690599, 1378899001491922875750], [291804693239683, -145902346619842] Independent points of infinite order: P1 = [290587700315187, 35560151863295610182] P2 = [106766193961999, 4861413895971145034450] P3 = [-264270280028326, -9936399301133425055150] P4 = [291954973618919, 4848036938914499570] P5 = [291809089917774, 354927978591676275] P6 = [174449619894979, 3230671166037168098030] P7 = [209395100444959, 2320240812968672738930] P8 = [291667302317624, 3620764823518895075]
Dujella - Peral (2020)
y2 + xy = x3 - 55770783304388775819212152590x + 41845524204552863364522334541356125554692 Torsion points: O, [-44145633494436, 1554943571411546972578], [-44145633494436, -1554943527265913478142], [346003030922684, 4708270212533873981218], [346003030922684, -4708270558536904903902], [-236532652199492, 118266326099746] Independent points of infinite order: P1 = [306541429369044, 3427939023665242824898] P2 = [527877698364, 111380063363099860258] P3 = [244334067358908, 1000837542844271276066] P4 = [258256536657212, 1692178187168780721570] P5 = [-231496040870596, -739318290282078949982] P6 = [-232703773019716, -647120051349991086302] P7 = [-129154370822916, -2256209383051094209502] P8 = [-141999532315716, -2257877463627263982302]
Orozgani - Voznyy (2020)
y2 + xy + y = x3 - 394848720390105077262480299631448348x + 95429764858799172337292516330170489885737662330459006 Torsion points: O, [404768339758317670, -43860002820943512712767898], [404768339758317670, 43860002416175172954450227], [12178450045575520, -301036419205611101715632998], [12178450045575520, 301036419193432651670057477], [1419372898239240055/4, -1419372898239240059/8] Independent points of infinite order: P1 = [188483773922716420, 166443045834077945045313977] P2 = [285492638450965795, 77283492156381293216478977] P3 = [138580951221873295, 208261029474092738111835227] P4 = [-160572989326911455, -393308582159239972159818523] P5 = [335631746114620420, 26729550091877592970593977] P6 = [288346947876254545, 74502679266027085573616477] P7 = [370812727541218075, 1534537762304236713093497] P8 = [-54313344054805300055/121, -568175096999767492486448919113/1331]
Dujella - Peral (2020)
y2 = x3 + x2 - 501209781246999256490762769859365x + 4318850679978610403682556735125251594711776528588 Torsion points: O, [13380565488343061, -89613459229291740574195], [13380565488343061, 89613459229291740574195], [22271218715732631, 2050117674281252757453545], [22271218715732631, -2050117674281252757453545], [12974179118756332, 0] Independent points of infinite order: P1 = [-23109125276272989, 1886893085756507043367295] P2 = [-6362651022135647, 2692636685196866018898573] P3 = [-103279381073879251/4, 1731362925548952501170365/8] P4 = [12152715043087263, 150356508771213140966297] P5 = [1238891693218551, 1923488383537153698072535] P6 = [48482451844844469/4, 1252483548280505433427535/8] P7 = [1519097654444189792988/5041, 59048814612568808292252707881252/357911] P8 = [101180999822402832929/7744, 17677296234985567854288478255/681472]
Dujella - Peral (2020)
y2 + xy = x3 - 68609682232337291238386381786680895670x + 177883367742624591465578320609206700407604463038260637212 Torsion points: O, [11909531944555196831/4, -11909531944555196831/8], [-4317373632019022586, 19839919012216684733198308968], [8737034211418638114, -15664815133538748051199012182], [8737034211418638114, 15664815124801713839780374068], [-4317373632019022586, -19839919007899311101179286382] Independent points of infinite order: P1 = [-169146628675159146, -13765305111071154393978042312] P2 = [16457354487027335178, 59212614597059995055570481786] P3 = [2282995292301345282, 5757335474252130223204716948] P4 = [2310709723529812074, 5628859904571995037614765148] P5 = [9735872145565365614, 20802509374175766715012051568] P6 = [13785353085795488675834754/185761, 50874511187443807472885878226647457388/80062991] P7 = [2556969091130589305520013191/23406244, 128933572745036084500876674750533052423471/113239408472] P8 = [7213557269817243112221775926/327718609, 573120568507545973924076114356577534388936/5932689978727]
Dujella - Peral (2020)
y2 + xy = x3 + 2759310394700302714594168699773100722994915x + 10984377272880698572753499030828003947438720031331881909529234225 Torsion points: O, [-7259117311544598198545/4, 7259117311544598198545/8], [4936671698474058177250, -380678955713678232882089556615185], [57348955666426979170, -105559506713125482825599356642385], [57348955666426979170, 105559506713068133869932929663215], [4936671698474058177250, 380678955708741561183615498437935] Independent points of infinite order: P1 = [-883221748988727794030, -88647110031751459882214087644385] P2 = [-350682220029931326558, -99867962695784523989737036680849] P3 = [-1323591443241393171230, -70805263425535487056564993714385] P4 = [8171801294187850187770, 761073064344327628367584511752615] P5 = [5364069331145931260470, 424413904868392140047536067800615] P6 = [28025960197238759005953010/169, 148375795598871832943093181830163651355/2197] P7 = [-43409824495273980830, -104232980821247751655178035776785] P8 = [324516864097628516505730/529, 1382330969723786105758800794457125705/12167]
Dujella - Peral (2020)
y2 + xy = x3 - 211386149196435146955497603911210x + 2434876668936235238811922136488704637935627947172 Torsion points: O, [22014929661006884, -2907046286048624421643242], [22014929661006884, 2907046264033694760636358], [-74068089074960289/4, 74068089074960289/8], [1646186089030084, 1446152403850906312819958], [1646186089030084, -1446152405497092401850042] Independent points of infinite order: P1 = [-1013748445477166, -1627306741962137754509292] P2 = [9492869505661572, 1132987818073412597604150] P3 = [13715510664137884, 1454546027695989607437758] P4 = [585396054440084, 1520306764723133020749958] P5 = [14157428948145084, 1509902415917612347889958] P6 = [7170535864674784, 1134816796010557389088058] P7 = [9034029556734784, 1123614002691060218797158] P8 = [-4212130541906686, -1802922880312725262052262]
Dujella - Peral (2020)
y2 + xy = x3 - 22473804120743025586469191535253225461374725963685096x + 1296578288999059294904801949174145155220000283044908446573856214321031379698240 Torsion points: O, [176913592243300052654125136, -1690494788148679258734844929280049440360], [349641037759238852700004735/4, -349641037759238852700004735/8], [92414053502370461638235984, -94509193331425033786427931743792495080], [92414053502370461638235984, 94509193331332619732925561282154259096], [176913592243300052654125136, 1690494788148502345142601629227395315224] Independent points of infinite order: P1 = [88521675659497152816223136, 28688797308875343434657663086555761224] P2 = [102213516606924367942508234, 259495623644375633460872359784673279170] P3 = [382627726774576695812140496, 6979663224689628216626696333026802740760] P4 = [253529244123495724276484107184/2401, 37362293204484962510024001607775497679415704/117649] P5 = [10926416459517161598011018302016/3721, 36071239198427387443057345208565387348043370360/226981] P6 = [1900073625005146674673283546674256/20912329, 6559355296904110091997769144968445666955368489592/95632080517] P7 = [324480224422027726365830841991935465086/3659557522009, 218984475469322475505146313080601587663524581651467624790/7000722560930650973] P8 = [79978577969536729405416154766199386960/688938180529, 287126799039652592485508480716368991441382541615789030440/571834535417222167]
Orozgani - Voznyy (2020)
y2 + xy = x3 - 7923788923260228676409807151085980x + 271251944009258509680643055407258125899930873264400 Torsion points: O, [127493164551740760, -36515223677286890733645180], [127493164551740760, 36515223549793726181904420], [52620481624914360, -26310240812457180], [57735248734674360, 2494459331251689616982820], [57735248734674360, -2494459388986938351657180] Independent points of infinite order: P1 = [-22614887974879890, -20949499726584677147828430] P2 = [70292188847595960, 7847585978387335739990820] P3 = [-6574246839341640, -17973890632906998186537180] P4 = [52625289196914360, 42950397217618419542820] P5 = [42403337228846520, 3391146420980614932628260] P6 = [67431150670666632, 6599127904296906975219876] P7 = [3167035214992926840/169, 24986217656601361866655575540/2197] P8 = [57418884623595960, 2362788232734840756413220]
Orozgani - Voznyy (2020)
y2 = x3 + x2 - 310679136976653430401071541589614309365x + 2098187012647280976559379484632993338068568676926664553900 Torsion points: O, [9611912174245979020, 0], [12402747154659164245, 12361380131813114237235124725], [12402747154659164245, -12361380131813114237235124725], [-2396167943567965625, -53187108528928230643886644545], [-2396167943567965625, 53187108528928230643886644545] Independent points of infinite order: P1 = [933403837423146985123, 28511987141062263685925189147751] P2 = [-20311604672406041855, 5366294033713827517358191125] P3 = [5649493397243583445, 22876208009783726475608039925] P4 = [13096642613239840273, 16604106353612917247428414101] P5 = [9570572990492206908, 1197743647899262536299984484] P6 = [9346125212941958845, 3305368781815846419845342325] P7 = [391750841814281834855095/36481, 3640459997906364771170484289703775/6967871] P8 = [2590471414338435237491318920/86843761, 112640964336268772367975704933275984355550/809297008759]
Orozgani - Voznyy (2020)
y2 = x3 + x2 - 46615055051824934699319066817744605x + 2841197833749770970755254122508160323483127463371100 Torsion points: O, [-241608309854211556, 0], [24019467732463215, -41657972713779625989427125], [242183981326888965, -75872358863458825420083375], [242183981326888965, 75872358863458825420083375], [24019467732463215, 41657972713779625989427125] Independent points of infinite order: P1 = [-205889247797347035, 60918080376491033505020625] P2 = [-11406092108810154465/49, 11266977697762716979334599875/343] P3 = [175088231079526155, 6850957681165155428519235] P4 = [17591348713884203214165/169, 2333177463689411112177015284049285/2197] P5 = [-37448033720322637365/289, 402320694385288221115086694125/4913] P6 = [-13982374111635866235/121, 108823485695023127158015048125/1331] P7 = [1079527426863731165, 1100262724512090570734365425] P8 = [3587421603214094138865/3136, 211214777712432375372110423604375/175616]
Dujella - Peral (2020)
y2 = x3 + x2 - 146905528537335347940544434480123778570818472145x + 15206892013124396995602743355719941966717098947792384035631815810457553600 Torsion points: O, [4935349175324539640372815, -11605838004960284636285232539681620695], [-2497263880331409337164096, 0], [118264614406356326305, -3899599292158152558706049282025950745], [118264614406356326305, 3899599292158152558706049282025950745], [4935349175324539640372815, 11605838004960284636285232539681620695] Independent points of infinite order: P1 = [-1073776478763585507316295, 3758533731183961963482775132796580105] P2 = [-51641516819243373498071, 3900556462539830854227187757272016745] P3 = [327592002234417872535521603737/223729, 450604338874719952630937252417175925562074383/105823817] P4 = [11750571367110262738690853021881928320/569815129321, 40307865533722745028710043890949516057359331667633236840/430131218334379381] P5 = [6279452099205085000620266434942814545/4411085056, 15735574855058497963128705486973514468933987058544314585/292966625079296] P6 = [266700494019746904001662678498388703665/4005517901641, 4355517081542809070463988621737711983029136362579559830605/8016559412468362939] P7 = [-94762279658288669458848207988032344135/736292161167616, 77953371993751552597264673627770093071745115211809131685805/19979069850803554545664] P8 = [814195609150355061378421449025076426134971121/31116512786688337849, 23239716265237252227690746528419852771188194971161980754978359791125/173574682606796800079690092243]
Orozgani - Voznyy (2020)
y2 + xy = x3 - 1325987071254184619193124875708458567010x + 798417471793923780571603906054728066456339575901227372100 Torsion points: O, [-36711517139185885084, 18355758569592942542], [52923320030270366820, -280810490712004618354335785010], [52923320030270366820, 280810490659081298324065418190], [-6397194198083411580, -94969547203071369558777285810], [-6397194198083411580, 94969547209468563756860697390] Independent points of infinite order: P1 = [-31732983096642196380, -104505469432394272819978485810] P2 = [-3531837120270215680, -73739623958384227323840219310] P3 = [-1517831231373660060, -52986274294310163355754844210] P4 = [-16373295612728329860, -134609672517320696096124999210] P5 = [-2371531082367656220, -62687312563720706959820629170] P6 = [-34611836965214970780, -72311845697840093383801077810] P7 = [2203553615944904247558820/7569, 3245401992836309801005469032927451170/658503] P8 = [75968723275507343398786202820/1125721, 20938818788788524494827292659460174833957590/1194389981]
Dujella - Peral (2020)
y2 + xy + y = x3 - 23938380757142625186132412578769408x - 305601630803810576497626945680991249901865603967694 Torsion points: O, [-591567337254347721/4, 591567337254347717/8], [-39750470709288920, 24148510463773910662461017], [237507441446176750, 86061596716758580688048282], [237507441446176750, -86061596954266022134225033], [-39750470709288920, -24148510424023439953172098] Independent points of infinite order: P1 = [-138645304121929328, -18660928868947910593374751] P2 = [-53920901960923688, -28782014977084874499415351] P3 = [-90735320977543625, -33458038530799091435725033] P4 = [-86430196006108205, -33432742796788699909682683] P5 = [-3439789970272000031/25, -2447288809140229262040562307/125] P6 = [-346764080563439049/25, -609413142350805531975753589/125] P7 = [17335329811888567794398187433/91435478689, 1227384593086494730300585734331634584952411/27648534352415887] P8 = [51312862660628072909493485259293605609/229660272952661838400, 258104126880795926416437370778732533289765217531032312617/3480397235138546079222681152000]
Orozgani - Voznyy (2020)
y2 + xy = x3 - 9787812222851471841774232010444366390x + 15413207617286010670581630857823649728433524383709320100 Torsion points: O, [648703588979992780, -3055618395059253197534797190], [648703588979992780, 3055618394410549608554804410], [3568919887518906700, 5093063677049334111491591290], [3568919887518906700, -5093063680618253999010497990], [-14923332920101931105/4, 14923332920101931105/8] Independent points of infinite order: P1 = [1428920534013412492, 2084416355642675589390558586] P2 = [150042351540854255500, 1837500030693071703723105738490] P3 = [-3654458059904729270, -1541699275759735224514346690] P4 = [208713986497939603330/121, 2547140045182814763487186949360/1331] P5 = [-2749350261257206478, -4641249202718661000758609744] P6 = [53320218192481164940, 388696977422634679529319058810] P7 = [-1114132125762873620, -4993512005108421719098429190] P8 = [2007159386599588780/289, 19245688920330635010952300519130/4913]
Dujella - Peral (2020)
y2 + xy = x3 - 425377876033165241249056156241611769932720x + 106723466161352608728840289894228261543807522752144901070854400 Torsion points: O, [417052139467585151840, 1362948538877209600205850624080], [23218569109228451840, -9841713149918850263992939775920], [417052139467585151840, -1362948539294261739673435775920], [23218569109228451840, 9841713149895631694883711324080], [369145749764614618976, -184572874882307309488] Independent points of infinite order: P1 = [330939789898145672840, 1481183918992092384137148744080] P2 = [314097150675826963040, 2025185481386257816598488608080] P3 = [316361317914867254240, 1952746727394375640119448473680] P4 = [-66039961527454488160, -11598594147350432074566312935920] P5 = [-579392825138364624160, -12597002624584430241495636479920] P6 = [343514237194364051840, 1065592452942505127582932224080] P7 = [121931831931083721321890, 42576450056864827845678949593720530] P8 = [407840214133865471840, 1036730232509275527337211904080]
Voznyy (2020)
y2 + xy = x3 - 105655545052152165394401101837567565730660x + 13218568588811424938466556570008310440422613292838843710307600 Torsion points: O, [100123172364211631000, 1908847810684075479860241861260], [187326769206971886920, -93663384603485943460], [191702617009143285320, -95785355284146166156267517860], [191702617009143285320, 95785355092443549147124232540], [100123172364211631000, -1908847810784198652224453492260] Independent points of infinite order: P1 = [157347908276697566990, 699690218795598035889118104890] P2 = [119985310393112100680, 1506260504513243205505666299740] P3 = [186231028058286914120, 33038595618517804119750325340] P4 = [182428842511426450760, 123422970083537413110713956700] P5 = [22265375978780443070, 3298051871412887939674694241290] P6 = [-34451441424512406460, -4100934519327383181922571009680] P7 = [188020334683969190216, 2450983640172216301652839772] P8 = [611142604859508581960, 13300633218196221766566891057500]
Voznyy (2020)
y2 + xy = x3 - 1381349373625762513686831531904414489931720x + 651575405687142897063169210909959373292116752441285664912014400 Torsion points: O, [994614827924973948640, -16173934709572511911911300829720], [994614827924973948640, 16173934708577897083986326881080], [415955974959128081040, 12205053143790704107966454829880], [415955974959128081040, -12205053144206660082925582910920], [-1363528229064303847024, 681764114532151923512] Independent points of infinite order: P1 = [727972907131020302160, 5636999524831146507053662381880] P2 = [-887576998160114704880, -34327867020876204334957933184200] P3 = [664207528626484794360, 5205984775480707524735908096760] P4 = [-9414223431116862286790/9, -833060189010918693377908509786340/27] P5 = [5079808810242945567760/9, 194175007069426595851252164707560/27] P6 = [509134637480103624409360/729, 103208184775525580709196870023145640/19683] P7 = [620293705045708770199471/900, 140082304105479990350939009943615779/27000] P8 = [-3030178502129748269400128240/2442969, -81594862029663765027410378872898556433240/3818360547]
Voznyy (2020)
y2 + xy = x3 - 10923333106094368592569146579270869124176030x + 11965731175581542220550751977617158070089139321353602622984584900 Torsion points: O, [679468023029935302460, -69694836565193728391116012981230], [-3756186778611513449764, 1878093389305756724882], [3323598652331476682460, -111240506891695377097414352421230], [3323598652331476682460, 111240506888371778445082875738770], [679468023029935302460, 69694836564514260368086077678770] Independent points of infinite order: P1 = [-1018703829339607066128, -148445966293547271783755125886114] P2 = [-649650086761669557540, -137068937954261399851373302821230] P3 = [992844847871527242460, 45817506975714915313223740378770] P4 = [961712652232629324940, 48477862126133372847567251891490] P5 = [4775276346884823379260, 262098617084701334939325789537970] P6 = [2564725045426673292460, 28647354528520900013834152578770] P7 = [74901421815457795742140/9, 19043756694631956601523650864146790/27] P8 = [-71439682737732400947460/49, -54007386215176257788048279526161890/343]
Voznyy (2020)
y2 = x3 + x2 - 13154736167751129328875003007476495602768965x + 18355582284682890470036795670838147359800285640848631133636010900 Torsion points: O, [185414461856522792615, 126185887612499013506533355965845], [2056933204831837612820, 0], [2303691909261172481045, -16637539036891501143031613294025], [2303691909261172481045, 16637539036891501143031613294025], [185414461856522792615, -126185887612499013506533355965845] Independent points of infinite order: P1 = [395055620411793801545, 114979936248759850761501229814775] P2 = [1988541717365544908015, 7754191874137099995898297066245] P3 = [1962995142384853027445, 9849176646866574567068093927625] P4 = [2152168030986307559765, 3584709973502222938340678205495] P5 = [-1883446793342636805520, 190920249977875760546849931915510] P6 = [1574502784856751682745, 39328092816255610748237535581175] P7 = [1975214222417891142736745/784, 762071101219496698895926494189533955/21952] P8 = [1910825936338491459958326988145/151019521, 2543000704356051138851539176946186118496173175/1855878893569]
Voznyy (2020)
y2 + xy = x3 - 51089367517798676829723895318110449185540x + 2879237793413416665346166984484966139389506753894735695619600 Torsion points: O, [14165771512706216480, -1469135840833477115869874675140], [-250194642095318163320, 125097321047659081660], [266912694120715476680, -2873731777220446072307503158340], [266912694120715476680, 2873731776953533378186787681660], [14165771512706216480, 1469135840819311344357168458660] Independent points of infinite order: P1 = [202705486949495096930, 923153673855306055750439497910] P2 = [-191813921367936803320, -2370983042353367798186470518340] P3 = [-90588673553895507760, -2600760906561151801232717907340] P4 = [-249915352976531903320, -195246135917920605737914518340] P5 = [-144821421065372987320, -2690854436408513847366494478340] P6 = [1897677875090490991960/9, 32860345527136426677906282420820/27] P7 = [3904937407620293619080, 243614362686394574420149762697660] P8 = [2499974428234990443680, 124497701422329055571562670394660]
Voznyy (2020)
y2 + xy + y = x3 - x2 - 277050557398932185521519176618499051803887x + 56114800713030089465499522469688410877476458557512193760689399 Torsion points: O, [50015849662965161907, 6510222776138830051339432894246], [1199793431050579939947/4, -1199793431050579939951/8], [328530095607488093107, -744494912469271844169312411354], [328530095607488093107, 744494912140741748561824318246], [50015849662965161907, -6510222776188845901002398056154] Independent points of infinite order: P1 = [247809373815079372227, 1636130122772686211642514520726] P2 = [288352647983135929267, 449742655379851573922194235686] P3 = [1820038979109551897791/9, 78057524718755484411986823935506/27] P4 = [2699039010161309944123/9, 537692066112150996164761035442/27] P5 = [94315542995145701898763/9, 28929239304584156047363807668983042/27] P6 = [-547337234519614288973, -6616998272899964847957504564954] P7 = [135403994059735938619627/361, 15286271626991321173258718882689314/6859] P8 = [55606388353046689598443/9, 13066442068917136587180006544862242/27]
Voznyy (2020)
y2 + xy + y = x3 - x2 - 65338547599245730579050023973180473069864657x + 182357248778705611042258346549991633001949842946478772279153458881 Torsion points: O, [-3680333558369631404409, -610717048550421794633185472918396], [-3680333558369631404409, 610717048554102128191555104322804], [7769733561219784112791, -379134963130126535410426759790796], [7769733561219784112791, 379134963122356801849206975678004], [3384107504030451386775, -1692053752015225693388] Independent points of infinite order: P1 = [-910139869377620329809, -490989355714208861840870906247596] P2 = [3383271490991666733291, 5090034217181175259978265706004] P3 = [17344067625306212349391, 2065552210051583524087837643643604] P4 = [63232074923447651123119/9, 7148992612016304995568865494790108/27] P5 = [33768769393751504655991, 6040156330002767506122991071829204] P6 = [6253512674846068714768581/1936, 6028184748652686585768802244478333131/85184] P7 = [9037909689199749342540631/1089, 16536165593580851191021835978999230132/35937] P8 = [134511829243363001523783432166921/6713281, 1560057776921245977340435627434165042467062322184/17394111071]
Voznyy (2020)
y2 + xy = x3 - 1329503354952662818491247976620878070870251525x + 13761559006707473493545961760708015062364703164056773083847181486657 Torsion points: O, [11492653241635973437298, -5746326620817986718649], [40786950851405858077554, 5233291263363568190432049061169223], [40786950851405858077554, -5233291263404355141283454919246777], [-20365428211184233198446, 5691299431597007216857713975641223], [-20365428211184233198446, -5691299431576641788646529742442777] Independent points of infinite order: P1 = [-13844806481240844130446, -5432726905320741134715074593614777] P2 = [3301234308336377952114, 3067333411648845946521558090437703] P3 = [-27536843198396145250446, -5430590150251021381522614886734777] P4 = [43894528623287886002034, 6322699218242593451836825865761863] P5 = [-6230708733535593122526, -4669413268414659555673156753007817] P6 = [145986490848327642205554, 54138195632458432200292982382641223] P7 = [7064026043139537763956694184/3721, 593606646342972393636363906007932892906763/226981] P8 = [-991196593320437971438742286/32761, -30404466972552695184880647591329206026837/5929741]
Voznyy (2020)
y2 + xy = x3 - 790638548430497935939182180579515874145x + 8556078777481404699596344173356841529764723216812399782025 Torsion points: O, [31729007733738009740, -124146864457052325144013899895], [16361647859358061690, -8180823929679030845], [17173239030018664190, -6556526299979410626389683345], [17173239030018664190, 6556526282806171596371019155], [31729007733738009740, 124146864425323317410275890155] Independent points of infinite order: P1 = [-1314000888707969560, -97942379902113056909111780845] P2 = [62528615845117940, 92231456065079043124622844155] P3 = [13128618241570159940, 20950986787895447207265984155] P4 = [16500683187495319130, 1638777127174014130943129555] P5 = [25733079707048955440, 72461975136623856389936469155] P6 = [78019225318373651390, 649441343524489657544624283155] P7 = [73578211617551483133140/5041, 4009626457372641537593047050394855/357911] P8 = [424259826024240549977835710/28058209, 1133839785024003904481124486534843013315/148624333073]
Voznyy (2020)
y2 + xy = x3 - 26819431744393193363136196752966191683367670x + 39338664332562485745512396981064358538238969343729438537694964900 Torsion points: O, [-2896082710331698659060, 304499025753560736517091804559930], [1627547155651383425676, -813773577825691712838], [5799573398272589478540, -280831536606596724353280167148870], [5799573398272589478540, 280831536600797150955007577670330], [-2896082710331698659060, -304499025750664653806760105900870] Independent points of infinite order: P1 = [12686711344065717544440, 1319487786637843767557955561419130] P2 = [4729294096199381056140, 135196630301377123146598169363130] P3 = [79631025890528252808940/9, 18990467062752064438381310629022110/27] P4 = [390547973208122505068624460/529, 7717931481471536774849550405811401394710/12167] P5 = [429943884062266879500, 166994878833198926838999289104570] P6 = [-63945329524305787860, -202616337594766742344818322716870] P7 = [91019304923914025950860, 27416216854257311653169829822303930] P8 = [43033492235071261319417849340/6105841, 6754267388870840366562649499237804580677430/15087533111]
Voznyy (2020)
y2 = x3 - 93305147895336633310719675997889412x + 10969994009953900000456072377977726813144039733934441 Torsion points: O, [123030379305435122, 36781414319675701927296045], [176277529846152827, 0], [177852173906939052, -1087713333345519813457525], [177852173906939052, 1087713333345519813457525], [123030379305435122, -36781414319675701927296045] Independent points of infinite order: P1 = [-10818768103067404, 109444846736162445923490075] P2 = [94958492075628702, 54462184374335041209030125] P3 = [176475682211159852, 64481834884601978318475] P4 = [173347882614364902, 2181599013410112376158925] P5 = [-276240138982155828, 125160372279316495924958155] P6 = [154819510485261252, 15343338862342361547967675] P7 = [183382640839379502, 5143908973211267693509075] P8 = [172044690979681502, 3123158337893446624077075]
Voznyy (2020)
y2 + xy = x3 - 432475962966159032775706109951102832268512705x + 3461702207305424411532852744089352068208424552118342215792515686025 Torsion points: O, [11989191936069743583786, -5994595968034871791893], [12229494650368994919210, 42303053522345790199088078447595], [12229494650368994919210, -42303053534575284849457073366805], [6771634864124346028410, 918502301337417767619095997443595], [6771634864124346028410, -918502301344189402483220343472005] Independent points of infinite order: P1 = [3819996021169679363610, 1365792276788855140842680866896795] P2 = [11962887411529068695850, 7605866442070877914789065835755] P3 = [12587677879776314715690, 111117292976982973799088402183915] P4 = [11851861985407060858410, 29119141806618300109217995343595] P5 = [13301698019788615225386, 250151454758124777167737377516267] P6 = [45771022577790898908810, 8919445604468036602153704734651595] P7 = [-66332920828609383500606678/16641, -4858476948686353350824761545741474692501/2146689] P8 = [51626766968102539057436640/4489, 28655708571241969057939600270365434385/300763]
Voznyy (2021)
y2 + xy = x3 + 221683892998694086877646823657708664080x + 311592422275998184661510782250789695954227526204157075712 Torsion points: O, [4741234476723626464, -38330502106512569133618478832], [4741234476723626464, 38330502101771334656894852368], [35692705357384677184, 231722890843097194485389764528], [35692705357384677184, -231722890878789899842774441712], [-1393367962100335136, 696683981050167568] Independent points of infinite order: P1 = [-620499207510716336, -13183278734612454115526658032] P2 = [4138046779012598944, 36052576892719735534052960848] P3 = [2869935197473425664, 31168078720652570228170397968] P4 = [36392186428798932154336/49, 6943838962027646268711096410483824/343] P5 = [-45417262381897319639/64, -6352066113375916664951661190849/512] P6 = [469787724100529407864/121, 46695450691472519247047904466928/1331] P7 = [9989412022536475323616/169, 1030329590209696481108761569353296/2197] P8 = [49374421299364497184, 362799839532741316403704078288]
Voznyy (2021)
y2 = x3 + x2 - 5170974715410910774849544503221x + 5323633362599289915534558079645209396913390980 Torsion points: O, [2344524239492247, -78022588786769770714725], [-2675901289983228, 0], [572900695033941, -50489732362013358961239], [572900695033941, 50489732362013358961239], [2344524239492247, 78022588786769770714725] Independent points of infinite order: P1 = [1131180466205679, 30360360847470873350901] P2 = [2304613127860947, 75145821078068046676125] P3 = [-1068551272440928, 98127525113569389842250] P4 = [-892901633207541, 96067260166220572341651] P5 = [1267932239672372, 28382773293350226342900] P6 = [5174216544891129, 342191014037883801788151] P7 = [1642409266059380169, 2104852481976159352448069751] P8 = [1859879268036609, 46258488110798311707849]
Voznyy (2021)
y2 + xy + y = x3 - x2 - 17248025995550682354403935081231953225x + 21135451520957035302588460129690773884926555338415426505 Torsion points: O, [-18666384651289037877/4, 18666384651289037873/8], [4550410936717549351, -6072210880639926792412869860], [4550410936717549351, 6072210876089515855695320508], [550209327915873255, -3436857833741947674692890436], [550209327915873255, 3436857833191738346777017180] Independent points of infinite order: P1 = [-199828473734441013, -4957228943179188377718439784] P2 = [-456972726601525089, -5377908708803680458921273980] P3 = [-1722175879685881263, -6762529263787259966933577554] P4 = [12392078138926162215, 41356604104724660079678709180] P5 = [122206503684602536219/9, 1292191419834498623643655862420/27] P6 = [198487531674675597255, 2795795145240421589323593757180] P7 = [559900410099949381897/81, 11108277577945053979329277646774/729] P8 = [72869800421444892743521/9216, 17225915332910961661515435879178943/884736]
Voznyy (2021)
y2 + xy + y = x3 - x2 - 7936978077852508063472757532162291676962337x + 6386910811633910740335979602803590580053933240244933341068376049 Torsion points: O, [-1568172025225627954113, 122380825259062345392858344229316], [-1568172025225627954113, -122380825257494173367632716275204], [3141569144926547122807, 111615079625618585997371727141796], [3141569144926547122807, -111615079628760155142298274264604], [895042070073304996407, -447521035036652498204] Independent points of infinite order: P1 = [827047535459206365687, 19706838269479188422019836853796] P2 = [-2961150536275592809283, -62649088827482745479478122051064] P3 = [326012083287270196407, 61919382119662208004460527021796] P4 = [283434893693091194406007, 150889346970069130916137788787085796] P5 = [-2298911726931064893993, -111729966946678050098747016191804] P6 = [2352412607351391973407, 27087828245336587746771989040796] P7 = [-2152609967254892329205393/3721, -23572030818122893237754980112091117324/226981] P8 = [56016777204498095920322407, 419253964546252873827876010704531557796]
Dujella - Peral - Petricevic (2021)
y2 = x3 + x2 - 172776333763562394336633780299756144005x + 869942592543961417372061466993054347921106655396853257100 Torsion points: O, [-15169814843694687956, 0], [9281325049847865365, 8116058918243114322509700675], [9281325049847865365, -8116058918243114322509700675], [5998667102992428215, 7026447332807221797327274425], [5998667102992428215, -7026447332807221797327274425] Independent points of infinite order: P1 = [2527031333355558380, 21200677369144034683799918040] P2 = [-3249304495936788367, 37376990511575323191687459069] P3 = [1510715774562123008035/9, 58543499481663853086229602077275/27] P4 = [4693398741268761875, 12744430699860387170820192015] P5 = [11443167892261194440, 19780599240762047362247923350] P6 = [-7441435957418448635, 41756165160837964586820395325] P7 = [-10476850990089905525, 39116609813694714688567947585] P8 = [-14264108759078557067, 20789396123321333752612408131]
Dujella - Peral - Petricevic (2021)
y2 = x3 + x2 - 614780887033107484961506860461687245x + 184544177748948585400720863719548637345200144466275100 Torsion points: O, [-904838888398474340, 0], [354295554260196095, -105844756393375120603831635], [557609673451111685, 122935650493338774481844025], [557609673451111685, -122935650493338774481844025], [354295554260196095, 105844756393375120603831635] Independent points of infinite order: P1 = [366475330273191785, 91985397440817029672939625] P2 = [403797510188428760, 46231495850354898333972150] P3 = [-869785244224605877, 247499590499538800856044469] P4 = [319895889971085260, 143576901197966333317463100] P5 = [479663748838023335, 3977277068765037625236675] P6 = [519570600837973660, 73362537091648599106026000] P7 = [254854077694095335, 210755040966108213346811325] P8 = [112256023492508585, 341973543959769455214055575]
Dujella - Peral - Petricevic (2021)
y2 + xy = x3 - 34686102262412371752226318609983088048435x + 2417306610689748579173219399726144324717100598593499784329697 Torsion points: O, [-857545932178525503089/4, 857545932178525503089/8], [152113871636922659534, 812881226655603983153269892633], [152113871636922659534, -812881226807717854790192552167], [67191934973526310094, -624528208358629982301227474407], [67191934973526310094, 624528208291438047327701164313] Independent points of infinite order: P1 = [33798152587659516434, 1132955680681324670049280076333] P2 = [-40989983601626424316, -1941705145975672653192534089767] P3 = [132684187467283985834, 388493057409855031222497191633] P4 = [126516833990154256334, 232429874729442430614137924633] P5 = [-108796903079445067186, -2214326900030695901394109242727] P6 = [246585455731138512464, 2976188124009893854220658027473] P7 = [1001600989758935907337934, 1002402428241680472635764144455966233] P8 = [2867448660920439838365493677955774/1806924719961, 152533399930325471116174484643661569198269713388747/2428902540141255459]
Dujella - Peral - Petricevic (2021)
y2 + xy = x3 - x2 - 1177529352307012277828878583295824754564x + 15552651211285355901829461385443316774788137825358033375648 Torsion points: O, [79135743506933709507/4, -79135743506933709507/8], [20172619963090134937, 2781375600910689033750911844], [20172619963090134937, -2781375621083308996841046781], [11250023377244000187, -61067630314212040331285458281], [11250023377244000187, 61067630302962016954041458094] Independent points of infinite order: P1 = [20180468620550125752, 2842432924199477932888204344] P2 = [13032240088842686199, 49195449746739562801865724111] P3 = [129893119914996471937, 1433242939364910585078481336844] P4 = [21798059142058482004, 15564763866294361826207861036] P5 = [79444604863928494803/4, 2507017433246267995878836217/8] P6 = [-1030034942892074472632547/35344, -1053083749455047263507623439024021707/6644672] P7 = [4536096065525632673814862548/241087729, 28511440603935483947659920782551979806452/3743369168183] P8 = [948342860106476259031435732/50680161, 3028989604970369115906409862501977522196/360792066159]
Dujella - Peral - Petricevic (2021)
y2 + xy + y = x3 - 20653380135957060833720716764294344855686212593x + 1141604178775196738940319287373885079139741573209749296167630517737808 Torsion points: O, [201911540300131372149189, -72132049712203656419472834020689650], [84802460710489073258743, -42401230355244536629372], [92666854273586677958624, 4843986729562200495363031514426480], [92666854273586677958624, -4843986729654867349636618192385105], [201911540300131372149189, 72132049712001744879172702648540460] Independent points of infinite order: P1 = [67968055693672225359018, 7198830748872651684732921644618583] P2 = [67703495752764793349087, 7323588334125999035811121904836240] P3 = [93024010061432685949464, 5032304355011852590373850101504175] P4 = [88961311988409914181879, 2881395710941604584685934436455620] P5 = [81129234459580356317018, 6468709185847807810289680275598] P6 = [423039863005273252801490264/961, 8285683696787936257562326843103359430920/29791] P7 = [20854773576377292999119761/289, 25523416477305745343591216964925699360/4913] P8 = [-8061791204231283734869610849/50625, -225594253521956601042223500172872498419776/11390625]
Voznyy (2022)
y2 + xy = x3 - 6826769885904115166611204219475161635834835x + 6742217023453350616048669822573098704811581685428870748162968225 Torsion points: O, [2043817089577608032030, -36427419468515354484298900362535], [1019093652704051376410, -29042740677257771032483784419375], [1019093652704051376410, 29042740676238677379779733042965], [2043817089577608032030, 36427419466471537394721292330505], [-3010976968621048779634, 1505488484310524389817] Independent points of infinite order: P1 = [1323487911020295027350, 5031683070798030587977719831785] P2 = [1309069378214776139150, 6986050125010033866912158263865] P3 = [-2437957827399685103170, -94314656440469347371760841886295] P4 = [2373306619031389944182, 62514386238422505892509490046561] P5 = [3269850306554791713891011/2500, 890168362584542110289640547151043859/125000] P6 = [93078398857490688602652020/1369, 897340147748128626396176583848182233365/50653] P7 = [2101604474125777632731609/1600, 411835883451966530187193002494568743/64000] P8 = [-1026496912427933166085474/625, -1817085569425336964063266973744075551/15625]
Voznyy (2022)
y2 + xy = x3 - 25853323816065315457787471905625274987069027397618789040x
+ 50577415650937833586235885002297347331633100687873853942465471598294820571240249600
Torsion points:
O, [334176163893471418730026600, 204878426794302787680817238815346121804040],
[3210034441342137956668274080, -25779477316677262064849501785227178688240],
[3210034441342137956668274080, 25779477316674052030408159647270510414160],
[334176163893471418730026600, -204878426794303121856981132286764851830640],
[2888614182560149487922659680, -1444307091280074743961329840]
Independent points of infinite order:
P1 = [1968616456254114242907066520, 85506801268839778567976268268905526012120]
P2 = [2698155997292062083642933280, 21536344722284891899471793553937423484560]
P3 = [2985441248076514673093543680, 1629281476112521541677355435721799434160]
P4 = [1892169706815051906028256320, 91831837819483479625936346936919278977360]
P5 = [12092419204311406428685604095/4, 55859680455265198913591848856122173147905/8]
P6 = [-648911390272670366296673522960/121, -248954725676361967557371269244769451630593040/1331]
P7 = [222079012010374437417045715683040/66049, 692033308386786094528766272464947417623904473040/16974593]
P8 = [294642636186866414268109679578135918584898979620/25465632507241555489,
146541853120276678872198658091724825600976068091406483894874353708858620/128508454698272284694397698737]
Voznyy (2022)
y2 + xy = x3 - 85066758104523445035539436020909137878292300686575065x + 37330067806453671160706332466183911720023160077115360593503213742837956678788217 Torsion points: O, [-1670662740412888593051958993/4, 1670662740412888593051958993/8], [16462276767622488880908974, -5994508876943095936370959633684533032137], [16462276767622488880908974, 5994508876943079474094192011195652123163], [591868723933750016363240774, 13939813852285094193139889967299344677263], [591868723933750016363240774, -13939813852285686061863823717315707918037] Independent points of infinite order: P1 = [-108172805323214457302445826, -6728016734978898908509323548673395973637] P2 = [-13122345998559239935591606, -6200329315790499826937545725635197817317] P3 = [-208976124690860095923122626, -6780913551276889485967862758594256930437] P4 = [6033621937412612306257728104, 468161963942055458161987822084354554992603] P5 = [12661988320200891235948834918/9, 1403571389394556148508040050246366150781801/27] P6 = [1367342673989798799618816368384/841, 1579986238680108147893685717941195201737532407/24389] P7 = [5080551020330558304551480247749534/4932841, 353699833957083298866892994325444193281327437414243/10955839861] P8 = [-9447875556788530995314565044844962746/24778222921, -14764720757197557159755627168414562487938607387287840247/3900364848217531]
AttarBashi - Voznyy (2022)
y2 = x3 + x2 - 49633701791747400409142421775786786721738471393616205x
+ 4280941354553130375635226702887600048623193546543075036961109435514981980255100
Torsion points:
O, [-257417975671109019783401860, 0],
[158510302317856686115820735, -629397653374101306136696955690383918755],
[101197556615552899499823365, -542669941981480888804006521536461274025],
[101197556615552899499823365, 542669941981480888804006521536461274025],
[158510302317856686115820735, 629397653374101306136696955690383918755]
Independent points of infinite order:
P1 = [85027924316099720258511965, 821840114310867525285391007887679395575]
P2 = [52959878987788351013177345, 1341970815648882780503291439299697463545]
P3 = [119561064285294888636311083, 236199906249848437909694093191918022181]
P4 = [121595776861164588776897720, 208689223749073378632768407349920428170]
P5 = [151880551738457325825078499387465151180/752665558969, 1028756992180472857484495150092486258404174470232793063740/652984790335822547]
P6 = [396242200922147407407128533702035707/2701608529, 55520571336132527715345745991579181619335152391394077/140421506511833]
P7 = [6772064675118982770339519530439647025665/36534239454736, 265874125542154838996580531011515049075826497299281032532375/220825949453670270016]
P8 = [206377540702264540380446857184568429903834958559110672652935/150909585148734849229335441030729,
92581873275705628864885241692954391685211376434724375046644390239994014894399578291559375/1853852759901583079300079820686630038390374234683]
Voznyy (2022)
y2 + xy = x3 - 9254811548723503345333418712013855208879588110x + 286991879667739369915954052477683925086216943203871782929404616964100 Torsion points: O, [-109027932320099406874180, 54513966160049703437090], [99185850820528894540220, -18569312282845726501710967757913310], [99185850820528894540220, 18569312282746540650890438863373090], [17795845294228914189500, -11310636096629632568999124976365790], [17795845294228914189500, 11310636096611836723704896062176290] Independent points of infinite order: P1 = [-21947635486225124460100, -21898423744076733363927019897535710] P2 = [-21583716237927021708868, -21833235785114295974952921791773918] P3 = [25209636240492962957372, 8348821489604260476330825179630882] P4 = [87113394430466790750620, 11910291165595466343071421324977090] P5 = [127976730061937621051300, 34620800167560285216581096256081410] P6 = [212376061542682795117728380/2809, 656636135683680986938531809694729807930/148877] P7 = [4624316512237952270538781180/178929, 610531626887405599408654872773894797898830/75686967] P8 = [24522015264431820102486851875580/198443569, 89729758056628723320809517346208248318295344270/2795474556503]
Voznyy (2022)
y2 + xy = x3 - 1740589504796660841615043085595067489876242493654516590x
- 70750305189086385814143275849155585108007161913139154694318224868647088669763900
Torsion points:
O, [-283742934522498886410221040, -20007136477642099392835126058056148939790],
[-5194001682076663848266433505/4, 5194001682076663848266433505/8],
[1970970923375495957762320680, -64461470144066260559829323593456237372890],
[1970970923375495957762320680, 64461470144064289588905948097498475052210],
[-283742934522498886410221040, 20007136477642383135769648556942559160830]
Independent points of infinite order:
P1 = [-762757482683526710335659960, -28515361482073719895356904437460479814650]
P2 = [-519080890064834044456182468, -26322855261610629204272359815856436400678]
P3 = [-118776850985001033756577440, -11589466697045666259901696111051160782290]
P4 = [111946849423516369373053636865/64, 24212848586335404189222407229841426408300645/512]
P5 = [-1579107426568612927437618220320/4489, -6711880127087842183718408181269464299028690470/300763]
P6 = [-10380860485530289971192316167930/214369, -363657376539551678093226864191802439924499426580/99252847]
P7 = [-110605440677080521513031151705346/94249, -545699644751927727460945418138764839781030246014/28934443]
P8 = [1527665003365892488923397723625644742113089390/405173087596062241,
55892544391217506978422029136534270658695620941109840358733208583540/257905667802370610477129039]
AttarBashi - Voznyy (2022)
y2 + xy = x3 - 47610347777825922170742561210931023688972532793469325x
+ 2641031799139167877772712418336213908091986900363120817513509285343929532580625
Torsion points:
O, [-241923827883177107233440894, 120961913941588553616720447],
[255881646301555842476885650, -2685586546919274340712257594875531851825],
[255881646301555842476885650, 2685586546919018459065956039033054966175],
[15146602940635011803434150, -1386856767217759668355707581772291907325],
[15146602940635011803434150, 1386856767217744521752766946760488473175]
Independent points of infinite order:
P1 = [59624194884831100836088450, 119456342184588451230192571161181098175]
P2 = [55168641577913261496940900, 427017220843832393037131157783574110925]
P3 = [-22926782512294638764040350, -1928868247088511426777964973533604801825]
P4 = [54816232439229201505896881650/169, 10145026638000370416916339456847073500188075/2197]
P5 = [374359667194253962582358677090/10609, 1095425072380685773876633150665143433961535305/1092727]
P6 = [2936863014283588568772085317285700/4297329, 151520167007964867405731784847495325455735767392725/8908363017]
P7 = [759202798842533186274570852130/169, 660739315294837103322860990692211735360033035/2197]
P8 = [657358949560028243350772352580652021569824217319648045162871084683865341871709922288791844693759135765654207131187617310669318646777993662499493632850/
3540894787621732962226452094450973466661975129033616532691911229346035490738618675094039987576161579819916724549343566075609,
94379767815824000411899648933699630762731717465875500651731034617047452313848319583991147473151699545739090874527236594810408058734924031400811213382292673644831598129752207452768609817442042238149568528484384564766417849475/
210702424915440031422772269173731323546502132333279430606277843649997702192981352574297337745560305151217854735714182119385509750736557836550920424656404930686158870611929160137521416477]
Munasinghe - Voznyy (2022)
y2 + xy + y = x3 - x2 - 36859958791013684324907963838942499497862x + 23449327138648046223140652779503145192559860680711214206058261 Torsion points: O, [4846799602400062561, -4823980531002234246806371866261], [4846799602400062561, 4823980530997387447203971803699], [532977173079226026801, -12458081461883516862976864035581], [532977173079226026801, 12458081461350539689897638008779], [-1315512962139304843845/4, 1315512962139304843841/8] Independent points of infinite order: P1 = [12679798198901094271, 4794161962532424441321849416379] P2 = [30212170192194895900209/49, 5259459131829424760824546246537117/343] P3 = [-769769289735201318799869/3481, -936374020777941711106684992267940999/205379] P4 = [579094569180972633760789/16129, 9645294414588309031138917193278318477/2048383] P5 = [2906551995068542936369, 156432076429138941496166564214531] P6 = [-296955725096592688591402031/908209, -639372875905663292734513728786768147997/865523177] P7 = [2440298165408925038995969/169, 3811778360183774138400764624836805943/2197] P8 = [854761188169772350751120055/954529, 24823179211103671262174662832102000771021/932574833]
Munasinghe - Voznyy (2022)
y2 + xy = x3 - 37576926806605887754679085810830390x + 2737155512459556183162688256701608496421121409928100 Torsion points: O, [-223243736353871604, 111621868176935802], [155772823202659660, -25759385829905214403681670], [155772823202659660, 25759385674132391201022010], [72089984125455700, 20071986370847587796183890], [72089984125455700, -20071986442937571921639590] Independent points of infinite order: P1 = [693237361870460800, 556634600135806993848275290] P2 = [439449701777617132, 266624778434675151004037146] P3 = [-48664556753892650, -66712597694268234765103010] P4 = [-215934060218608868, -27979001489953197191064278] P5 = [147427195093331546890540/1079521, 13848318818838690178145767476815590/1121622319] P6 = [15945144920376185790124/112225, 613623163430768600444642503408262/37595375] P7 = [3381701433479062389196/40401, 108429498373646111224627291720682/8120601] P8 = [1425622534274460501368392/177241, 1701695342350008356868979223224825042/74618461]
Munasinghe - Voznyy (2022)
y2 + xy = x3 + 1114576068250409775930417524504355x + 841544762862529397696785590766286677674724572071025 Torsion points: O, [-361915575570613521/4, 361915575570613521/8], [123005798580150, -29011753894698984048902505], [123005798580150, 29011753894575978250322355], [192891177550215630, -90738304721660979134353845], [192891177550215630, 90738304528769801584138215] Independent points of infinite order: P1 = [-85592584908051120, -10912666227615087167796345] P2 = [-52148436013473468, -25329938992533476363219169] P3 = [49463491128045480, 31901328969874359823975905] P4 = [5699422790035157723742/121, 430275306648794872312052673165297/1331] P5 = [2760645993685936065/64, 15945169776756218890556314995/512] P6 = [961678471575582036702/961, 29851658556797686874426592764121/29791] P7 = [3551893923383425990/9, 6763480694821527386699388845/27] P8 = [80946665015304987036/25, 728327835311300329732165652769/125]
Munasinghe - Voznyy (2022)
y2 + xy = x3 - 110781474591466851956219159698845852097675x + 13852166491638858179503882044322608611984730039813257955280625 Torsion points: O, [167338590745708548350, -83669295372854274175], [267718329767152029950, -1839059232991326330340052379775], [267718329767152029950, 1839059232723608000572900349825], [-99397136943998887810, 4886870672585718002125406944385], [-99397136943998887810, -4886870672486320865181408056575] Independent points of infinite order: P1 = [-81389279983305928450, -4725404835872389277044414261375] P2 = [-300158220387981572290, -4478994833284318340189738299135] P3 = [-19311279833457045250, -3998036627960862567299826690175] P4 = [216009616490562060350, 36670311508657885520206661825] P5 = [224563737724251749150, 546955701783210072627730229825] P6 = [95511922994481213950, 2035319375147388883029582749825] P7 = [-29307401963666844418, -4132034713327792666012726481023] P8 = [19195104333831047064076862/58081, 51118745524233415526661898187060495441/13997521]
Munasinghe - Voznyy (2022)
y2 + xy = x3 - 67757553274092587061628782194601883626392055x + 214675456753773510670251762205513747318963432801805512157289482025 Torsion points: O, [4857256826684526288510, -12514243018911806962570475206755], [4857256826684526288510, 12514243014054550135885948918245], [7413177868426928622510, -346077130258087498877197164085755], [7413177868426928622510, 346077130250674321008770235463245], [19045466445850182638415/4, -19045466445850182638415/8] Independent points of infinite order: P1 = [4761455794716327391170, 150968122391996708261386351185] P2 = [4774735524863017492110, 2440254057821945186059435161645] P3 = [19151616514908042638415/4, 32815755840234965388922716111585/8] P4 = [19120511042050227600915/4, 25050308185814728545459272455335/8] P5 = [311579681240596466044090/9, 169396526356992233483803010883737615/27] P6 = [152680419788189165245566/25, 21158979166851635263901348656810521/125] P7 = [2678223472632270156147140/289, 3039042093702388598520607510201658935/4913] P8 = [3498498172369215855534406914/734449, 481935865352611161708279444744897319161/629422793]
Munasinghe - Voznyy (2022)
y2 + xy = x3 - 217173843033194233708051218683681x + 1296255342131335981209050575790522540432885378121 Torsion points: O, [5022527830085770, 576360026261327087449291], [5022527830085770, -576360031283854917535061], [12770038554047818, -778072488924283993745333], [12770038554047818, 778072476154245439697515], [-68458819008845649/4, 68458819008845649/8] Independent points of infinite order: P1 = [10086009621919594, 363129894809044227187723] P2 = [53811062594584468, 12059305586736571886572315] P3 = [133184970835499355802/1369, 1520389277215307860626429372991/50653] P4 = [156546727137057786/25, 53308556731766419539607551/125] P5 = [73715614506730330, 19643248127311962805265131] P6 = [1665237942825926836/169, 738603953618359362998322871/2197] P7 = [170762389832187898, 70310790011077286043563227] P8 = [-619803316160629550/49, -487430666850618963690347627/343]
Munasinghe - Voznyy (2022)
y2 + xy = x3 + 185493427042831767108608546421665x - 1218346058263944640066733893202153202955151076775 Torsion points: O, [11597407561077830, -1578843422092113014198035], [11597407561077830, 1578843410494705453120205], [52420056632991110, 12351045647693639170065965], [52420056632991110, -12351045700113695803057075], [22456707641669839/4, -22456707641669839/8] Independent points of infinite order: P1 = [17326249980156422, 2682700361936738238131021] P2 = [5652409320367730, 103593798214152010475465] P3 = [10470869874367966, 1368191646125384581675357] P4 = [21566759737610150, 3579579286701181925772365] P5 = [40620634244756834390/121, 259101650445524647263953579095/1331] P6 = [208554313796693515/36, 48623497759652387313898645/216] P7 = [6470551934450430123910/31329, 521584054475775449377521638231485/5545233] P8 = [454238041410947650/9, 315690783463390939047934195/27]
Munasinghe - Voznyy (2022)
y2 + xy + y = x3 - 2418992830512219693257679268259976468x + 1660107168665183848507078232148975411645640358858493058 Torsion points: O, [414413496914417954, -853706426527534070206387350], [414413496914417954, 853706426113120573291969395], [1555497962910323684, 1288802172054555054283219830], [1555497962910323684, -1288802173610053017193543515], [-7298086438714790153/4, 7298086438714790149/8] Independent points of infinite order: P1 = [-409703061860402851, -1606986177527397998109120345] P2 = [98574096211261424461/9, 969394508401462813374410867665/27] P3 = [1119199971801493052, 595558514525875105325615037] P4 = [6712338646682972009, 16966163841246036481806601155] P5 = [4503055348878367227497, 302176649668600518380007566379795] P6 = [939211800122822489, 465464229157132116964159275] P7 = [76619255637628242521/64, 354715051685121095756012397495/512] P8 = [359447656019105566669359569/689640121, 13319571636895435770973081602434549479935/18110639217581]
Munasinghe - Voznyy (2022)
y2 + xy = x3 - 2206246913758920700080508117050131473558x + 39886782724584794039786640243024969909428705549074471629860 Torsion points: O, [27414146550352259084, -2666261452411761082403717158], [27414146550352259084, 2666261424997614532051458074], [17887932821053332788, -78392178369131539504129492102], [17887932821053332788, 78392178351243606683076159314], [27100800076051676620, -13550400038025838310] Independent points of infinite order: P1 = [26744468394323105204, 3362524499288077876295699834] P2 = [136554698603921744825870/5041, 77007071317228105971630070660210/357911] P3 = [822723048997554000617582/27889, 101489765088420756856544397121045132/4657463] P4 = [6810735172152669325018166/49729, 16842489385075104135895179457327370804/11089567] P5 = [58661372288599611008, 335154113029874211937897695878] P6 = [52566976014375078092628236/148225, 377941096988999842013854438702042061786/57066625] P7 = [618759325020684518973788/22801, 195644494968053779071841015521398/3442951] P8 = [65324075576921829900453356/2679769, 106640117107527798709185030178826031346/4386781853]
Munasinghe - Voznyy (2022)
y2 + xy = x3 - x2 - 955989762848853233263858372033029x + 34862761706198775886373338650021003208359210024585 Torsion points: O, [56506158968424081, -12698998670870125709525388], [56506158968424081, 12698998614363966741101307], [-168849298615036365/4, 168849298615036365/8], [2254031940355111, 5720085856268509777101092], [2254031940355111, -5720085858522541717456203] Independent points of infinite order: P1 = [494717480406439101/16, 377893914800652448541922033/64] P2 = [-5743427050330781, -6337504317004543345409068] P3 = [3242682854760849, 5638872835876536596256372] P4 = [-1325064451812690239/81, -4950968818992126309333504172/729] P5 = [1449952232080955088949/64009, 80697083439382687717193010029444/16194277] P6 = [14264120631919373781, 53872420235519908642427629812] P7 = [12802937092744397399601/958441, 4642156287968437569437560186942908/938313739] P8 = [-188445434981816011273941/4748041, -33181284649328319694991105205600669/10345981339]
Eroshkin - Voznyy (2022)
y2 + xy + y = x3 - 414955855906881003254032680324969820853x + 3251808552654345251939688471830478721073431650847841119148 Torsion points: O, [11541184378451535183, -5770592189225767592], [881623059964249749, 53727638612022286024035385450], [12982054680309265224, -7262452611494546681457525725], [12982054680309265224, 7262452598512492001148260500], [881623059964249749, -53727638612903909083999635200] Independent points of infinite order: P1 = [10391648518922632269, 7866983797547387996791025560] P2 = [-12936131680912539591, -80342731820455534672091815220] P3 = [11999343367467825189, 571931418195258539212013770] P4 = [12222277143975967929, 2432374174026800953688052730] P5 = [19485143884450844889, 50638668897681429524770434490] P6 = [11524851207330803799, 509994278085955165679466100] P7 = [5158298927911613029881/64, 359635032392867462369795130489905/512] P8 = [370009712520659141344734/34225, 34260908941597273037972244590370182/6331625]
Eroshkin - Voznyy (2022)
y2 + xy = x3 - 4750748188170523240720741072266924674551312530x + 134628043293106539881392261202128977499247056555366489416547284624900 Torsion points: O, [-80185451665365586600764, 40092725832682793300382], [22250341777465656126660, -6319645610648930433459323940101730], [22250341777465656126660, 6319645610626680091681858283975070], [61741225519785428944260, 8755985309011687377469321427226270], [61741225519785428944260, -8755985309073428602989106856170530] Independent points of infinite order: P1 = [-42363734867993578818300, -16120107838696244057774336152036770] P2 = [-3137681932573838592828, -12227161952814160412075499558684258] P3 = [-4048551388100465137140, -12401424619650214655751797673110730] P4 = [1166402643908321467951266/25, 476597325768031786322732581378019724/125] P5 = [-6740816883113700569314140/121, -20026749405104857326861815311058941830/1331] P6 = [510184078554673764613874820/27889, 34175319543734767288928478667634319329010/4657463] P7 = [4392236843470004948037191624196/819025, 9204346128635504085144182490079915303817590254/741217625] P8 = [279699358797899714560004877540/4791721, 78636132084104820957424628193897049458565110/10489077269]
Voznyy (2022)
y2 + xy = x3 - 14052474413049624010723778242692663225x + 11394716418289477835756503336520961099472877092490478457 Torsion points: O, [76210615303822854, -3213131079280730009775065477], [-4102440743890140902, 2051220371945070451], [4617498448492886954, -6705107755915716663294271277], [4617498448492886954, 6705107751298218214801384323], [76210615303822854, 3213131079204519394471242623] Independent points of infinite order: P1 = [754929963877532154, 1102874215634254543374315923] P2 = [624617491830825204, 1691445459616208488601094473] P3 = [271435613935539754, 2756877407330226347820267523] P4 = [3373071561807075154, 1540199100755294965981781923] P5 = [-160460364929629886554/49, -1619583408110170211978219361111/343] P6 = [577447934654456398818/169, 3973360193497849761643200553511/2197] P7 = [3268928900002710084, 624188632341359770719857753] P8 = [249599453273027297556/529, 26848417137801597270806941607701/12167]
Dujella (2001)
y2 + xy = x3 - x2 - 45123702275641081919424x - 1963535841750202515136116268762932 Torsion points: O, [-185908156668, 92954078334], [344607416557, 153003436850034459], [344607416557, -153003781457451016], [-75521527458, -31836073229860926], [-75521527458, 31836148751388384] Independent points of infinite order: P1 = [-46184748668, -4687994158267666] P2 = [-60161183646, -23095727833899384] P3 = [-48542581178, -10606589957382016] P4 = [-55854944093, -19559910217201666] P5 = [-185253203193, -6173748038545641] P6 = [-64106657393, -25801849446340566] P7 = [-45896523588, -3287014604709246]
Dujella (2006)
y2 + xy = x3 - 31124678862448817636407940x + 66835225530144951377745363438177411600 Torsion points: O, [3234077113480, 40624133358323260], [3234077113480, -40627367435436740], [2536040165080, -2052397774202172740], [2536040165080, 2052395238162007660], [3220528153480, -1610264076740] Independent points of infinite order: P1 = [28959993461320/9, 268083677343528020/27] P2 = [7671451839880, 16719376910549900860] P3 = [-21698790966705/4, 69762015022586294205/8] P4 = [3219393486280, 4790107476198460] P5 = [7588642289980, 16360070989734833260] P6 = [-2034896926520, 11033795763492203260] P7 = [1858293133480, 3926015569011743260]
Eroshkin (2007)
y2 + xy = x3 - 841913947832430618894580x + 295136017837598326614751155711520400 Torsion points: O, [667332397160, -174598124235145780], [-1058632940440, 529316470220], [667332397160, 174597456902748620], [401533787720, 147709535370407660], [401533787720, -147709936904195380] Independent points of infinite order: P1 = [-66649549720, -592412943604904500] P2 = [349723116710, 208500601797241970] P3 = [116593882760, 445599531600982220] P4 = [490218516062, 14855023338761192] P5 = [168034756136, 398007187783655372] P6 = [342150521960, 217092549535759820] P7 = [406678659560, 141446471939830220]
Eroshkin (2007)
y2 + xy = x3 - 8034015051455135062999285730x + 289348572973066562201234135502825455736900 Torsion points: O, [-104000906778140, 52000453389070], [31559939385460, -259287856260895148930], [31559939385460, 259287824700955763470], [76099405897000, 344478640455444367630], [76099405897000, -344478716554850264630] Independent points of infinite order: P1 = [67148375096860, 229440835734440214070] P2 = [-21739950377660, -673596907070996876210] P3 = [-6632888557628, -585102965527994657714] P4 = [-52920008223740, -752532224932127441330] P5 = [28187521974790, 292036985720387317090] P6 = [37197034000612, 204874522324991904142] P7 = [43362951743740, 150024312364188466390]
Eroshkin (2007)
y2 + xy = x3 - 822259949983210124060751x + 286775782051582928617737165270930681 Torsion points: O, [535079801286, -267539900643], [584705383110, -76780918112411619], [584705383110, 76780333407028509], [1274038014006, 1143314401264057917], [1274038014006, -1143315675302071923] Independent points of infinite order: P1 = [160504431390, 398665542695590701] P2 = [-115474044474, -616591949781999843] P3 = [192070044378, 368686646528688837] P4 = [541104466374, 16715448906014493] P5 = [440598323286, 100106751037992957] P6 = [539087782536, 13146152721528357] P7 = [538400443590, 11811127630377501]
Eroshkin (2007)
y2 + xy = x3 - 51054993026763259730885310x + 140295994906362117844167089363816108100 Torsion points: O, [16111853758239/4, -16111853758239/8], [4627603818420, 1769896228442004690], [4627603818420, -1769900856045823110], [56375302020, 11722539518574675090], [56375302020, -11722539574949977110] Independent points of infinite order: P1 = [3522275931120, 2040851885423177490] P2 = [2659435984970, 4829867772309556640] P3 = [4234397012610, 179227639595181750] P4 = [4222794188832, 45758176345977486] P5 = [6671554403460, 9829966339234300650] P6 = [9657738289782, 23409735015050279286] P7 = [7358694486180, 12770040775324262730]
Eroshkin (2007)
y2 + xy + y = x3 - x2 - 45374649173740836605820102362x + 3720066318230759490581315479518302807124761 Torsion points: O, [128336794962481, -102854390133902441241], [128336794962481, 102854261797107478759], [44278012708881, 1340811652622470193959], [44278012708881, -1340811696900482902841], [122348007122481, -61174003561241] Independent points of infinite order: P1 = [-81706520877519, -2623356956662003561241] P2 = [-62237678361039, -2510577534231057953561] P3 = [115442739052081, 142831727702898531559] P4 = [121158369112369, 32771575184217466599] P5 = [108287374802481, 276331769484406678759] P6 = [124251519318801, 21138819990513227719] P7 = [124109673231201, 17914148013272118919]
Eroshkin (2007)
y2 + xy = x3 - 533024166437861795831860x + 150145561559705338985839395548651600 Torsion points: O, [-843254960680, 421627480340], [353471641820, -76812672080584660], [353471641820, 76812318608942840], [493903097270, 85825911577001090], [493903097270, -85826405480098360] Independent points of infinite order: P1 = [225881035820, 203151228866431340] P2 = [-199633635190, -498596928696485410] P3 = [379553028866, 50131880774897702] P4 = [268669162916, 162270575082307472] P5 = [329053583870, 101885757234320840] P6 = [316093339430, 115076505790470290] P7 = [-232169239720, -511256044385040460]
Eroshkin (2007)
y2 + xy = x3 - 3027369717001109222247250443030x + 2028817184758375459182141696978493700290404900 Torsion points: O, [-2009255022303540, 1004627511151770], [896256825536460, 5954684828112112111770], [896256825536460, -5954685724368937648230], [1117198419525660, -6407493369462133642230], [1117198419525660, 6407492252263714116570] Independent points of infinite order: P1 = [719144428256460, 14953932762832583791770] P2 = [191272884896460, 38167541407197495151770] P3 = [-263920449615540, -53003951094727421776230] P4 = [95788311456540, 41709824304933169890570] P5 = [775746301887210, 12131641521829168430520] P6 = [-697452700998540, -61652212024596037573230] P7 = [665290658317260, 17584134432951765506970]
Eroshkin (2008)
y2 + xy = x3 - 165622879312545076279689272890746x + 818377467155538128945404717298826491824235027940 Torsion points: O, [8747576267131284, 197342405753318848488246], [8747576267131284, -197342414500895115619530], [-1055097540542892, -995967465143662385937354], [-1055097540542892, 995967466198759926480246], [7126469030754708, -3563234515377354] Independent points of infinite order: P1 = [6097805914754708, 187556538864956915662646] P2 = [7739550190564476, 11613251360835905805870] P3 = [2300450906945940, 670480663392912136839990] P4 = [8074157605384596, 86503689476159534451510] P5 = [5686582350100884, 245840560739210811777846] P6 = [5104993505865108, 325445490174819334094646] P7 = [-3097342426993716, -1140900428066739076886754]
Eroshkin (2008)
y2 + xy = x3 - 7124549942935826931044066x + 7319360155313501266864951695617016900 Torsion points: O, [617523082948, -1776308031346216754], [1598858413924, -124308508474598834], [1598858413924, 124306909616184910], [617523082948, 1776307413823133806], [1534675231588, -767337615794] Independent points of infinite order: P1 = [1353468402148, 394833692638471246] P2 = [-118478415284, -2856886785679150610] P3 = [1379258899300, 341468869627858510] P4 = [-200668339100, -2956509884462198450] P5 = [2211778113316, 1543168340947208590] P6 = [196629775204, 2434350708655533646] P7 = [978986723668, 1132605317857492366]
Eroshkin (2008)
y2 + xy = x3 - 822259949983210124060751x + 286775782051582928617737165270930681 Torsion points: O, [535079801286, -267539900643], [584705383110, -76780918112411619], [584705383110, 76780333407028509], [1274038014006, 1143314401264057917], [1274038014006, -1143315675302071923] Independent points of infinite order: P1 = [160504431390, 398665542695590701] P2 = [-115474044474, -616591949781999843] P3 = [192070044378, 368686646528688837] P4 = [541104466374, 16715448906014493] P5 = [440598323286, 100106751037992957] P6 = [539087782536, 13146152721528357] P7 = [538400443590, 11811127630377501]
Eroshkin (2008)
y2 + xy + y = x3 - 4019175690941783130628x + 97050922917328246600400524493006 Torsion points: O, [47323693630, 3582099886172822], [47323693630, -3582147209866453], [128914071400, -41488914336241798], [128914071400, 41488785422170397], [158454146295/4, -158454146299/8] Independent points of infinite order: P1 = [-21470236145, -13169894998135303] P2 = [6797578855, 8369247193969697] P3 = [40568361277, 875555712946313] P4 = [39706357882, 254801927431934] P5 = [31943322940, 1122165893548322] P6 = [-49413353270, -13228743202800553] P7 = [24325376740, 3698212836832562]
Dujella - Eroshkin (2008)
y2 + xy + y = x3 - x2 - 82332276908073834616547402x + 287541668542010063173870439227562187401 Torsion points: O, [5357890870801, -472504457312885001], [5357890870801, 472499099422014199], [5120414604081, -465418402990226921], [5120414604081, 465413282575622839], [-10477415138799, 5238707569399] Independent points of infinite order: P1 = [1953110661201, 11583955051308889399] P2 = [4902790317201, 1316766148617553399] P3 = [-3076314896879, -22620969178104943881] P4 = [5172320878501, 259446562402368799] P5 = [1267674645321, 13609124264904414319] P6 = [-4883644704239, -23940515530725784841] P7 = [5132894729761, 416080642067811079]
Dujella - Eroshkin (2008)
y2 + xy + y = x3 - 41061306153084043265108x + 3185903340945571830683716617085118 Torsion points: O, [110033611989, -55016805995], [143847305214, -15995081577800645], [143847305214, 15994937730495430], [-30120225081, -66297445027539305], [-30120225081, 66297475147764385] Independent points of infinite order: P1 = [58085745864, 31572195682253005] P2 = [67056207819, 27092556752728645] P3 = [-49402075188, -71371174655444750] P4 = [102305844864, 7474867295631130] P5 = [46255763829, 37222952221019245] P6 = [-114023465736, -79908620275049795] P7 = [-118478078886, -79922932947100745]
Eroshkin (2008)
y2 + xy = x3 - 1523372635414000905181910527726x + 723243212874903410571391010646562847229006980 Torsion points: O, [697959663027580, -348979831513790], [791511270622844, -3653843709347513251774], [791511270622844, 3653842917836242628930], [35976792126956, 25855052062111292942354], [35976792126956, -25855052098088085069310] Independent points of infinite order: P1 = [561238227098684, 6712060319827202302850] P2 = [374680735006076, 14320077810680157304130] P3 = [686296076050616, 1002787707780741619910] P4 = [-560717155492996, -37431708463155880204990] P5 = [678321148470884, 1419922026769708037666] P6 = [361042809522293564/529, 14671607665824712289745358/12167] P7 = [734470260787580, 760771999563439987010]
Eroshkin (2008)
y2 + xy = x3 - 3726896606489538014807823629390x - 1065145370395664163469346840915100916019739900 Torsion points: O, [3056664594482380, -126893679880281021886190], [3056664594482380, 126893676823616427403810], [-1328649861082520, 39257048432445075840310], [-1328649861082520, -39257047103795214757790], [-292515363927620, 146257681963810] Independent points of infinite order: P1 = [-387790567665620, -17938601857657080778190] P2 = [-581331287466620, -30082513078255057312190] P3 = [-508441467177620, -26425835943837652786190] P4 = [2333741368028380, 54291906891132792703810] P5 = [-298275933778370, -4467775901762557061690] P6 = [2603086474436380, 82898059700700975523810] P7 = [2777911298075080, 100092095418999114324310]
Eroshkin (2008)
y2 + xy = x3 - 54059464705737223501792212385x + 4787734047854039033545219031800955876871497 Torsion points: O, [173473070950634, 793839676003369155083], [173473070950634, -793839849476440105717], [472318017697274, -9198979192758376947877], [472318017697274, 9198978720440359250603], [145248077152234, -72624038576117] Independent points of infinite order: P1 = [-106978355783488, -3057225316048442830627] P2 = [407968471326934, 7115809301665634542483] P3 = [34571576919914, 1720503642820954580363] P4 = [1770192589310474, 73865656604392517397323] P5 = [-19724131498006, -2417919867928123342837] P6 = [156968131536874, 411895274952756795403] P7 = [-777338126866, -2197670598490440689917]
Dujella - Eroshkin (2008)
y2 + xy = x3 - 699112954366367467920156400x + 5722163130057598068986876309705284428032 Torsion points: O, [9356543694304, -4678271847152], [28109600724704, -91000939199534643952], [28109600724704, 91000911089933919248], [-13918500153136, 112944286895464717328], [-13918500153136, -112944272976964564192] Independent points of infinite order: P1 = [-2319224044576, -85621772128587684592] P2 = [-19980795007696, -108231314617690247152] P3 = [3084205353854, 59960762043281605148] P4 = [-8602165270046, -105354216093065334452] P5 = [-8942053648106, -106106824584020535332] P6 = [8544143171744, 19302450572437221968] P7 = [-9703877652256, -107668475781078537712]
Dujella - Eroshkin (2008)
y2 + xy + y = x3 - 5871521435329649314324031629344788x + 172993600167184429589198294960718574003359733763906 Torsion points: O, [50026756825466850, -2112157387935390374766038], [50026756825466850, 2112157337908633549299187], [112061677002855645, -30368921158594179389981513], [112061677002855645, 30368921046532502387125867], [45389724976446825, -22694862488223413] Independent points of infinite order: P1 = [13751724756837405, 9739129381467531623506987] P2 = [2072162199261765, 12682103647933379722415047] P3 = [28757641336076406, 5284422155549216622773239] P4 = [-21766829310093075, -17043620298012166054485413] P5 = [49531516023267525, 1920268459223220554249587] P6 = [311262675619341225, 168825123175264112083874587] P7 = [-86121186531920475, -6317223662181808961737913]
Dujella - Eroshkin (2008)
y2 + xy + y = x3 - x2 - 960030060545458886002887849322805356175498x + 362055559646249146707021073044994258163432080303497826046420681 Torsion points: O, [570599534796257472721, -202077054325406019870532266953], [570599534796257472721, 202077053754806485074274794231], [758174730999734226393, 8366946312319657185484591168831], [758174730999734226393, -8366946313077831916484325395225], [565957128180916193937, -282978564090458096969] Independent points of infinite order: P1 = [302402190465795542337, 9969662239818276823425759660391] P2 = [-36503726239229752362225/841, -489996817120924115497412908474740637/24389] P3 = [-10627898494304311983365/81, -16067148979418971637722844583511907/729] P4 = [19984604975097918012261157/35344, 1573607074949468850736100773958865/6644672] P5 = [153752006639685347310843025/1159929, 19237122998953125515470914485199788558131/1249243533] P6 = [87448670109363398545681569421/4243600, 25831364797662483060401244279320098647203439/8741816000] P7 = [-709692878534678985967437575/822649, -17470222587226670588579630248713748783419/746142643]
Dujella - Eroshkin (2008)
y2 = x3 + x2 - 92415860650236343941767865x + 339812153247400733310842691312151100400 Torsion points: O, [6909772426305, 5580892492438097835], [6909772426305, -5580892492438097835], [-1595669488665, -21982140267680708115], [-1595669488665, 21982140267680708115], [5187612265584, 0] Independent points of infinite order: P1 = [5059548243113, 1322560829889679611] P2 = [2329919087475, 11710623159368235795] P3 = [5956798424325, 822948425306202195] P4 = [5911086067635, 270077175616413165] P5 = [4213852192935, 5020842023157814035] P6 = [5997383704203, 1129752105506331021] P7 = [9900583970025, 19882451547851887995]
Dujella - Eroshkin (2008)
y2 + xy = x3 - 14449832020856516030717699280x + 667048026760547478386730660166577486342400 Torsion points: O, [81342134662560, -172833966506633526480], [81342134662560, 172833885164498863920], [194935071880320, -2292976280019735004080], [194935071880320, 2292976085084663123760], [72082042220960, -36041021110480] Independent points of infinite order: P1 = [72959231988960, 34131852917983817520] P2 = [72183037296960, 10821322957220681520] P3 = [-59084864531040, -1146537313307031222480] P4 = [64271200856480, 61892037296444510000] P5 = [39821144111520, 393426603764064175920] P6 = [72397034898960, 19489256450671913520] P7 = [36083711289930, 438892550626700856300]
Dujella - Eroshkin (2008)
y2 + xy + y = x3 - 2775271711608913149065000293562148x + 56273815466836272280793492720347500222386983036078 Torsion points: O, [30419896594579709, -15209948297289855], [30539861846287934, -37625933430885973733130], [30539861846287934, 37625902891024127445195], [37410378037431539, 2192495549212538777462685], [37410378037431539, -2192495586622916814894225] Independent points of infinite order: P1 = [23527031657479259, 2000655201679940358341295] P2 = [17732988323174264, 3554750357534057941439610] P3 = [30436311237146339, 6193452439775111945325] P4 = [30420923954511659, 978699312440024698095] P5 = [16081107760461884, 3975296090112913905079170] P6 = [7514721685079492, 5986884421179295713505257] P7 = [34118644627116959, 1141141183475891614655145]
Dujella - Eroshkin (2008)
y2 + xy + y = x3 - x2 - 447557589334393730351824217x + 3643868079922687465968426756008094647609 Torsion points: O, [12330077305767, -6165038652884], [13017185672167, 4863377085108668716], [13017185672167, -4863390102294340884], [24751450966047, 87919023142864239436], [24751450966047, -87919047894315205484] Independent points of infinite order: P1 = [12378455027367, 706804200079139116] P2 = [13274227846399, 6470977876774945332] P3 = [11978561665023, 1235741779388591308] P4 = [6202585988457, 33263790847686514576] P5 = [-9143473891253, -83496560120664187764] P6 = [-4602833014143, -74875794704841561074] P7 = [12367420151767, 608557163570093116]
Dujella - Eroshkin (2008)
y2 + xy = x3 - 3418877004771000403942399401264510x + 76895638096171882779790294730021122439698272834372 Torsion points: O, [33066753943523484, -16533376971761742], [37490621371389084, 1189383687224792717607858], [37490621371389084, -1189383724715414088996942], [1726222621743804, 8426092755843902278048818], [1726222621743804, -8426092757570124899792622] Independent points of infinite order: P1 = [28696729638957564, 1554629089706794412541138] P2 = [35759513207518284, 604549560434576731724658] P3 = [-11929275082666212, -10769528108369840615640654] P4 = [19914401209264284, 4087599553495003645403058] P5 = [21438527488223484, 3667876888745444119458258] P6 = [-988057659082596, -8959504511869625204066382] P7 = [34667553044632692, 190692351587248200351570]
Dujella - Eroshkin (2008)
y2 + xy = x3 - 492846919517842269542923229020x + 51349587205341386622021930561564828983536400 Torsion points: O, [106651142448440, -53325571224220], [926456309866040, -19747041447198830289820], [926456309866040, 19747040520742520423780], [-452900735476600, 13478195174708149200020], [-452900735476600, -13478194721807413723420] Independent points of infinite order: P1 = [103098163305272, 1278213246139570460516] P2 = [37096316376800, 5754809409709130827580] P3 = [23035839331640, 6325240594018567732580] P4 = [-44624499484360, -8558841692238034584220] P5 = [-256901914735240, -12688882382832902109340] P6 = [86677934390252, 3046613018124846715712] P7 = [-578597171822080, -11950302374007020949220]
Voznyy (2019)
y2 + xy = x3 + 358804192012993775138370x + 38355557903006419927041938707320900 Torsion points: O, [1388323126260, -1792318404040559430], [-415131437281/4, 415131437281/8], [158341173060, -314863466865742830], [158341173060, 314863308524569770], [1388323126260, 1792317015717433170] Independent points of infinite order: P1 = [-2502620820, -193539636517234350] P2 = [-41564685048, -152873019876940794] P3 = [59641572270, 244882301332109910] P4 = [86853728460, 264904141061822370] P5 = [38028071964820/9, 236911052815360278950/27] P6 = [43519964480, 232493268154096850] P7 = [569694173520780, 13597619921833645132050]
Voznyy (2019)
y2 = x3 + x2 - 3644556202475792269518216279468858086405x
+ 84686319731701109368750690123396573251362730371973553418100
Torsion points:
O, [18964173200804056615, 149634880162561915766528758875],
[34796269593421942644, 0],
[35567807949339641365, -7292088587989896288245022375],
[35567807949339641365, 7292088587989896288245022375],
[18964173200804056615, -149634880162561915766528758875]
Independent points of infinite order:
P1 = [33397751500810106800, 14782315447325747671195555710]
P2 = [10662355826536264240, 216884585579242517737407857250]
P3 = [30336154988284996240, 45192083152648098137140419750]
P4 = [30421173736485368365, 44360466201973680330105894375]
P5 = [97389258562231353415, 808362818770172035675816589925]
P6 = [45068824145269032615, 109426704356314995618934294875]
P7 = [8209343546510456740, 235202382470193943414901791500]
Voznyy (2019)
y2 + xy = x3 - 379182143604577428048375150248709410351240x + 119439444845999205909039638251442235171869686073489510859585600 Torsion points: O, [-2943451660168556992641/4, 2943451660168556992641/8], [711776418853572531280, -14496576905961913575742954007240], [124365538579084476880, -8614278185466188569356043420040], [124365538579084476880, 8614278185341823030776958943160], [711776418853572531280, 14496576905250137156889381475960] Independent points of infinite order: P1 = [-159251929816652702670, -13258435675498075975181987558790] P2 = [234489482690010071730, 6589286668496541140498542626810] P3 = [263816407837796106730, 6145433879995852010424134191810] P4 = [38831844354250083016516/121, 7387163240857668695242371001465112/1331] P5 = [4246163864350408571280, 273984145341898524425204325075960] P6 = [1091388671299218195963760/49, 1139739173469581084421310134086451400/343] P7 = [-110881052565373000920118788848/152744881, -6583112395199996168503880338967354335155256/1887773984279]
Voznyy (2019)
y2 = x3 + x2 - 89280997598876690534935351936005x
+ 298360732693992690511174782786675112436099714100
Torsion points:
O, [-10811048042186956, 0],
[8781358813361685, -437610219765512058526905],
[8781358813361685, 437610219765512058526905],
[2528572946672295, 297949839218968516856955],
[2528572946672295, -297949839218968516856955]
Independent points of infinite order:
P1 = [-597819986672400, 592892100941631170502690]
P2 = [6929473532734800, 111477060444273579201510]
P3 = [3567283670611785, 158951570698240272514695]
P4 = [4097199969093455, 36585829836172420237515]
P5 = [2320810454503619055, 3535541293375506225002053365]
P6 = [7615014145368873444, 21013855300643216828225891580]
P7 = [1502873358525043741/225, 13589014692689874149682761/3375]
Voznyy (2019)
y2 = x3 + x2 - 683296280266159149478668116716868339845x + 6874806981839357142636691301220260598519026095365342406100 Torsion points: O, [15071505734358181204, 0], [15359069197330993685, 1797780623720453310021057975], [15359069197330993685, -1797780623720453310021057975], [8654052888622325735, 40120439016949728002033743275], [8654052888622325735, -40120439016949728002033743275] Independent points of infinite order: P1 = [15025368730457183285, 425780269085801019594197175] P2 = [14447839800407097635, 4300575588730943467395525075] P3 = [5301544734267991760, 58320565823305314299141921550] P4 = [1906048856275312536136915/1369, 2631025394986677305914952404525550775/50653] P5 = [33282848856756688262555/2209, 10060793028174427310047831353645/103823] P6 = [8264337748462978578240365/2809, 23757186275805612020621973612558825675/148877] P7 = [2149460699744144583831540001/141895744, 596907116632457416064423538567941232465/1690262102528]
Voznyy (2019)
y2 + xy + y = x3 - x2 - 45759282422993769515525690163600632x + 3486039421495312317742621236734755107295292724214139 Torsion points: O, [94801640615732013, -47400820307866007], [196592991262446637, -45696490565155265770143639], [196592991262446637, 45696490368562274507697001], [-89862666452259843, -82900076375008855234001159], [-89862666452259843, 82900076464871521686261001] Independent points of infinite order: P1 = [-5813926566561123, -61252624499187751254769079] P2 = [-83753958701081811, -82042973049661894045649303] P3 = [37714409349690477, 42589895598837915192433321] P4 = [39028221395025357, 41947394221910608890981001] P5 = [87259210355776317, 12550976586701175927014281] P6 = [150695593197088413, 3533811225281441036413513] P7 = [89172119619431707, 10707670528746249029692291]
Dujella (2001)
y2 + xy = x3 - 46211161865740185355x + 110998663417922709680844055025 Torsion points: O, [2967450110, -1483725055], [6326811710, 268105806209345], [6326811710, -268112133021055], [-2924705530, 470251457903345], [-2924705530, -470248533197815, 6] Independent points of infinite order: P1 = [-2791455490, -467163905997055] P2 = [443358350, 300994310491745] P3 = [1073542940, 250251834090065] P4 = [5292480590, 121122182401745] P5 = [-2070296240, -444741481882055] P6 = [47432888960, 10229215180208345]
Dujella (2005)
y2 + xy + y = x3 - 25187421680278445693x + 48654137710470248344196743556 Torsion points: O, [2904641535, -1452320768], [4685242485, -183013398562718], [4685242485, 183008713320232], [2973947160, -7124753763893], [2973947160, 7121779816732] Independent points of infinite order: P1 = [2822283975, 6954343660492] P2 = [-979245690, -269034436509293] P3 = [2908598655, 789015540112] P4 = [619219245, 182468948735122] P5 = [1650637535, 107591777378232] P6 = [3630285285, 71132120660482]
Dujella (2005)
y2 + xy + y = x3 - 8681604817982520137993x + 787867843662491679357445631664056 Torsion points: O, [8355021360, -26756612403914168], [8355021360, 26756604048892807], [156085683645, -56881258134422228], [156085683645, 56881102048738582], [-122859173865, 61429586932, 2] Independent points of infinite order: P1 = [-32068158783, -32144860624255496] P2 = [-29810853390, -31940263346584418] P3 = [-122202453495, -4886480574238688] P4 = [-64863539190, -32834225137298993] P5 = [217564817460, 95902795270148932] P6 = [4708554135, 27333025804220932]
Dujella (2006)
y2 + xy = x3 - x2 - 24641984875424581038634209x
- 24571734768259940862407109555298069587
Torsion points:
O, [-4359551072022, 2179775536011], [8039911064347, 17233977404728400004],
[8039911064347, -17233985444639464351], [-1748544931818, -3629030032481723181],
[-1748544931818, 3629031781026654999]
Independent points of infinite order:
P1 = [-1112660361497, -1211996535271093884]
P2 = [-2838294220061, -4743880335803740135]
P3 = [-2275924564521, -4441018522047020379]
P4 = [38890306676394, 240493160869696681371]
P5 = [1552226360783953, 61154772385499844149171]
P6 = [902137984435375398/73441, 777542618042183179695244761/19902511]
Dujella (2006)
y2 + xy + y = x3 - x2 - 1885102854395997091056548x + 973413771881424764788534967357439431 Torsion points: O, [513988260093, 374540094579630325], [1099311362821, 479166013869157597], [1099311362821, -479167113180520419], [513988260093, -374540608567890419], [-1581348239163, 790674119581] Independent points of infinite order: P1 = [924719112261, 144759594450207901] P2 = [-583009680075, -1369043837190113843] P3 = [530245547685, 350614046229935197] P4 = [987116640237, 272842136804095141] P5 = [1267219218195, 787103093900430247] P6 = [1109096203237, 496936432152555741]
Dujella (2006)
y2 + xy = x3 - 83818010737520230021560x
+ 9334402101835969395681636158145600
Torsion points:
O, [8870692320, 92690752089959640], [163751652720, -81875826360],
[185537412720, -13038096734226360], [185537412720, 13037911196813640],
[8870692320, -92690760960651960]
Independent points of infinite order:
P1 = [65058758970, 64472262197329890]
P2 = [92503745280, 48707976211031880]
P3 = [110833991250, 37496896782862410]
P4 = [172895207040, 3314040055803720]
P5 = [180319408320, 9137174862722040]
P6 = [94101612552, 47752152781196016]
Dujella (2006)
y2 + xy + y = x3 - x2 - 724963083845838467147663x + 237586593680168135061122941755311831 Torsion points: O, [491495434995, -245747717498], [493839544051, 2739455152573062], [493839544051, -2739948992117114], [380666127315, 129532726725666982], [380666127315, -129533107391794298] Independent points of infinite order: P1 = [262390922995, 255789260108384902] P2 = [275645287155, 242275644241791622] P3 = [501060887283, 11545420509573766] P4 = [-695790343437, -636521420764992890] P5 = [216858734995, 300949033958838502] P6 = [-1006381515605/9, -15207828875734886206/27]
Dujella (2006)
y2 + xy = x3 + 177804364014978081877274x
- 5522974673744579179969706095233820
Torsion points:
O, [30896215148, -15448107574], [194163931244, 190578307857850826],
[194163931244, -190578502021782070], [1137471946508, 1291678171375136426],
[1137471946508, -1291679308847082934]
Independent points of infinite order:
P1 = [31146904016, 6730312822548074]
P2 = [63685875854, 77839257311805860]
P3 = [136650441836, 146033458083911114]
P4 = [159692378380, 164144512375241290]
P5 = [160382465228, 164678914082385386]
P6 = [48280943168, 56339420189611286]
Dujella (2006)
y2 + xy + y = x3 - x2 - 7155075168979273725951497x + 7366639344211346802891522902591893769 Torsion points: O, [1549129854727, 10281986467072636], [1549129854727, -10283535596927364], [1851564002727, 682828996106512636], [1851564002727, -682830847670515364], [1544505854727, -772252927364] Independent points of infinite order: P1 = [1345876154727, 417959815081072636] P2 = [1567336854727, 49593159736072636] P3 = [1549084968067, 10185220698738496] P4 = [1546809150727, 5277875453952636] P5 = [1760363607687, 475668162437671036] P6 = [2295338038509, 1742550910112745682]
Dujella (2006)
y2 + xy + y = x3 - 42784589788168290967245543x + 105998799994358063694286205461334210806 Torsion points: O, [3380159641235, -1690079820618], [-1681038746335, 13159443095497371432], [5061214509260, -4370853615511242243], [5061214509260, 4370848554296732982], [-1681038746335, -13159441414458625098] Independent points of infinite order: P1 = [2050191887510, 5186493508637867757] P2 = [507711015461, 9187353302890575624] P3 = [4191738243485, 555557137882996632] P4 = [1904470506536, 5605740765024339309] P5 = [16350134082035, 61459697532243620382] P6 = [-4949313954533, -14018421643985139622]
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