Dujella (2001)
y2 + xy = x3 - 662057554395863819655x
+ 6555937806015269208934798118025
Torsion points:
O, [15204607110, -67941800897355], [14508246060, -66888206628705],
[7767913230, -1371809902183875], [23282395290, -1939686489026055],
[23282395290, 1939663206630765], [15204607110, 67926596290245],
[7767913230, 1371802134270645], [14508246060, 66873698382645],
[-29710565514, 14855282757]
Independent points of infinite order:
P1 = [6528464250, 1584915470789805]
P2 = [-1251382860, -2717068690242585]
P3 = [234157109127026470/3122289,
107363591829490639800339875/5517084663]
Dujella (2001)
y2 + xy = x3 - 4281263352573652971565x + 107821663654697042219512111579217 Torsion points: O, [151106661871/4, -151106661871/8], [38658903974, -298124191759837], [38658903974, 298085532855863], [37778521874, 553359104063], [37778521874, -591137625937], [19466574194, 5644185762393983], [37738137374, -13037357834437], [37738137374, 12999619697063], [19466574194, -5644205228968177] Independent points of infinite order: P1 = [38884390274, 374658605091263] P2 = [68144084374, 11511432778916563] P3 = [63596755816498/1681, 1295465435236059911/68921]
Dujella (2001)
y2 + xy = x3 - 194893737997038726814052934940x
+ 33116538928063906147760473209688087642871600
Torsion points:
O, [254754441578780, -3513286725747626740],
[155923053598730, 2553216176076833653760],
[1019524782879295/4, -1019524782879295/8],
[258559200504980, 101940657731359903760],
[254885906826230, -121678567430089990],
[254885906826230, 121423681523263760],
[258559200504980, -101940916290560408740],
[254754441578780, 3513031971306047960],
[155923053598730, -2553216331999887252490]
Independent points of infinite order:
P1 = [20645366256649420/81, 6181433476946512840/729]
P2 = [366203161320830, 3294756456379543927760]
P3 = [6763257201404423015251311798240171890/30430663076172557016361,
4686465337444992434378968860543553400778455713416972160/
5308442572234136882937273541037141]
Dujella (2001)
y2 + xy = x3 - 489947814397230700269047753x
+ 4173986155348349327100911472235093494297
Torsion points:
O, [50821743663663/4, -50821743663663/8],
[18672290044426, -39188206919547108605], [18672290044426, 39188188247257064179]
[12982660805878, 1174990135682956555], [12982660805878, -1175003118343762433]
[-7723858718018, 86588016541465379419], [11756274291562, -6233765322000803261]
[-7723858718018, -86588008817606661401], [11756274291562, 6233753565726511699]
Independent points of infinite order:
P1 = [1210503846669361840932/193237801,
98719822627082311300356878237469/2686198671701]
P2 = [11716484125164953506/641601, 18647683095020784752143426699/513922401]
P3 = [406163047331649294562/31550689,
63512630297765411472994259035/177220220113]
Dujella (2001)
y2 + xy = x3 - 1065792807399105888102105x - 14138522318461624729140413052612423 Torsion points: O, [-13267924006, 6633962003], [1192775315994, 641549883979002003], [1192775315994, -641551076754317997] [3843399621594, 7256940917155203603], [3843399621594, -7256944760554825197] [-289481697006, 519740967164688003], [-896540313126, 469854104209178643] [-896540313126, -469853207668865517], [-289481697006, -519740677682990997] Independent points of infinite order: P1 = [3250496816394, 5555659957899356403] P2 = [186533412086244, 2547582657528201264003] P3 = [525289619690230026/182329, 355310265239928169781449449/77854483]
Dujella (2001)
y2 + xy = x3 - 184412619490429624603376436635x
+ 30449869006658311731557296945588399421430225
Torsion points:
O, [241399646091870, -120699823045935],
[261551664901870, 330152418666287954065],
[261551664901870, -330152680217952855935],
[470634689151970, 6921204132746982815065],
[470634689151970, -6921204603381671967035],
[199559393560870, 1263266348110425395065],
[-234545329000640, 7797454476683252627575],
[-234545329000640, -7797454242137923626935],
[199559393560870, -1263266547669818955935]
Independent points of infinite order:
P1 = [-1116794535560755430/22201, -20816234916764614772949826615/3307949]
P2 = [125853840882825662670/1042441,
3356524891621704135156972742965/1064332261]
P3 = [981601603524680197854529/834516544,
915120379740248722266702111911541259/24107513923072]
Dujella (2001)
y2 + xy = x3 - 1720200171313840213498718405x - 3751937785045595550204425248421402406975 Torsion points: O, [48890378542210, -170317335580283576105], [-40338426667790, 20169213333895], [-4908547052750, -67627506573466181945], [-24420189561290, -153924652688932355105], [158261820685810, -1920405983267376707705], [158261820685810, 1920405825005556021895], [48890378542210, 170317286689905033895], [-24420189561290, 153924677109121916395], [-4908547052750, 67627511482013234695] Independent points of infinite order: P1 = [8732856352345330, -816074068024243690346105] P2 = [435045913630802142/10201, 21929693359406092588790967/1030301] P3 = [-1178704981454444510/80089, 3072547107159783254014685365/22665187]
Rathbun (2003)
y2 + xy = x3 - 10596063090767790103x
+ 20246425576229652155786091497
Torsion points:
O, [10660983062, 1057809698659349],
[3063510998, 128593280399765], [1234385882, 95118461651849],
[-1465751194, 180634502985845], [-3962951978, 1981475989],
[-1465751194, -180633037234651], [1234385882, -95119696037731],
[3063510998, -128596343910763], [10660983062, -1057820359642411]
Independent points of infinite order:
P1 = [76999022, 139395067572389]
P2 = [-1803119302, -183001883318563]
P3 = [-9954485811022618/2588881, -268032218567773557918019/4165509529]
Rathbun (2003)
y2 + xy = x3 - 15875150677713173875x
+ 24822054816914290733556790625
Torsion points:
O, [6482435150, 440810876209625],
[2656504910, 37370358331865], [1980656990, 33895148327225],
[-292649650, 171589331512025], [-4610716594, 2305358297],
[-292649650, -171589038862375], [1980656990, -33897128984215],
[2656504910, -37373014836775], [6482435150, -440817358644775]
Independent points of infinite order:
P1 = [642290510, 122026581035225]
P2 = [172849001273/64, 20776308116988049/512]
P3 = [5193847730, 287188032457025]
Rathbun (2003)
y2 + xy = x3 - 92677956255664016180x
+ 299418090541143369157794628752
Torsion points:
O, [1190849074, -436740106860842],
[7866118444, -239011952852072], [-8179534256, 714308411013028],
[22077982264, 3002472582804988], [3843260968, -1921630484],
[22077982264, -3002494660787252], [-8179534256, -714300231478772],
[7866118444, 239004086733628], [1190849074, 436738916011768]
Independent points of infinite order:
P1 = [1384052854, 416890415479138]
P2 = [16854993713896/1849, 36614073002814544516/79507]
P3 = [-31232439846128/5329, -311521602654411394748/389017]
Rathbun (2003)
y2 + xy = x3 - 255845251297258429380x
+ 1656026164827548903395128129552
Torsion points:
O, [30856178784, 4810379926953468],
[11347840344, 462634572184428], [7465457694, 402609054032778],
[-2811437556, 1533982175210028], [-18574240056, 9287120028],
[-2811437556, -1533979363772472], [7465457694, -402616519490472],
[11347840344, -462645920024772], [30856178784, -4810410783132252]
Independent points of infinite order:
P1 = [-63488808, -1293162455707332]
P2 = [-18555573606, -120509508651522]
P3 = [94325517211656/169, 915729403935302259276/2197]
Rathbun (2003)
y2 + xy = x3 - 66668901366044310944470x
+ 6625719732081856769026747158085412
Torsion points:
O, [148993766924, -53522427505702],
[149076537164, -1969149062182], [89869949864, 36878583765742718],
[151332026204, 1513981122546458], [149073495628, -74536747814],
[151332026204, -1514132454572662], [89869949864, -36878673635692582],
[149076537164, 1820072525018], [148993766924, 53373433738778]
Independent points of infinite order:
P1 = [1848170969068/9, 1078216082430740030/27]
P2 = [2743563893303564/1681, 142006313746134666811018/68921]
P3 = [1017670335636899916836459780176268/6778938733428979045681,
391836738288044475865952612598693870267434913046/
558139248511289461872926040243671]
Rathbun (2003)
y2 + xy = x3 - 333848836163677156595x
+ 23118493712440422090809079478881
Torsion points:
O, [148277045254, 56865096858614161],
[36395104798, 7692648382380793], [8491176460, 4571203342778761],
[-16817037614, 4896616359342253], [-32372614898, 16186307449],
[-16817037614, -4896599542304639], [8491176460, -4571211833955221],
[36395104798, -7692684777485591], [148277045254, -56865245135659415]
Independent points of infinite order:
P1 = [29709174118, 6278717358451369]
P2 = [-3028247394408758/106929, -109791324853798192416781/34965783]
P3 = [-20222528897455117220/1730310409,
-362916327837846171969380434387/71975722083173]
Rathbun (2003)
y2 + xy = x3 - 1139407008286275015150x
+ 4292069755092734127597502522500
Torsion points:
O, [-6104308140, -3319620265808310],
[36165309900, -3222865110114750], [-30055759950, 3374475194761350],
[114272212800, 36963058325032350], [3815690300, -1907845150],
[114272212800, -36963172597245150], [-30055759950, -3374445139001400],
[36165309900, 3222828944804850], [-6104308140, 3319626370116450]
Independent points of infinite order:
P1 = [-32516929000, -2638219862445850]
P2 = [74384137104564450/1369, 20287119188878733936485800/50653]
P3 = [86742979800, 23624955623054850]
Rathbun (2003)
y2 + xy = x3 - 2706794767207398160775x
+ 104036717500887330936430796523657
Torsion points:
O, [199799974054, 86828697615339973],
[54738736054, 10949194874871973], [19080776374, 7702965541524133],
[-27178198346, 12550998610129573], [-65531503946, 32765751973],
[-27178198346, -12550971431931227], [19080776374, -7702984622300507],
[54738736054, -10949249613608027], [199799974054, -86828897415314027]
Independent points of infinite order:
P1 = [12082890934, 8549547651801253]
P2 = [38947494828286/49, 242567093115030121579/343]
P3 = [1519521249241436901034/316448521,
59229051536758204828502259789437/5629302740069]
Rathbun (2003)
y2 + xy = x3 - 85367971368866370224970x
+ 9600329958761086926144205117637412
Torsion points:
O, [631745385924, 455851087460469798],
[224002906164, 41442833641353318], [177215981364, 6108786589295718],
[170086545204, 945392262521958], [169127032628, -84563516314],
[170086545204, -945562349067162], [177215981364, -6108963805277082],
[224002906164, -41443057644259482], [631745385924, -455851719205855722]
Independent points of infinite order:
P1 = [146601221364, 15362951610935718]
P2 = [56905918813679219488776489/151913118692416,
325306579707736365878791552403549806887/1872375369472109694464]
P3 = [96508987742246211949072385592/416995227452521,
29981356635497501660225358545379694291287690/8515234779380334432181]
Rathbun (2003)
y2 + xy = x3 - 2868129375368734318380x
+ 56353767705358492933999767345552
Torsion points:
O, [-9326148216, -9071445418980252],
[39302992344, 2083252730094228], [22639945944, 1738944202331028],
[101054281944, -28257440648100972], [-61515958056, 30757979028],
[101054281944, 28257339593819028], [22639945944, -1738966842276972],
[39302992344, -2083292033086572], [-9326148216, 9071454745128468]
Independent points of infinite order:
P1 = [10720966872, 5180429592265620]
P2 = [1882741944, 7138660979279028]
P3 = [2343190105641/64, 332731274056480761/512]
Rathbun (2003)
y2 + xy = x3 - 26807678961979361599180x
+ 1671973481886398199216900733380752
Torsion points:
O, [888030698144, 823507677766192628],
[240726282344, 95752385344073828], [135263153594, 22818198562595078],
[108081934844, 6093295672313828], [102267872344, -51133936172],
[108081934844, -6093403754248672], [135263153594, -22818333825748672],
[240726282344, -95752626070356172], [888030698144, -823508565796890772]
Independent points of infinite order:
P1 = [25884341468374/121, 100722806369203064318/1331]
P2 = [1361808057962889832/4870849, 1361095593766655035862613788/10749963743]
P3 = [51016257797402488328/1153349521,
937381582801799984507863640996/39168903082681]
Rathbun (2003)
y2 + xy = x3 + 18102609072937378371095x
+ 2391315383141885864187311821586777
Torsion points:
O, [949839828644, 936229893979266803],
[217748396894, 129063950086167803], [48024969314, 58064227520336723],
[-49624126006, 37024167548117603], [-90776305606, 45388152803],
[-49624126006, -37024117923991597], [48024969314, -58064275545306037],
[217748396894, -129064167834564697], [949839828644, -936230843819095447]
Independent points of infinite order:
P1 = [-87018262856, -12535506208626947]
P2 = [513146707222814/1681, 13142663455928799782563/68921]
P3 = [-45811830943919866/516961, -3549341061576412485995423/371694959]
Rathbun (2003)
y2 + xy = x3 - 1072509749585005340703485x
+ 427513459352382138507725842537962225
Torsion points:
O, [1685047150810, 1845203675439914215],
[700476245170, 141231423321407215], [609714290320, 15847413174326215],
[599321700070, 1831862037273715], [598242577570, -299121288785],
[599321700070, -1832461358973785], [609714290320, -15848022888616535],
[700476245170, -141232123797652385], [1685047150810, -1845205360487065025]
Independent points of infinite order:
P1 = [43806710477602314328/18003049, 267082543841383277041350540349/76386936907]
P2 = [-992152721110320832310/3029071369,
-143765053846529113732474509645925/166711000935653]
P3 = [532198552387045624317507142839104944471445739430/888781210181180408156315747995117969,
917092949578682197451636864032880764153538672188479485117341955228305/
837900205329316833742346751713820715453665076473023047]
Rathbun (2003)
y2 + xy = x3 - 883386649322495701946465x
+ 319496253706806704712837565584338121
Torsion points:
O, [472836276850, -86677601425546061],
[559261410106, -19345595033594837], [-425132819636, 786266892279582091],
[897336196078, 499346659568304079], [535622962602, -267811481301],
[897336196078, -499347556904500157], [-425132819636, -786266467146762455],
[559261410106, 19345035772184731], [472836276850, 86677128589269211]
Independent points of infinite order:
P1 = [923422235134, 539598911257448035]
P2 = [1265858243273134/2209, 3957357675610324296353/103823]
P3 = [5623099856733941638/11992369, 3800403463396504157613701953/41529573847]
Rathbun (2003)
y2 + xy = x3 - 578032640617033128241903x
+ 168987816077776276363859737591053497
Torsion points:
O, [354870041822, -92472377442045931],
[462441823958, -23993149080307555], [-412063127908, 580695542956764269],
[827619715946, 507422848787929745], [427743075782, -213871537891],
[827619715946, -507423676407645691], [-412063127908, -580695130893636361],
[462441823958, 23992686638483597], [354870041822, 92472022572004109]
Independent points of infinite order:
P1 = [414918855542, 24137568977415389]
P2 = [42468784175672, 276716836050073032869]
P3 = [730611006350059703475636166/1420365067928361,
4714938399116980835597864208519845010095/53530336601880796638891]
Rathbun (2003)
y2 + xy = x3 - 494272503533200381660985x
+ 132893239202578155784198210732683897
Torsion points:
O, [271190070034, -137098135330462517],
[453570966634, -44913528763095917], [-469279817816, 511369849893950683],
[965030437534, 744729259818884983], [379061621338, -189530810669],
[965030437534, -744730224849322517], [-469279817816, -511369380614132867],
[453570966634, 44913075192129283], [271190070034, 137097864140392483]
Independent points of infinite order:
P1 = [13333866418350886/16129, 1101706034236993487249989/2048383]
P2 = [54370606829471706/124609, 758670409981598324883891/43986977]
P3 = [4694892336701935390378/30238079881,
1286827926598908104084852021554241/5258129948586971]
Rathbun (2003)
y2 + xy = x3 - 15325167875235731315350450x
+ 23091703604460609373920789898685034116
Torsion points:
O, [3487446996740, 3472939753539243134],
[2307197462276, 122867543937109118], [2262122720564, 5072324104146446],
[2260255719428, 209333176199294], [2260181346052, -1130090673026],
[2260255719428, -211593431918722], [2262122720564, -5074586226867010],
[2307197462276, -122869851134571394], [3487446996740, -3472943240986239874]
Independent points of infinite order:
P1 = [77879905120064521796/40056241, 203629328363079386881286653102/253515949289]
P2 = [73196114392468886856548/1688634649,
19724938692728179133509815910076038/69391063631357]
P3 = [428085016334277869001881769701089410876884/9065900384331594613571986225,
279154917788487378073866612864510646089872490498549588731628782/
863209903109579807119314925210780149411625]
Rathbun (2003)
y2 + xy = x3 + 192796122563125780368450x
+ 155909350241595531287647769098776132
Torsion points:
O, [3507818764164, 6632884885021574058],
[808754647404, 916966143330134898], [168255649254, 439444677255394998],
[-236657510496, 311493738427033998], [-421170712996, 210585356498],
[-236657510496, -311493501769523502], [168255649254, -439444845511044252],
[808754647404, -916966952084782302], [3507818764164, -6632888392840338222]
Independent points of infinite order:
P1 = [-2235437621475684/5329, -13577640508208784297534/389017]
P2 = [-6563367046446208196895114/17768863687969,
-13871657044343452221125672285189397354/74901322099123669297]
P3 = [33261764081430725032478384312429530656/254365028362998992122425625,
1737135501914033296063645895307920908229269565852060488746/
4056823399097871207147470251834702671875]
Rathbun (2003)
y2 + xy = x3 - 7649243335383073965811655x
+ 8142795550383366515479921899421152777
Torsion points:
O, [5607542507644, 11898564071547668053],
[2053730226394, 1046685535270043053], [1663129993294, 146044986191326453],
[1606965253894, 21298269816338053], [1599791163894, -799895581947],
[1606965253894, -21299876781591947], [1663129993294, -146046649321319747],
[2053730226394, -1046687589000269447], [5607542507644, -11898569679090175697]
Independent points of infinite order:
P1 = [1600431707644, 4514321257268053]
P2 = [1602500041714, 10635144525625873]
P3 = [78837975718070756866/6932689,
680985123836895324840312597461/18253770137]
Dujella (2005)
y2 + xy = x3 - 40831178941372542828065222070x
+ 3175629333206587210466338025198789238575556
Torsion points:
O, [465215339181983/4, -465215339181983/8],
[157781537176938, -813140072400800683992], [157781537176938, 813139914619263507054],
[117773943758376, -19688075661400169322], [117773943758376, 19687957887456410946],
[110241951843390, -118838833098688209036], [-54726329163216, 2290472925613647419346],
[-54726329163216, -2290472870887318256130], [110241951843390, 118838722856736365646]
Independent points of infinite order:
P1 = [112662024425394, 74127591495502625166]
P2 = [20231332765150776/169, 124969135011225177512670/2197]
P3 = [248886292340818383/2116, 1618592576503357055893119/97336]
Dujella (2005)
y2 + xy = x3 - 3167417955766446777616642470003x
+ 2169731181079804686115895249944813736109996897
Torsion points:
O, [1028154118808462, -514077059404231],
[1030174366001778, 142986412430918688705], [1212296521936926, 10561655507654855860329],
[1212296521936926, -10561656719951377797255], [1030174366001778, -142987442605284690483],
[1049250402097752, 1209996117079378246119], [2951047671053622, 136096532596926808677129],
[2951047671053622, -136096535547974479730751], [1049250402097752, -1209997166329780343871]
Independent points of infinite order:
P1 = [9266412390358954/9, 2968242966904450017323/27]
P2 = [403778104293132324267731/388641796, 4860545641493396128491075164585555/7661684366344]
P3 = [6520074015413231830275412733639212/5909509097602379721,
61190425985854807375390278556652060333546915014231/14365710438695529224855275269]
Dujella (2005)
y2 + xy = x3 - 14160511348505020530242089048319085x
+ 648583081924884489422144357690310684311298281049297
Torsion points:
O, [69003372881528514, 131203519896793021308063],
[84881244665194434, 7627307885852590927732383], [84881244665194434, -7627307970733835592926817],
[-18876236921122446, -30152187527912573732838657], [66573602916759234, -961249207578287083570017],
[-18876236921122446, 30152187546788810653961103], [66573602916759234, 961249141004684166810783],
[68622632259372738, -34311316129686369], [69003372881528514, -131203588900165902836577]
Independent points of infinite order:
P1 = [91320903775662677556242/1555009, 8567258309690234922128237970906673/1939096223]
P2 = [18942233649606180601773779132631/237733164285604,
18743277203672268287493979635186078073425137871/3665512091387685263192]
P3 = [3034801337589873317300864753365734216499168283442/42307481769541122508826763202609,
380997704306416185608090500601993179461021753393520834679570511112324887/275185637834082845614665336359288299276879287977]
Dujella (2006)
y2 + xy = x3 - 17872399539372964708236646896139510x
+ 919649651172241073723029335429666977203870924072100
Torsion points:
O, [308738504436059039/4, -308738504436059039/8],
[77184628635132620, -1236780537791346310], [77232656061117620, -23114453065829525871310],
[77184280329867620, 166367622420839753690], [70610207655852620, 3118378125398762298293690],
[70610207655852620, -3118378196008969954146310], [77184280329867620, -166444806701169621310],
[77184628635132620, 1159595909156213690], [77232656061117620, 23114375833173464753690]
Independent points of infinite order:
P1 = [113263590664242620, 18664818323928735933503690]
P2 = [73099539110282253312295897880/947073473329, 12673737245861541299429202929474997770/921670121553896233]
P3 = [3298757670805004277852010/41254929, 356041144555318865565047209218847090/264980408967]
Dujella (2006)
y2 + xy = x3 - 241674368637382436130973196439385370x
+ 45729241997248669057664305104858534991896264733452900
Torsion points:
O, [283827619337213140, -141913809668606570],
[284804581878173140, 902008425100717608033430], [283827908802733540, -258354253302585094970],
[283827908802733540, 258070425393782361430], [284804581878173140, -902008709905299486206570],
[283811097217008760, -15254661247734420494990], [228064527019301140, 49742430337787415444345430],
[283811097217008760, 15254377436637203486230], [228064527019301140, -49742430565851942463646570]
Independent points of infinite order:
P1 = [281388466189995640, 2247531347057661990993430]
P2 = [3792810840651454000753017700/14964384241, 50380138896345475438585006249200030158470/1830578159817289]
P3 = [973668208940655607987704058900/3430492961281, 807178624692949282133240627874963320170/6353818412673255679]
Dujella (2006)
y2 + xy = x3 - 11021417385938715332603261187894955x
+ 445352851144395353746731567265819211866421289871025
Torsion points:
O, [-1023883331071690, 21369052934972669064848345],
[60695061667093310, -34712740020738770826655], [59816038578440510, 338563914411535305730145],
[60594965644053310, -30297482822026655], [68513295869053310, -3441735765048914797026655],
[68513295869053310, 3441735696535618927973345], [60695061667093310, 34712679325677103733345],
[59816038578440510, -338563974227573884170655], [-1023883331071690, -21369052933948785733776655]
Independent points of infinite order:
P1 = [12465074529838037440/121, 26727283965781025762863517915/1331]
P2 = [197362312008760012965600686750/2792805409, 87679054346047469560500152338568126681996335/147591387449423]
P3 = [7279860000102634788037293654382091349288590/119648721640899198102598489,
129033596312999870021054550871158305470046193004499101202552765/1308766271828219336158964843799348502237]
Dujella (2006)
y2 + xy = x3 - 38875889469082213659860930876707285x
+ 2950316463860325033045384057841591682836609405168097
Torsion points:
O, [113940507718716434, -60040997449360005918217],
[7188152804511434, 51684059806945676446496783], [112727434442902034, 646666984605054519867383],
[125942934649610834, -7199456935245733986467017], [125942934649610834, 7199456809302799336856183],
[113940507718716434, 60040883508852287201783], [112727434442902034, -646667097332488962769417],
[7188152804511434, -51684059814133829251008217], [113816638297963538, -56908319148981769]
Independent points of infinite order:
P1 = [84950117860335938, 16150836175292900655793751]
P2 = [-34119999775758233133653374/190633249, -170064689234686698704283970923093661111/2632073268943]
P3 = [121570467310812872851585737298651724/860011038331575601,
13334803949103178814177187581412024104613227441787503/797546545453279973964623401]
Dujella (2006)
y2 + xy = x3 - 71257460691961675173754316523320370x
+ 7321390120337424024246609088090663066342591280763012
Torsion points:
O, [-8015742362007036, 88837247474479955213419518],
[151823965812582924, 1555855907262811837739478], [151823965812582924, -1555856059086777650322402],
[-8015742362007036, -88837247466464212851412482], [154065224310056964, -77032612155028482],
[154368657019319364, 166312644394631247945918], [176008550745896964, 15232805839753172605291518],
[176008550745896964, -15232806015761723351188482], [154368657019319364, -166312798763288267265282]
Independent points of infinite order:
P1 = [565897425112079083044/3721, 313487097535584725080273087158/226981]
P2 = [381662697015232613357860899/2406294916, 362234760560965741181926595054602905477/118038390809464]
P3 = [1022273400893140482593904664548/1241270059129, 984929546973308861615650762035046601912881050/1382927522086978867]
Dujella (2006)
y2 + xy = x3 - 4238819163950333612296472587853300x
+ 106220970522341035586146111878778198927882318975632
Torsion points:
O, [50349955394968504, -4521027931276388488109252],
[35626477581489454, 652330711897084269230698], [-16935180628906496, -13158614018286746783234252],
[50349955394968504, 4521027880926433093140748], [37921994976441004, -106145718898450014629252],
[37921994976441004, 106145680976455038188248], [37483023338718504, -18741511669359252],
[35626477581489454, -652330747523561850720152], [-16935180628906496, 13158614035221927412140748]
Independent points of infinite order:
P1 = [52598459480241004, 5365109675503022071770748]
P2 = [11386837739738465147336974/327284281, 5488187059489077001036733642975022958/5920899927571]
P3 = [495853421966934580421465164/3977951041, 9764349642399898070864959668938141641928/250893350106911]
Dujella (2006)
y2 + xy = x3 - 220359657496467741418150313873591015x
+ 39814921951574944336532299033911263640999340112193225
Torsion points:
O, [270816100429600630, -135408050214800315],
[324318677092538230, -49606979822935602075536315], [324318677092538230, 49606979498616924982998085],
[271855156972960630, -727728837240255818000315], [271855156972960630, 727728565385098845039685],
[-52146824856430730, -226194995513372069242932155], [264543940064404630, 5815475515295121402759685],
[264543940064404630, -5815475779839061467164315], [-52146824856430730, 226194995565518894099362885]
Independent points of infinite order:
P1 = [45626454289284532720/169, 2025062418036112881114791695/2197]
P2 = [47813516951160931710665830/139736041, 110509836262490288318628102954671531785/1651819740661]
P3 = [-26386122583162159892375556671690/51589986968689,
-50709454036154035911544421438941429495752276595/370551117431084079113]
Dujella (2006)
y2 + xy = x3 - 1829791340653224667774114991260030x
+ 30126481652601492426131833796965804347432944395076
Torsion points:
O, [98611768400657183/4, -98611768400657183/8],
[31597344905782268, -1963791351963980011997902], [31597344905782268, 1963791320366635106215634],
[24847002476702876, -39158154824457032356942], [24847002476702876, 39158129977454555654066],
[-8783446032243556, 6746904608084263758516146], [23718566855425340, -264229789668437098231246],
[23718566855425340, 264229765949870242805906], [-8783446032243556, -6746904599300817726272590]
Independent points of infinite order:
P1 = [-26185984518095269783/1024, -254233324676475203287785567941/32768]
P2 = [66341418779904786303192614876/2694243202225, 70792055663019156398833666405919002118654/4422371205780148375]
P3 = [3538295972881588182892789262554811/15495486995956900,
207015376560826646116842621903629502005116893781349/1928891702330401394503000]
Dujella (2008)
y2 + xy = x3 - 78495183659714260569230485446839778x
+ 5272104352807515304061804334811509687856386729800772
Torsion points:
O, [-249582843133818348, 96520681499430631158452814],
[-12933452548430568, 79278967287136183705915854], [-249582843133818348, -96520681249847788024634466],
[-12933452548430568, -79278967274202731157485286], [287599720998302943/4, -287599720998302943/8],
[267824530150038708, -58823605770453272381840130], [814371604401805296, -693858781237529230113433566],
[814371604401805296, 693858780423157625711628270], [267824530150038708, 58823605502628742231801422]
Independent points of infinite order:
P1 = [26905083000245500697198910102804600156/38109524548662000625,
129231298831152382588579508838210724768673275439902465254/235261193485177213949257015625]
P2 = [61089994062969540332174951906751450791115336/156777029010923424547615081,
361164280318356859510509894669634451734406422359914688472536013554/1963015122063684646944903524705914228021]
P3 = [251987439926933604515814172885394133558380170782/1013663390482789098698972779489,
34172780721022020782576171613275674988774580421758766731741921047779680/1020564935200664946695843626286255613092313263]
Dujella (2008)
y2 + xy = x3 - 2707084078782823399463620124873144405x
+ 1702941498964699709396875520306791902694958494215053025
Torsion points:
O, [838252747503423310, -150777770893893676923719105],
[-1898447295304972014, 949223647652486007], [45873975438784210, -1256524304845457629141412105],
[838252747503423310, 150777770055640929420295795], [45873975438784210, 1256524304799583653702627895],
[1063229977901742610, -163172832458654714397562505], [1063229977901742610, 163172831395424736495819895],
[2270216825346754210, 2694013516618984399895517895], [2270216825346754210, -2694013518889201225242272105]
Independent points of infinite order:
P1 = [-9222522812219858510/9, -49792379587455274006495781635/27]
P2 = [-634376402773896638959710/413449, -398269099977964027763935852971893235/265847707]
P3 = [730817967871035095096236969096489751544550/54640731806117262803761,
620239691235355355514699216073263334217062911426845560825980995/12772466164302796378973199146131241]
Dujella (2008)
y2 + xy = x3 - 5207948535449509181956620222384153276635x
+ 141731197956455666679691319855852979111513623376407070170961
Torsion points:
O, [49593773618723283358, -73670654680072313752108553807],
[146904257962504960783/4, -146904257962504960783/8], [22408636891743128974, 190474670820835661791531209505],
[-53541525876671066210, 516803139599795962381500035761], [49593773618723283358, 73670654630478540133385270449],
[117853563723184375726, 1079295397457421748303848017473], [117853563723184375726, -1079295397575275312027032393199],
[-53541525876671066210, -516803139546254436504828969551], [22408636891743128974, -190474670843244298683274338479]
Independent points of infinite order:
P1 = [-39865331034157693964, -534782224368394300690522260527]
P2 = [33345598889978869465534100386/945870025, 1283133825472785724024352659311193345627619/29090232618875]
P3 = [643268314919899950976556302319854/702637915225,
16265788218548020443810910513269212047485993312947/588975692868627875]
Halbeisen - Hungerbühler (2020)
y2 + xy = x3 + 5293547134850809824017490x
+ 6826227600095067112732673622930895236
Torsion points:
O, [3486608746236, -8226027957794040702],
[3486608746236, 8226024471185294466], [-529440859332, 1968553323956104578],
[-529440859332, -1968552794515245246], [15216023467260, -60085770169861013886],
[845619603444, 3450685619787083370], [845619603444, -3450686465406686814],
[15216023467260, 60085754953837546626], [-1062773106948, 531386553474]
Independent points of infinite order:
P1 = [1010512893852, 3634183948006442754]
P2 = [3014456060, 2615757019457603714]
P3 = [601175152269044879988/1104601, 14740269151253192813607013008798/1160935651]
Halbeisen - Hungerbühler (2020)
y2 + xy = x3 - 39701107025795917660524150x
+ 96283534037205796520906829841806833316
Torsion points:
O, [4013807675748, -1263324931834676646],
[3603850560180, 112012523079105714], [14548958049183/4, -14548958049183/8],
[4013807675748, 1263320918027000898], [3640972661196, -10257766066627014],
[3640972661196, 10254125093965818], [3603850560180, -112016126929665894],
[269247312204, 9252763588969205370], [269247312204, -9252763858216517574]
Independent points of infinite order:
P1 = [993189587964, 7604768763658330890]
P2 = [3636910638924, 2303641762361466]
P3 = [2154043266252, 4556333227109597754]
Halbeisen - Hungerbühler (2020)
y2 + xy = x3 - 2480326241012580304944925x
- 1402906396176513515346594129482119375
Torsion points:
O, [-1095106045150, 547553022575],
[2089833884450, 1593980173879652975], [2089833884450, -1593982263713537425],
[6921719914850, 17693215609532622575], [-955718522590, -307629247999645585],
[-744253114150, -175592573089202425], [6921719914850, -17693222531252537425],
[-744253114150, 175593317342316575], [-955718522590, 307630203718168175]
Independent points of infinite order:
P1 = [-1045949795150, -217047336714477425]
P2 = [50524789064232275/3844, 11271464502756421040770225/238328]
P3 = [37844049171441170/19321, 3006745824542929149242525/2685619]
Halbeisen - Hungerbühler (2020)
y2 + xy = x3 - 3793122382984646673201565x
+ 1974201166254477402446876557520899121
Torsion points:
O, [431401291490, -646630019888048209],
[-804455252146, 2122498123892673371], [-804455252146, -2122497319437421225],
[431401291490, 646629588486756719], [-2168737451998, 1084368725999],
[5393586549026, -11765175228112374289], [5393586549026, 11765169834525825263],
[1799183125298, -986785051919593537], [1799183125298, 986783252736468239]
Independent points of infinite order:
P1 = [11104707804710, 36458526637479146759]
P2 = [-2164085893294, -218745636390395569]
P3 = [-514051064939834213138088794/539247118673025, -27216246041119346695314820369163755669139/12522232119453791277375]
Halbeisen - Hungerbühler (2020)
y2 + xy = x3 + 1870492062399819849103795x
+ 2286281039061178286752017180059512977
Torsion points:
O, [-3480434574353/4, 3480434574353/8],
[2180874953554, -4091248054861348337], [-471394064306, 1140084703696697803],
[-471394064306, -1140084232302633497], [2180874953554, 4091245873986394783],
[487407411634, -1820374973114534177], [9517671067894, 29702812548176811703],
[9517671067894, -29702822065847879597], [487407411634, 1820374485707122543]
Independent points of infinite order:
P1 = [-657374515886, -878969851319063537]
P2 = [22706541531669534, 3421578325383599681908443]
P3 = [16272160305082, 65888670105326810863]
Halbeisen - Hungerbühler (2020)
y2 + xy = x3 - 2131550042943031725358974350x
+ 36418914581477208149806309881617631907332
Torsion points:
O, [33310985187004, 48759349874298996898],
[33310985187004, -48759383185284183902], [84122316521404, 672610510486469979298],
[84122316521404, -672610594608786500702], [-36100922796596, -257527357646502428702],
[11836007415484, -113348986629396199262], [11836007415484, 113348974793388783778],
[-36100922796596, 257527393747425225298], [22260945481404, -11130472740702]
Independent points of infinite order:
P1 = [-2652145990788, -205069356720783443742]
P2 = [22156390739644, 8255675452418246818]
P3 = [-2657883692196531982939580804/50166863282449, -8950273816851169177472986951491564811886/355324718768136876793]
Halbeisen - Hungerbühler (2020)
y2 + xy = x3 - 1435983599532108719724495745x
+ 20753472873396097403723003199124449840137
Torsion points:
O, [24856510238714, -20431110553512484357],
[80595535770287/4, -80595535770287/8], [-26169794181286, 201023076142439725643],
[13839174573014, 59423573981033691443], [54706898324414, -325460495198763104257],
[54706898324414, 325460440491864779843], [24856510238714, 20431085697002245643],
[13839174573014, -59423587820208264457], [-26169794181286, -201023049972645544357]
Independent points of infinite order:
P1 = [4485605013218753534/11881, 9454039574036064986644061147/1295029]
P2 = [81272816480585506/729, 21973771706243206324294169/19683]
P3 = [825402156330811480788908114/142044420861121, 190070176103262071508346029088936422178157/1692919356439425885919]
Halbeisen - Hungerbühler (2020)
y2 + xy = x3 - 2446800403624787148272921600x
+ 45778092039845990356291117513520578560000
Torsion points:
O, [33647611340800, 39289186953720140800],
[33647611340800, -39289220601331481600], [78771931163200, 584653774446957798400],
[78771931163200, -584653853218888961600], [15938444316160, 104061545605529443840],
[-36208306845800, 294791468932219023400], [-36208306845800, -294791432723912177600],
[15938444316160, -104061561543973760000], [25432279603200, -12716139801600]
Independent points of infinite order:
P1 = [-19736778881300, -293907759731588279600]
P2 = [48046641813702400/2209, 5541539003593223160704000/103823]
P3 = [103305450858418075/27556, 875806313110032765150829525/4574296]
Halbeisen - Hungerbühler (2020)
y2 + xy = x3 - 16279724833902226833099679153x
+ 793980497406106755832599857244880504971497
Torsion points:
O, [274437464029103/4, -274437464029103/8],
[82586596909658, -113044753932043959205], [-85783842290758, 1248697727527759355819],
[48691818467222, 341663833411989269159], [176955512429246, -1858560349739348749741],
[176955512429246, 1858560172783836320495], [82586596909658, 113044671345447049547],
[48691818467222, -341663882103807736381], [-85783842290758, -1248697641743917065061]
Independent points of infinite order:
P1 = [700486352692631729254/275625, 18516633669621202333646692136083/144703125]
P2 = [497924271318769834202/3972049, 6731694721714220853615087985955/7916293657]
P3 = [-80024734741207076852624230521066251262355230842693422/44531470332925430899276163250901300922449,
-8526310407020117951240879015417934759473619950572478744281022390264432267837727733/9397245055199527342921710035978373998664749887186917243096793]
Halbeisen - Hungerbühler (2020)
y2 + xy = x3 - 99044688529404975515677803x
+ 376740197039794337343808242206739093297
Torsion points:
O, [-6700572041958, 27194786387411734989],
[3789767197422, -7470864829635895791], [3789767197422, 7470861039868698369],
[-6700572041958, -27194779686839693031], [21394390297103/4, -21394390297103/8],
[13830726669966, -40651526676401192655], [13830726669966, 40651512845674522689],
[6445951243938, -2476712897744605623], [6445951243938, 2476706451793361685]
Independent points of infinite order:
P1 = [5095299173742, 2088635748332576769]
P2 = [4955192250968, 2761187268780530825]
P3 = [3330339793965149544/180625, 5328778864620308107286537847/76765625]
Halbeisen - Hungerbühler (2020)
y2 + xy = x3 - 33409871049595789493438014860x
+ 2265031895782925431611293693882473023856272
Torsion points:
O, [329651887641384, -5203344902499556643292],
[329651887641384, 5203344572847669001908], [131242147589784, 375272116712522445108],
[131242147589784, -375272247954670034892], [-142279851195636, 2034289439403622273488],
[47826641261784, -881219659050445298892], [47826641261784, 881219611223804037108],
[-142279851195636, -2034289297123771077852], [88643029349784, -44321514674892]
Independent points of infinite order:
P1 = [56967974611284, 739337671047549099108]
P2 = [202317691642374, 1946016951876727303728]
P3 = [4789220894052073321203037172496/90352987634781169, 21778808286320742180473053909285420809482336724/27159000084327854079924553]
Halbeisen - Hungerbühler (2020)
y2 + xy = x3 - 95417202260747608424522150x
+ 262438432730862964443787004759716822500
Torsion points:
O, [26268503917180, -126024375630603437750],
[26268503917180, 126024349362099520570], [8843001342700, 10496421309263101450],
[8843001342700, -10496430152264444150], [2367307818400, -7058562168535865750],
[-3861305952980, 23943740017130946250], [-3861305952980, -23943736155824993270],
[2367307818400, 7058559801228047350], [-10928467623444, 5464233811722]
Independent points of infinite order:
P1 = [-393327882500, -17317846908071636150]
P2 = [-3316272212300, -23289408173559344150]
P3 = [311304365960650860/29929, 102942949216641634481989650/5177717]
Halbeisen - Hungerbühler (2020)
y2 + xy = x3 - 130476053803276486484649645x
+ 572856611649641795861855406275159027025
Torsion points:
O, [6394017201026, -3197008600513],
[7002935231250, 1604028163584427455], [7002935231250, -1604035166519658705],
[12921827582790, 32318285165272280055], [5195194710090, 5935202716934277255],
[-6457771568220, 33854602887968597805], [12921827582790, -32318298087099862845],
[-6457771568220, -33854596430197029585], [5195194710090, -5935207912128987345]
Independent points of infinite order:
P1 = [-80640493886025990/37249, -208999888698745972684318665/7189057]
P2 = [14552613668941833/64, 1753369398797249787445167/512]
P3 = [347354158646757570/17161, 177364021384398339575200725/2248091]
Halbeisen - Hungerbühler (2020)
y2 + xy = x3 - 325430360660257035211580x
+ 5091489639774218456006931737233040400
Torsion points:
O, [-966986246840, -2121787404250200380],
[2275443844060, -4016520882448160780], [2275443844060, 4016518607004316720],
[-966986246840, 2121788371236447220], [487194521200, 2246904630337840780],
[9505186614310, 29339017998229602970], [9505186614310, -29339027503416217280],
[487194521200, -2246905117532361980], [-1783370778440, 891685389220]
Independent points of infinite order:
P1 = [227525471560, 2242593127500639220]
P2 = [652204859922310, 16656198017417231686720]
P3 = [142204278362789392/109561, 94953251108265735766954372/36264691]
Halbeisen - Hungerbühler (2020)
y2 + xy = x3 - 5326844044032061890662494615x
+ 181258498775060395380874546926076987997417
Torsion points:
O, [59699207036774, -275713337242424503387],
[-24733949795626, 545784719179919067413], [-24733949795626, -545784694445969271787],
[59699207036774, 275713277543217466613], [30067948223894, -219715976919032189227],
[189785175412274, 2450726993135333125613], [189785175412274, -2450727182920508537887],
[30067948223894, 219715946851083965333], [-86195786653226, 43097893326613]
Independent points of infinite order:
P1 = [76837652206774, 474981764080068186613]
P2 = [14474163995614918588814/516961, 1741360778476443241344846322528867/371694959]
P3 = [37610312830411385233649/375429376, 5878314467775783913886997287132863/7274319589376]
Halbeisen - Hungerbühler (2020)
y2 + xy = x3 + 10632839892159041612719430x
+ 22657953328196959760173568723050755812
Torsion points:
O, [21844232110064, -103336097649767602282],
[1178203061204, 6068041524340938038], [1178203061204, -6068042702543999242],
[21844232110064, 103336075805535492218], [-1682780691436, 841390345718],
[5003063798564, -14180434631498014282], [5003063798564, 14180429628434215718],
[-869753869036, 3571002454567120118], [-869753869036, -3571001584813251082]
Independent points of infinite order:
P1 = [2830128858895249/256, 158178831842337679643473/4096]
P2 = [15618628222466789/1936, 2144036330868515815133857/85184]
P3 = [14554302618987651510063476/6871912609, 55524877821189429433723901725091625014/569660939548273]
Halbeisen - Hungerbühler (2020)
y2 + xy = x3 - 1197832954117748094446427078x
+ 15852620368947956323573112891286419927172
Torsion points:
O, [-159739523406177/4, 159739523406177/8],
[47616294412218, -258412920874358367768], [47616294412218, 258412873258063955550],
[22344750401736, 15614239738397197170], [22344750401736, -15614262083147598906],
[1030316485422, -120911402227843695426], [17652986956752, 14437960687460091054],
[17652986956752, -14437978340447047806], [1030316485422, 120911401197527210004]
Independent points of infinite order:
P1 = [286677254447952770182902/10675229041, 60932326783743177021185331128721294/1102975339745161]
P2 = [3877096543200822576255838266/152860558415041, 79914493241365476717293694497312969333730/1889918876004315695839]
P3 = [108897209806429055664446197752941376/131221935689893779025,
35904851961740625218435871779827686425364480188851566/1503175400093538689013440113625]
Voznyy (2021)
y2 + xy = x3 - 226699248793198320090525x
+ 36451011398146777593145443493400625
Torsion points:
O, [1082169126150, -1028806423850520525],
[386947576050, 81653577585456975], [386947576050, -81653964533033025],
[1082169126150, 1028805341681394375], [-138850234950, -255443286013808025],
[162931743240, 61966170134782935], [162931743240, -61966333066526175],
[-138850234950, 255443424864042975], [-542155633950, 271077816975]
Independent points of infinite order:
P1 = [143060476050, 83349958698216975]
P2 = [440835562230, 148943182600505895]
P3 = [-4777520790, -193736836459279785]
Voznyy (2021)
y2 + xy = x3 - 2113588117957069801838332961615x
+ 1401523903710961189266988195794924314026431225
Torsion points:
O, [-469652058727670, 47860028699465752890085],
[-469652058727670, -47860028229813694162415], [1169368261281430, 22999588114290605309485],
[1169368261281430, -22999589283658866590915], [606663128375080, -18508493314598731589915],
[3665279906488270, -207111123290694494866715], [3665279906488270, 207111119625414588378445],
[606663128375080, 18508492707935603214835], [-1712330886450170, 856165443225085]
Independent points of infinite order:
P1 = [1009801147499830, 17231156402138284425085]
P2 = [-27072233302460961734/42025, -430390194466562532786128516279/8615125]
P3 = [162176823799497697220012079218360921729395094536827341413254235489241837230/13845914788886218500691255395138331170080256063904997277481,
2050237027829026321468983198851828873715314953279142410783216224478078751953801936738439196848903740849685412785/
1629230312795299081706030395134589959133367971764851045539409059847363719576240704545621]
Voznyy (2021)
y2 + xy = x3 - 147369010711322681744480185x
- 601670947958851357344090890325290503303
Torsion points:
O, [52903738184234, -373723495914326974717],
[52903738184234, 373723443010588790483], [15992408212634, 33640978139912133683],
[15992408212634, -33640994132320346317], [-8527260982786, 5910188546990735063],
[-6186073315366, -8557974306450410317], [-6186073315366, 8557980492523725683],
[-8527260982786, -5910180019729752277], [-4863254027366, 2431627013683]
Independent points of infinite order:
P1 = [134100289707706/9, 610042370963399381441/27]
P2 = [10194204654040442, 1029270941372095788600563]
P3 = [37425123989753393016460968619404471364855994952955128439878535733567013792024185840960470772229434/
195878994256441778859742559835575870433035337098275774351861175223399402228672253201,
228479719157379596377260926117240924278329555456736311297429175689901015002090539515641823664350743800760033430195379429875858823233688720259871333/
86692554109449870340744914610198974269472271775495910358930053998608105974116245448222664399583005357645353217319297882188551]
Li (2021)
y2 + xy = x3 - 1210379472580801037844903x
+ 512387361125615445963204443072148297
Torsion points:
O, [-1270326841098, 635163420549],
[1068700813446, -662903192410894491], [1068700813446, 662902123710081045],
[656261575158, 26458473883864197], [656261575158, -26459130145439355],
[614253874962, -25882196390947491], [281946972342, 439929004356637509],
[281946972342, -439929286303609851], [614253874962, 25881582137072529]
Independent points of infinite order:
P1 = [-215856637962, -873840931115788923]
P2 = [565761739578, 93239049378728505]
P3 = [3276367362093370398/5870929, 1472735125452823830385649043/14225260967]
Li (2021)
y2 + xy = x3 + 5272545770401481889345470x
+ 8832858910136387982635338300803944900
Torsion points:
O, [-1278708440540, 639354220270],
[-674357680540, 2229486249689060270], [3564107969060, -8538102617509011730],
[3564107969060, 8538099053401042670], [-674357680540, -2229485575331379730],
[822926380460, -3705276123635724730], [15562226115620, -62127217394393389330],
[822926380460, 3705275300709344270], [15562226115620, 62127201832167273710]
Independent points of infinite order:
P1 = [-81162534364, -2899032744033767698]
P2 = [2409461044460, 5960282742029120270]
P3 = [-22076837891260/169, -6268909651269708946810/2197]
Li (2021)
y2 + xy = x3 - 2259137098274533435928235x
+ 8523533695768703995463161323826782897
Torsion points:
O, [-2408055132162, 1204027566081],
[-1221859688286, 3075666018935656713], [-1221859688286, -3075664797075968427],
[2573929573134, 4445361390762018033], [2573929573134, -4445363964691591167],
[630302541684, -2711088888053133567], [10352954479254, -33087803680249586247],
[630302541684, 2711088257750591883], [10352954479254, 33087793327295106993]
Independent points of infinite order:
P1 = [1597179046014, 2998275457632049473]
P2 = [2122187892406087326/47089, 3089970228493069793592299529/10218313]
P3 = [-25067227506466176/11881, -2556804840163403411499213/1295029]
Li (2021)
y2 + xy = x3 - 3603011520783270803788210x
+ 2161759112390879192155440288494356100
Torsion points:
O, [-2147058117884, 1073529058942],
[4668967887620, -9333783146096052610], [4668967887620, 9333778477128164990],
[1619988110660, 759181434059988350], [1619988110660, -759183054048099010],
[567685355780, -547109322948867970], [-646687644580, 2054588894855403590],
[-646687644580, -2054588248167759010], [567685355780, 547108755263512190]
Independent points of infinite order:
P1 = [6226278345130/9, 438297355480128230/27]
P2 = [12153189878484680/529, 1335324823080358232687830/12167]
P3 = [1132392439730012401700/409293361, 30278907659257976604878152125010/8280413986391]
Li (2021)
y2 + xy = x3 + 5908460959676333713420270x
+ 12429464174119405709078869317910249476
Torsion points:
O, [-1515068775548, 757534387774],
[3857739981076, -9624671546392877234], [3857739981076, 9624667688652896158],
[-817920593432, 2655114009309547834], [-817920593432, -2655113191388954402],
[16837932023740, -69898063494582734594], [866322731794, 4265944536475596946],
[866322731794, -4265945402798328740], [16837932023740, 69898046656650710854]
Independent points of infinite order:
P1 = [443547948664, 3890682394666368286]
P2 = [-829254795080, -2638104269499896534]
P3 = [139488724848394445032/208889209, 12327549065309768285608213054406/3019075737677]
Li (2021)
y2 + xy = x3 - 10098363619404791332162325x
+ 14101889709200009208305551303184629857
Torsion points:
O, [-14904006513809/4, 14904006513809/8],
[2477273527954, -2070803364448923977], [2477273527954, 2070800887175396023],
[-926411754446, 4760467878404088823], [-926411754446, -4760466951992334377],
[7543827955954, -19163402314511715977], [1360166563474, 1697884330418306743],
[1360166563474, -1697885690584870217], [7543827955954, 19163394770683760023]
Independent points of infinite order:
P1 = [1676534590098, 1372582114866820791]
P2 = [2303081082441346/1849, 147806833491956729923861/79507]
P3 = [3813047871579914463148327670722/631895375536977841, 6604715492750184651701374716188027614241958353/502305305753825229328601111]
Li (2021)
y2 + xy = x3 - 12484218180691912023915860x
+ 23327036655267801149610539536041040272
Torsion points:
O, [-4240846557912, 2120423278956],
[3138503960104, -3880746661547709332], [3138503960104, 3880743523043749228],
[-1442038012616, 6191210118961471708], [-1442038012616, -6191208676923459092],
[10576215678184, -32776643447297849492], [1378905519364, 2955384779846109148],
[1378905519364, -2955386158751628512], [10576215678184, 32776632871082171308]
Independent points of infinite order:
P1 = [-1369222458536, -6152537912093452052]
P2 = [-204357700497284/49, -579260820438501946856/343]
P3 = [-221260210437513335327855571311/53261291581446400, -22985386077765212995389083334160771768307023/12291858177235852493312000]
Li (2021)
y2 + xy = x3 - 30215566721656927350766565x
+ 63845087369037367315870359690976692225
Torsion points:
O, [-6346317464270, 3173158732135],
[6180610171330, -10639241737032703865], [6180610171330, 10639235556422532535],
[3365631495730, 524147346580972135], [3365631495730, -524150712212467865],
[887033919730, 6143353603752388135], [2983598675470, -503532400903035665],
[2983598675470, 503529417304360195], [887033919730, -6143354490786307865]
Independent points of infinite order:
P1 = [784411283250, 6373876371416959335]
P2 = [3047865842650, 255343949233481335]
P3 = [41697628655410, 267026702135746021735]
Li (2021)
y2 + xy = x3 - 34603490370448632346424570x
+ 78347452820825831767531374479303971812
Torsion points:
O, [-6792489539436, 3396244769718],
[3420648100564, 74314185713409718], [3420648100564, -74317606361510282],
[4430546466964, 3464902525536648118], [2457258211564, -2855689726416962282],
[3371894386324, -73962825582985802], [4430546466964, -3464906956083115082],
[3371894386324, 73959453688599478], [2457258211564, 2855687269158750718]
Independent points of infinite order:
P1 = [3408520039564, 31278861744618718]
P2 = [3022829193364, 1169657671483886518]
P3 = [-63064327446641324/10609, -9399513729432980863565414/1092727]
Li (2021)
y2 + xy = x3 - 1691224513342223527148939835x
+ 26680615083036163890588874750442364962961
Torsion points:
O, [24855440223902, -12427720111951],
[51742340750466, -278748851273950792827], [51742340750466, 278748799531610042361],
[25867146282798, 15537368589205333233], [25867146282798, -15537394456351616031],
[185133429471720, -2461486061489956067841], [30886414774854, 62525862928343608065],
[30886414774854, -62525893814758382919], [185133429471720, 2461485876356526596121]
Independent points of infinite order:
P1 = [8529939403494, 113468977031455136961]
P2 = [-17935422933426, -226371336375618512079]
P3 = [-8742499258384918123655916719226/243406975764555625, -24342583503787471860492984426586499787192268707/120087977528605274475203125]
Li (2021)
y2 + xy = x3 - 2134425605477022095741422255x
+ 22950458237674939532853943319704480624025
Torsion points:
O, [45828511392719/4, -45828511392719/8],
[135772726093970, -1495332727697815984915], [135772726093970, 1495332591925089890945],
[44514516295760, 127062661718706059045], [-41197614453940, 202389053585464910045],
[-2544560551750, -168419587680042720595], [44514516295760, -127062706233222354805],
[-2544560551750, 168419590224603272345], [-41197614453940, -202389012387850456105]
Independent points of infinite order:
P1 = [59431874678960, 325606641362666118245]
P2 = [2555733097034852, 129182168352514712569967]
P3 = [115431118672409372010500/2766865201, 11747807583829925815211520738185845/145539876437801]
Li (2021)
y2 + xy = x3 - 5809553945548097180330936395x
+ 79917847507735185793053890322755946247025
Torsion points:
O, [-329365935809521/4, 329365935809521/8],
[77338270922090, 305275716699876762905], [77338270922090, -305275794038147684995],
[240297366632270, 3543916636889208573905], [240297366632270, -3543916877186575206175],
[-37304111774290, -494697683331635913295], [8658192270290, -173973185331597119095],
[8658192270290, 173973176673404848805], [-37304111774290, 494697720635747687585]
Independent points of infinite order:
P1 = [14044679211290, 33088983427617743405]
P2 = [2482137347716190/841, 6111728158405820510365045/24389]
P3 = [15216201720022201153790/86136961, 1708285480503875850075375824231905/799437135041]
Li (2021)
y2 + xy = x3 - 145895045176748655715397556450x
+ 21424713225425020220083793116567600010865732
Torsion points:
O, [214427274235748, -107213637117874],
[423000486815844, -5949644436860111400882], [423000486815844, 5949644013859624585038],
[233130165935604, 287620666938128790798], [-211061869151196, 6543347666807006521998],
[176273394023664, -1088356595047788019422], [233130165935604, -287620900068294726402],
[176273394023664, 1088356418774393995758], [-211061869151196, -6543347455745137370802]
Independent points of infinite order:
P1 = [-31853447008446, -5102906358662985706302]
P2 = [4615445389685634/25, 110563453374757181380092/125]
P3 = [1971371146755055534692/1168561, 85456360074588174134488532576958/1263214441]
Li (2021)
y2 + xy = x3 - 345742094100446485436908881610x
+ 78248087030579024156820464655302964840184100
Torsion points:
O, [338780521342516, -169390260671258],
[440516954599220, -3380448828001025168410], [440516954599220, 3380448387484070569190],
[341814151702340, 71113668686681287190], [341814151702340, -71114010500832989530],
[-131075396505100, 11014281441575683810790], [324770110995920, -465531247306703420410],
[-131075396505100, -11014281310500287305690], [324770110995920, 465530922536592424490]
Independent points of infinite order:
P1 = [245374019903300334350/734449, 107027834601181691439894768970/629422793]
P2 = [15051889979937727620020/43652449, 48771379395175271198939057878970/288411730543]
P3 = [831414423587749976158420/1282427721, 516714956494082956835153244348812290/45925019116731]
Li (2021)
y2 + xy = x3 - 1649319451127709410381250443395x
+ 815272754900199160875071385169431920901564737
Torsion points:
O, [740056468682414, -370028234341207],
[954746363972414, -10530009879341158621207], [954746363972414, 10530008924594794648793],
[746237907744914, 215219449043368783793], [-274063471394986, 35308722094480189740593],
[710857513588664, -1432137025156545372457], [746237907744914, -215220195281276528707],
[710857513588664, 1432136314299031783793], [-274063471394986, -35308721820416718345607]
Independent points of infinite order:
P1 = [155068565264703717854/1062961, 26342260612970608633378441571263/1095912791]
P2 = [205170444308503901879561/21977344, 92096913094058209396718831280296851/103029788672]
P3 = [6393842364674451518/1849, 15181856985446939938987723211/79507]
Li (2021)
y2 + xy = x3 - 1840125631182437596847003396105x
+ 960769760673675322147816906938110444677223577
Torsion points:
O, [783182606895418, -391591303447709],
[788414329887034, -253868719110040499357], [788414329887034, 253867930695710612323],
[783185651286394, 140377506800087203], [571661835169594, 9780474305874052904803],
[783059520881554, -5973116043023302637], [783185651286394, -141160692451373597],
[783059520881554, 5972332983502421083], [571661835169594, -9780474877535888074397]
Independent points of infinite order:
P1 = [593583940519748918120074/734464201, 24252094357633985981790621376965743/19904714311301]
P2 = [-459083085934525535933581766/299919427201, -2270088310444411740027351826253050105693/164250574387200449]
P3 = [293514431368235981444224793870743348876/254442274271002426660129,
2479172298718282094561569010108023968374380985703607339201/128346462511797246724070917584269617]
Li (2021)
y2 + xy = x3 + 6541033451929651740394059060x
+ 342634908698596598638012299260485871127696
Torsion points:
O, [-41475107868648, 20737553934324],
[-21397109069544, 439180303693505491956], [-21397109069544, -439180282296396422412],
[123984851170728, 1749156668523136530804], [29246456659800, -747631654965208057164],
[541331340481164, -12748138633789763958384], [123984851170728, -1749156792507987701532],
[541331340481164, 12748138092458423477220], [29246456659800, 747631625718751397364]
Independent points of infinite order:
P1 = [13881709848900504, 1635580185788458515904500]
P2 = [564052234144599679543896/6214011241, 635716801114937386035808842993004932/489844292116789]
P3 = [31573049959526852791514802972/21903925706569, 5619298518940686821917946524777717476237216/102513942646633090747]
Li (2021)
y2 + xy = x3 - 146855040649435110072971383895x
+ 21660801972374678995680425696340934734181737
Torsion points:
O, [221968285531414, -110984142765707],
[223447063133914, 53583840554503086793], [223447063133914, -53584064001566220707],
[300968740299814, 2173575425266220824693], [300968740299814, -2173575726234961124507],
[234053262746164, -332499611928146656457], [867581726130574, -23393998106353766312027],
[867581726130574, 23393997238772040181453], [234053262746164, 332499377874883910293]
Independent points of infinite order:
P1 = [1455869465165389358254/7123561, 8153275534395912636081099365537/19012784309]
P2 = [26409215157387682228966/110523169, 536350101225686760433438720859221/1161930075697]
P3 = [377380233209932851270754507823329/2029499178088206400, 2558185783288754664230995099135450646294405082827/2891234514240415031415488000]
Li (2021)
y2 + xy = x3 - 234641285178579425694262588160x
+ 43296533624151986620881498459788220914457600
Torsion points:
O, [-558692622582080, 279346311291040],
[712051633667920, -15402678143217376208960], [712051633667920, 15402677431165742541040],
[319739168140420, 980031490983775641040], [240198152792920, -891291001999336583960],
[-6440624626730, 6693840671791131132190], [319739168140420, -980031810722943781460],
[-6440624626730, -6693840665350506505460], [240198152792920, 891290761801183791040]
Independent points of infinite order:
P1 = [107858466358303339795480/347337769, 3976668977780888394133410093757120/6473334000853]
P2 = [265762609783212596362565635/786495827716, 1123004152835495987495837554781851739065/697500678826623736]
P3 = [-360872164669486349588505188/14917739797801, -403151952008688892460738578992205228280956/57617517390296894549]
Li (2021)
y2 + xy = x3 - 1243223868381590639185048699100x
+ 533432543666429173339376715654182488572810000
Torsion points:
O, [1050023013405700, -19639755858471195176600],
[-492723666315800, -32037112359298517305100], [564727185535660, 3383963521683616224340],
[2544218601242175/4, -2544218601242175/8], [662213297585800, 742437325628168923300],
[662213297585800, -742437987841466509100], [1050023013405700, 19639754808448181770900],
[-492723666315800, 32037112852022183620900], [564727185535660, -3383964086410801760000]
Independent points of infinite order:
P1 = [183169895771508901126/25921, 2449868698667692163469436727072/4173281]
P2 = [445320903679124564446/297025, 7310721555642318319965983220896/161878625]
P3 = [97045007034269777685951279303540934196446/145600001888943048152523841,
1666320474126227547508909711898062835538939857270447029372222/1756879886655075987923165334293552350111]
Li (2021)
y2 + xy = x3 - 1535533574731160493603735737760x
+ 305689878643681794013681184854590691457049600
Torsion points:
O, [-5315021544774145/4, 5315021544774145/8],
[1278849476514120, 20820076183022665660440], [1278849476514120, -20820077461872142174560],
[3995452146779520, 240733232326105653049440], [3995452146779520, -240733236321557799828960],
[-622314280922880, -31941626884607580742560], [113656042038840, -11516743707240902513880],
[113656042038840, 11516743593584860475040], [-622314280922880, 31941627506921861665440]
Independent points of infinite order:
P1 = [-975349583504380, -29589105789048111908560]
P2 = [-3956871784249935552241441906275459280/4035653389605291021481,
-7556135038474732609971894078307116091143344994229411760/256372116254186777038347114795371]
P3 = [-279169042145921029928989188804800280/408074065223354198761,
-265330754412484913761195359484790048999351278691739360/8243440197810143907988865498741]
Chen (2021)
y2 + xy = x3 + 6215637238957796354592397900x
+ 5410032000645730925330020513374060233330832
Torsion points:
O, [-655065477607233/4, 655065477607233/8],
[-91322499021596, 2020097371213468102048], [-91322499021596, -2020097279890969080452],
[242414464581304, 4600241532151903807948], [49621120180504, -2416741376823995708852],
[1032662093423404, -33362408202212090302952], [242414464581304, -4600241774566368389252],
[1032662093423404, 33362407169549996879548], [49621120180504, 2416741327202875528348]
Independent points of infinite order:
P1 = [20451502241790844, 2924766393510166700748988]
P2 = [19474144203518406544354/22801, 2717612766092643060458175969057898/3442951]
P3 = [100039765473468508270721424808/14675925060889, 31644027156451517307752984618965158540198844/56222250806485705213]
Chen (2021)
y2 + xy = x3 - 458778180951288801735133348085x
+ 76260643384786506397564064547784985879844225
Torsion points:
O, [-2995005453990545/4, 2995005453990545/8],
[1950603133475020, -81259608773034384315635], [1950603133475020, 81259606822431250840615],
[643199857546270, 6875336725965731650615], [129948704131270, -4340209001417325409385],
[-295640209168280, 13640162909278422393865], [643199857546270, -6875337369165589196885],
[-295640209168280, -13640162613638213225585], [129948704131270, 4340208871468621278115]
Independent points of infinite order:
P1 = [152162094080020, 3158330132006312890615]
P2 = [-527852637763700, -13090193648123060528435]
P3 = [-25782827454169371099485/35976004, -1311906222561608389566440024593295/215784071992]
Chen (2021)
y2 + xy = x3 - 264896980922319400237582843430x
+ 52168286784325563070348910812779741619323876
Torsion points:
O, [315552166345452, -157776083172726],
[697830211278076, -14392201631148741691334], [697830211278076, 14392200933318530413258],
[330777021170668, 859012947207095927434], [330777021170668, -859013277984117098102],
[2537085870403240, -125342843861569327897394], [404028417027244, 3330999381637373847946],
[404028417027244, -3330999785665790875190], [2537085870403240, 125342841324483457494154]
Independent points of infinite order:
P1 = [-100227950189204, -8815413388152603656054]
P2 = [493258235961630382053651348035511101560012/42532240150753509411193129,
346091307031282154109843424418461741409504686577986405902115886/277381432106387125208782771432704701867]
P3 = [2678401692674326337322785193080234295462956964304/355021090614450216894183934151689,
4373479416325812277877814747829648030766950790213745167519465753486566546/6689308582192525538925934701716677236788961585637]
Chen (2021)
y2 + xy = x3 + 600497577465576024013480406440x
- 66440136338551606968721873048473565043732928
Torsion points:
O, [108513934878384, -54256967439192],
[211195677118384, 8354785745037145200808], [211195677118384, -8354785956232822319192],
[1508804761489984, 65378704858762830922408], [562579181590384, -21200023540591545863192],
[6300689737347964, -503831567073341011177652], [1508804761489984, -65378706367567592412392],
[6300689737347964, 503831560772651273829688], [562579181590384, 21200022978012364272808]
Independent points of infinite order:
P1 = [1368634121995384, 57611553315180225576808]
P2 = [47239265668460824, 10268641555640923852824448]
P3 = [1589868596960784, 70049657212188322583208]
Chen (2021)
y2 + xy = x3 + 94706272151731301012396693050x
+ 59994546910041286570262731275290036142117732
Torsion points:
O, [-1248773928595809/4, 1248773928595809/8],
[582445275863704, -17684625219481506278102], [582445275863704, 17684624637036230414398],
[-175662027563396, 6159368720336856630298], [2523054880330204, -127907082323748312236102],
[120495778822144, 8553113944959456451018], [-175662027563396, -6159368544674829066902],
[120495778822144, -8553114065455235273162], [2523054880330204, 127907079800693431905898]
Independent points of infinite order:
P1 = [-57640651495274936/841, -177858508716190116784917178/24389]
P2 = [104339340153661333116/458329, 2997984718641382711283846895234/310288733]
P3 = [1857439050163153514551306094956/1599886642007889, 2665383070388684811551428402075607342061171526/63993198640943834821287]
Chen (2021)
y2 + xy = x3 - 91564544300291313593788076915x
- 846087973531608854732815719201615762479775
Torsion points:
O, [-1191463260897905/4, 1191463260897905/8],
[352814568466930, 3281204013484113422785], [352814568466930, -3281204366298681889715],
[1139261531814430, 37060823408108969447785], [-176368170845570, -3133196716757629452215],
[-29519647560470, -1353196718612155128815], [1139261531814430, -37060824547370501262215],
[-29519647560470, 1353196748131802689285], [-176368170845570, 3133196893125800297785]
Independent points of infinite order:
P1 = [-1554142272047186690/5329, -399174435955133426285812655/389017]
P2 = [2450357546042872030/7921, 463526523094184437584825665/704969]
P3 = [-569685783612572424818193150866/6381281387023929, -1311249009182798472582676855555550518963286261/509755409680965719464467]
Chen (2021)
y2 + xy = x3 - 73501536454742569210792610230x
+ 4214756116428460151027365021311414432056900
Torsion points:
O, [-1184778282969185/4, 1184778282969185/8],
[267148415105960, 1909151218489985734070], [267148415105960, -1909151485638400840030],
[821673727096610, 22328716817204245962320], [821673727096610, -22328717638877973058930],
[-126503619559930, -3389470120698613537780], [40531259741360, -1141153084548165424930],
[40531259741360, 1141153044016905683570], [-126503619559930, 3389470247202233097710]
Independent points of infinite order:
P1 = [243951320956640, 895572585202746196370]
P2 = [2563320805173972760/841, 4088011709416235207638918730/24389]
P3 = [76584772141565546840/1408969, 1031179448132153939448409238710/1672446203]
Chen (2021)
y2 + xy = x3 - 33203829041634697547391437695x
+ 4628236969850606474172342983150717123014937
Torsion points:
O, [-923114007128369/4, 923114007128369/8],
[-96921989900686, 2633618352910902509093], [-96921989900686, -2633618255988912608407],
[194753106772214, 2355511398385032471293], [66666668137814, -1646494683837498639907],
[714803598286874, -18604267659004305698347], [194753106772214, -2355511593138139243507],
[714803598286874, 18604266944200707411473], [66666668137814, 1646494617170830502093]
Independent points of infinite order:
P1 = [46298673497388914, 9962067219559759338566693]
P2 = [-379028413245427215875926/2485521025, -307186913495380854934589690706641653/123915650701375]
P3 = [-1776725917470153720605097663846174777557580127594/19790879678763450684360077601715729,
-7305793848605614786603460465641410778986318342005452610178505171838831269/2784182168597459200480787988836366571292518482866567]
Chen (2021)
y2 + xy = x3 - 32583917974166598527759227765x
+ 2704735273447412419379674398712690053258017
Torsion points:
O, [-851284889307793/4, 851284889307793/8],
[-59414629822126, 2104983929421483896663], [-59414629822126, -2104983870006854074537],
[146121300644114, 1031227437734292679703], [74953820844434, -826766225506564771177],
[460518158709074, -9239293881082962260137], [146121300644114, -1031227583855593323817],
[460518158709074, 9239293420564803551063], [74953820844434, 826766150552743926743]
Independent points of infinite order:
P1 = [130646511431858, 823226192885968647191]
P2 = [136545893032274, 895211277778743263063]
P3 = [79031185496537255073346/447195609, 14850086699829179720823605895489829/9456845543523]
Chen (2021)
y2 + xy = x3 - 121742801858876175580487838380x
+ 9106312593385081180859158136515307034352176
Torsion points:
O, [1211052038641983/4, -1211052038641983/8],
[1053304455768628, -32395416817744198779092], [1053304455768628, 32395415764439743010464],
[342818813960686, 2767721158008073454656], [4128763282895314, -264363750279988420594064],
[506953622972860, 8813423649077945673244], [342818813960686, -2767721500826887415342],
[4128763282895314, 264363746151225137698750], [506953622972860, -8813424156031568646104]
Independent points of infinite order:
P1 = [329760810576248044/1089, 3071484172613025659561596/35937]
P2 = [-47678273740104691966340/125372809, -893968534657381634058938073426008/1403799342373]
P3 = [1599239940965514699435898342/3313590386929, 47788496193680406582287050347704639193974/6031818048267305783]
Chen (2021)
y2 + xy = x3 - 608908485854584438061546155190x
+ 169881004497677065300402230973716494050333092
Torsion points:
O, [-3575392094892129/4, 3575392094892129/8],
[596301315291724, 4337979403252555332538], [596301315291724, -4337979999553870624262],
[1591911064602124, 56874803499250653938938], [-174556926253556, -16457564361344105659142],
[306021234930124, -3492944351352855237062], [1591911064602124, -56874805091161718541062],
[306021234930124, 3492944045331620306938], [-174556926253556, 16457564535901031912698]
Independent points of infinite order:
P1 = [271849683978508, 4943655246352676910586]
P2 = [-866649755833385401241/1094116, -14258133924247105437055337293957/1144445336]
P3 = [1973480494614761117098681/7693394944, 3730691825174961231262496003052103939/674803057328128]
Chen (2021)
y2 + xy = x3 - 533800709495763255903138777125x
+ 149953230423377060428282633780363808501390625
Torsion points:
O, [-3374175953434001/4, 3374175953434001/8],
[445253482571950, 740542804169895427675], [445253482571950, -740543249423377999625],
[803070633313000, 15465827432514249441625], [128692411295500, -9131730448096402995875],
[398620670946550, -713748012547017346925], [803070633313000, -15465828235584882754625],
[398620670946550, 713747613926346400375], [128692411295500, 9131730319403991700375]
Independent points of infinite order:
P1 = [268756204323304750, 139327275520628622749222875]
P2 = [5974072530664513600/12769, 2335618875522318623730161825/1442897]
P3 = [330911898270237792329575/21883684, 190138685639126867787946257991253875/102371873752]
Chen (2021)
y2 + xy = x3 + 458276662833075015242794212550x
+ 9389135584666280305178780644105310110728502500
Torsion points:
O, [-2037260410285100, 1018630205142550],
[2870759268422500, -185373698545320107145050], [2870759268422500, 185373695674560838722550],
[-1128066047162600, 86236118068802604680050], [-1128066047162600, -86236116940736557517450],
[12161647022930860, -1346751261384394659076010], [593040086834650, 99345267159619458755050],
[593040086834650, -99345267752659545589700], [12161647022930860, 1346751249222747636145150]
Independent points of infinite order:
P1 = [-580647374680100, -94484243811500566382450]
P2 = [2685427901923900, 173164168292722123542550]
P3 = [15627425213821205895962274176711852277585475/290211022414961169588552964,
61784354580530265849697030228659378597109466947116646444228184975/4943913399948617038176857011800059330312]
Chen (2021)
y2 + xy = x3 + 344254542927318752576865703420x
+ 6776821802504723734126192028632878827570126352
Torsion points:
O, [-1831764216749432, 915882108374716],
[-1013718643311416, 73390200390581563335868], [-1013718643311416, -73390199376862920024452],
[2572598914871944, 157126038816067148234428], [531877170010144, -84323113557207800267972],
[10894097664596104, -1141688900895068646553412], [2572598914871944, -157126041388666063106372],
[10894097664596104, 1141688890000970981957308], [531877170010144, 84323113025330630257828]
Independent points of infinite order:
P1 = [-754605557079416, -78021475582846835192132]
P2 = [-1025915767176056, -73101750839330551874372]
P3 = [40840115930159181802613312716830893961544/39465499963141770033562201,
22507265105720701357339172100061471139467211752347178827170228/247928477501755443162502801274350502051]
Chen (2021)
y2 + xy = x3 - 99084362485591589092907737100x
+ 12004804362068322177320995996166817880370832
Torsion points:
O, [727702179932991/4, -727702179932991/8],
[222406028676004, -984395769858983190152], [222406028676004, 984395547452954514148],
[182454819420904, 16194131444145074548], [571797513252424, -11928922255957980807692],
[187023045011404, 123959811113175100048], [182454819420904, -16194313898964495452],
[187023045011404, -123959998136220111452], [571797513252424, 11928921684160467555268]
Independent points of infinite order:
P1 = [7597477775491/4, 27500241043006768970759/8]
P2 = [2387645578460756679424/14371681, 19559472966397561591427686373108/54483042671]
P3 = [159094025140752288093899761885490664/220396412452037668441,
58220418002291148779634322145986253024064764540885028/3271950926373812685901440551261]
Rathbun (2022)
y2 + xy = x3 - 53175182646448982634917870x
+ 148831825068400959724189395389278203012
Torsion points:
O, [-8417611688772, 4208805844386],
[8970504360064, -19841366357128329182], [8970504360064, 19841357386623969118],
[4559702890444, 1081235127602383858], [3864850604134, -1023345984514497722],
[749188011364, 10460120178234932218], [4559702890444, -1081239687305274302],
[749188011364, -10460120927422943582], [3864850604134, 1023342119663893588]
Independent points of infinite order:
P1 = [12570019974304, 38295551919487787938]
P2 = [2303374006042841589/16, 3495800909630244759251459037/64]
P3 = [-1205547257021171151152/213656689, -51243224662765808671747888747790/3123019823113]
Rathbun (2022)
y2 + xy = x3 - 14006065039560929169609643425x
+ 638002401175414361429607337974351820355625
Torsion points:
O, [273280050841775/4, -273280050841775/8],
[74506462581750, 89784602611421901675], [68373333293100, 642334442203332825],
[74506462581750, -89784677117884483425], [8443898529720, -721345035582469052445],
[67803944632350, 7489719915027024075], [68373333293100, -642402815536625925],
[8443898529720, 721345027138570522725], [67803944632350, -7489787718971656425]
Independent points of infinite order:
P1 = [2459391732433975/36, 25583266525516836575/216]
P2 = [76806382804350, 123874864167360571575]
P3 = [90235259412562799331946000/1284071982561, 40709578020459311903986022578644202925/1455070564406665809]
Rathbun (2022)
y2 + xy = x3 - 4411278085770496675500817005x
+ 118111500868089424208219010824758994286801
Torsion points:
O, [-77093072481598, 38546536240799],
[-11081867407614, 406983740007140196831], [-11081867407614, -406983728925272789217],
[46833338704578, 119327540613593249439], [31186891892010, -104261764629131539929],
[126186770283714, -1253296218762806465889], [46833338704578, -119327587446931954017],
[126186770283714, 1253296092576036182175], [31186891892010, 104261733442239647919]
Independent points of infinite order:
P1 = [-264966563630510/9, -12734866672733264282683/27]
P2 = [25094418951628147970/289, 125708773361292156514015641967/4913]
P3 = [974927987758633438356679816773643026/23206932089100445693225,
294404312495641445738148293696638889687313526245227829/3535302635955512131957331041320875]
Rathbun (2022)
y2 + xy = x3 - 20057193028923924151408002453x
+ 1099906819116388159960580689014886490988897
Torsion points:
O, [-654567024131217/4, 654567024131217/8],
[89695078451118, -149969370777993583425], [89695078451118, 149969281082915132307],
[5502977941986, 994836251963150170119], [192731620229442, -2096034342241797266841],
[74297113166262, 140854062884429859279], [5502977941986, -994836257466128112105],
[74297113166262, -140854137181543025541], [192731620229442, 2096034149510177037399]
Independent points of infinite order:
P1 = [16555167977418, 878859453544412496975]
P2 = [-3004337420719474383070664382/39591491399329, -368234223464967389402621285523363536919753/249116671578555749233]
P3 = [313196407726715054484222916376181/3166642671739690000, 1629861538937116876394345331864981095823577174179/5635060584209610315047000000]
Rathbun (2022)
y2 + xy = x3 - 561492971046802549449135385221200x
+ 5121115505102875145590020455184344042391890687232
Torsion points:
O, [13683650332132704, -6841825166066352],
[13695597931773604, 2942089605589257856348], [13695597931773604, -2942103301187189629952],
[15261670342622704, 326376295205104462273648], [13831866570120214, -30655047696813049493522],
[33259815959843704, -4820630870970321426910352], [15261670342622704, -326376310466774804896352],
[33259815959843704, 4820630837710505467066648], [13831866570120214, 30655033864946479373308]
Independent points of infinite order:
P1 = [13676312390708704, 702667543029092629648]
P2 = [432538790766623464, 284052551027755518216477808]
P3 = [50753050382664834694/3721, 1887883101795889264155774118/226981]
Rathbun (2022)
y2 + xy = x3 - 11343905177123822620755687175045x
- 3983502885048515019140901226249648376079529663
Torsion points:
O, [-355105366759822, 177552683379911],
[13232400165728114, -1470664898402426348224057], [13232400165728114, 1470664885170026182495943],
[4066578603353714, 130900248741596961516743], [-2835066799267486, 73417182659223067185143],
[-1162141337151886, -87350798668018116064057], [4066578603353714, -130900252808175564870457],
[-2835066799267486, -73417179824156267917657], [-1162141337151886, 87350799830159453215943]
Independent points of infinite order:
P1 = [-2181951520678286, -101883599804403146259257]
P2 = [-408136850108386, -24049473076985176423057]
P3 = [-6543874611240466677809984542/2701194147961, -427671532039135434332888674689120263888219/4439496319192490291]
Rathbun (2022)
y2 + xy = x3 - 13494038328060943371631891783005730x
+ 603338366400860834935840770815757195641059910936900
Torsion points:
O, [268362666516689119/4, -268362666516689119/8],
[67177237660442660, 48226817997834566840270], [67177237660442660, -48226885175072227282930],
[76642636667178860, 4396103132270450094868070], [68078349603648860, -454561369382531330281930],
[176068439456945060, -60709163410493355713694130], [76642636667178860, -4396103208913086762046930],
[176068439456945060, 60709163234424916256749070], [68078349603648860, 454561301304181726633070]
Independent points of infinite order:
P1 = [67297762315053860, 102931825310827969453070]
P2 = [3230465495850863879260/47961, 1357445913777657831931114005130/10503459]
P3 = [106641993700583086159239239677930419401768176624384267298550020/1489393203201690074767048173538496207099676121,
118200586515463514185666028762392054246396452355806582174759420436860802252721587872835849430/57479641586611487310534457885374327429681376349773643040362549344669]
Rathbun (2022)
y2 + xy = x3 - 17782476581771407048750543755230x
+ 28862597212475811734896142544948201274441984452
Torsion points:
O, [-4869286986542756, 2434643493271378],
[3028988056074844, -52820004149038283579822], [3028988056074844, 52820001120050227504978],
[2446042595547244, 937615542509550661378], [2423260818928924, -934698002679422897582],
[1885022074906744, 45169687438213236703378], [2446042595547244, -937617988552146208622],
[1885022074906744, -45169689323235311610122], [2423260818928924, 934695579418603968658]
Independent points of infinite order:
P1 = [12693850734765067036/1369, 41187518692034635187967409834/50653]
P2 = [1148559628468148525091292/73441, 1230921350062481919634943425894406158/19902511]
P3 = [-7397385150141891839874798808179393495718614884/29838374297893051473802902656689,
-29723306734654309800587596725816206753949006111110083371323117923560286/162990666727474815333244821821521531355689323113]
Rathbun (2022)
y2 + xy = x3 - 1226444492184203850511228310313070x
+ 16531793020058856920505000267113594700487735520900
Torsion points:
O, [80877906260245535/4, -80877906260245535/8],
[21028477827549140, -200647688163179631241270], [21028477827549140, 200647667134701803692130],
[20221842662756540, 653929017176029441730], [35943895329259580, -4345895251946427424855870],
[20265466000085540, 11406243184607728732730], [20221842662756540, -653949239018692198270],
[20265466000085540, -11406263450073728818270], [35943895329259580, 4345895216002532095596290]
Independent points of infinite order:
P1 = [23292394221918770, 775833834832094789633480]
P2 = [30024116542109380805500/1595169, 685284705661573512359043103074910/2014698447]
P3 = [708544017267869300442843684397580/4394507685312889,
18448168893874019855101998064270379216857650611350/291316673711214605668787]
Rathbun (2022)
y2 + xy = x3 - 3969706228033862493448770151555x
+ 3044841895052891487437651848227601465018413377
Torsion points:
O, [-2300685947149906, 1150342973574953],
[1178598544261694, -1826664959062013364247], [1178598544261694, 1826663780463469102553],
[567607389452594, 31216629962082445539953], [1851525788736374, -45189959988779764204207],
[1122363039963344, 1797139522116288070703], [567607389452594, -31216630529689834992547],
[1122363039963344, -1797140644479328034047], [1851525788736374, 45189958137253975467833]
Independent points of infinite order:
P1 = [72682709506057265294/63001, 12180098734365710084662617403/15813251]
P2 = [253900193633960157866/218089, 112602946573541550857159242039/101847563]
P3 = [-9718903954011004062786373820599/32922578337640000,
-386722283259492321633006061165744809056946435751/5973663564535759912000000]
Rathbun (2022)
y2 + xy = x3 - 1043151842493411093151082232698440640x
+ 410082621762217363350890853503901150864455798195097600
Torsion points:
O, [-4717406942849711105/4, 4717406942849711105/8],
[593045104408744480, -4687408592479493077653440], [593045104408744480, 4687407999434388668908960],
[440283964202154880, 190127920283469334683242560], [752848022082106240, -226819600590490996569237440],
[586313625593670880, 4669605449259309748586560], [440283964202154880, -190127920723753298885397440],
[586313625593670880, -4669606035572935342257440], [752848022082106240, 226819599837642974487131200]
Independent points of infinite order:
P1 = [1535208283440764041992133/620944, 1760393045086251051701929289646265487/489303872]
P2 = [8957518221776800698620978286573670/15246815743132009,
6013907424508333549232488324918726664513661052630/1882646268590006977905973]
P3 = [4179640979785671199145663404366035575680/7134572537897004479161,
3186745186987742011405490466680147814361526815810839007040/602631649745821998777092624468909]
Rathbun (2022)
y2 + xy = x3 - 121926483196729998258808957720733060x
+ 16386685430850020153000358383600318033303796060675600
Torsion points:
O, [804380133599032255/4, -804380133599032255/8],
[266634027353951320, -53225341248341659400331860], [266634027353951320, 53225340981707632046380540],
[203217497879553220, 1197923078736880999674640], [-85762922705743220, 161903201889874948059928840],
[191805207818881720, -7544426789220645859863860], [203217497879553220, -1197923281954378879227860],
[191805207818881720, 7544426597415438040982140], [-85762922705743220, -161903201804112025354185620]
Independent points of infinite order:
P1 = [31986943365996220, 111889936190999286073964140]
P2 = [6770724858427363708418356/23804641, 7977158222610525091351330281776451808/116142843439]
P3 = [36055552139074291925003033797348525389369470523695071315/225641820855079043140597985027281161796,
106317339829426804179047624016087289851505391749997106917550218718387404803951242905/3389451262698687623153567869973780186320259265455337036344]
Rathbun (2022)
y2 + xy = x3 - 50107273123924732868868637637528089290x
+ 136864927330665042903386022260773432439681561919274232100
Torsion points:
O, [-8176007422637728204, 4088003711318864102],
[4368449415060854580, -1156931193920522581426718490], [4368449415060854580, 1156931189552073166365863910],
[792362185463754180, 9882271694310365131616927910], [8597835045369384180, -18483144196227895928617872090],
[3816063732573461280, 1105986598587163460519526810], [792362185463754180, -9882271695102727317080682090],
[3816063732573461280, -1105986602403227193092988090], [8597835045369384180, 18483144187630060883248487910]
Independent points of infinite order:
P1 = [6061390651560029988759666/130321, 14759503442577031276991678335730467092/47045881]
P2 = [4317270508420548728133489254888980/1572220119815361,
278637570414377719068715065205912769725900787962810/62340463153646556359391]
P3 = [671866585464797337101989968248901916391220/122448834067776525923329,
223143873299568683463520631421285465831916252376114898543693030/42848140690727205103563547891871233]
Rathbun (2022)
y2 + xy = x3 - 427137615280738382663108585x
+ 3397815850416943006878184135193702142297
Torsion points:
O, [12840251918074, -5500930964672201597],
[11931387135738, -5965693567869], [11937926122234, 33382341297508483],
[11937926122234, -33394279223630717], [12840251918074, 5500918124420283523],
[11861389559194, 423655976283252643], [2202305693434, -49677055786111157117],
[2202305693434, 49677053583805463683], [11861389559194, -423667837672811837]
Independent points of infinite order:
P1 = [11141648525434, 4677819547290618883]
P2 = [66153003375634, 514433117707947117883]
P3 = [79412797481202511141354/3308761, 22378737416011229223629165505272617/6018636259]
Rathbun (2022)
y2 + xy = x3 - 183216187136534262043404110x
+ 963465436550509088039018386333619840772
Torsion points:
O, [-19830123716, -31098209398511098142],
[-62583761195489/4, 62583761195489/8], [19626443563324, -70197132922268475422],
[6977273990284, -4978558517965876142], [8717094472684, -5361431242514990942],
[8717094472684, 5361422525420518258], [-19830123716, 31098209418341221858],
[6977273990284, 4978551540691885858], [19626443563324, 70197113295824912098]
Independent points of infinite order:
P1 = [467177936284, 29630606246458681858]
P2 = [-10675660203716, -41263988429440858142]
P3 = [7663365329574, 3075805773009903348]
Rathbun (2022)
y2 + xy = x3 - 133983532879288140247574465x
+ 823443965853545166244373007656596103817
Torsion points:
O, [-4744974315926, -36774449755601902037],
[-13900439955926, 6950219977963], [34779024044074, -195529189676268022037],
[4511350315474, -17629908235514749637], [10305960044074, -23178444067380022037],
[10305960044074, 23178433761419977963], [-4744974315926, 36774454500576217963],
[4511350315474, 17629903724164434163], [34779024044074, 195529154897243977963]
Independent points of infinite order:
P1 = [-1033252455926, -30996445552905022037]
P2 = [9437713317034, 19989167393889756523]
P3 = [1161298628159319834/177241, 1123874345079944144909774943/74618461]
Rathbun (2022)
y2 + xy = x3 - 16063710318140578822161011800x
+ 783640565283866640141324392711149883240000
Torsion points:
O, [74762065898600, -23600510152918766800],
[73107825945080, 994015671476649320], [38882680895600, -466718054937584363800],
[292698745563775/4, -292698745563775/8], [74762065898600, 23600435390852868200],
[73177781366000, 42086368262085800], [73177781366000, -42159546043451800],
[38882680895600, 466718016054903468200], [73107825945080, -994088779302594400]
Independent points of infinite order:
P1 = [22239589546100, 661354604501084118200]
P2 = [381248668748752268/5329, 9375368213268785045359352/389017]
P3 = [2794240061497669472/39601, 303518605261213852431751448/7880599]
Rathbun (2022)
y2 + xy = x3 - 4678520198160498424396858550x
+ 143350895123230863320137732461747895284132
Torsion points:
O, [54216266561404, -221500555052442879302],
[28877148264604, -179802489313669650902], [-321541661864033/4, 321541661864033/8],
[167726387229964, 2019193313309275588858], [-21110021466356, 482397393018740660218],
[-21110021466356, -482397371908719193862], [54216266561404, 221500500836176317898],
[167726387229964, -2019193481035662818822], [28877148264604, 179802460436521386298]
Independent points of infinite order:
P1 = [38473587792748, 142480486838519204986]
P2 = [78147147847804, 504956095531537053898]
P3 = [44995338849531023585213986444/7304497153255201, 211490351361885424189837819799618523140064038/624288717578609801241551]
Rathbun (2022)
y2 + xy = x3 - 41986504641522479520561450230x
+ 3289742830461789319759166359554074599564452
Torsion points:
O, [-236433001232756, 118216500616378],
[282039898767244, -3726011599308299383622], [282039898767244, 3726011317268400616378],
[132310686057244, -225224469799671193622], [132310686057244, 225224337488985136378],
[104495377767244, 208235080969152616378], [6039050005144, -1742528187669282588422],
[6039050005144, 1742528181630232583278], [104495377767244, -208235185464530383622]
Independent points of infinite order:
P1 = [-214679942639006, -1552206758434347039872]
P2 = [83332511121994, 607937899178264003128]
P3 = [51556918855444, 1123428780361417031578]
Rathbun (2022)
y2 + xy = x3 - 248335331098817316671250610205x
+ 47457383885704778743317441788800478419228977
Torsion points:
O, [1093349381969647/4, -1093349381969647/8],
[634833548886274, -12068652286657815940817], [-314352839427806, -9718985044960173348497],
[206406026299714, 2234520728814575189263], [206406026299714, -2234520935220601488977],
[-314352839427806, 9718985359313012776303], [634833548886274, 12068651651824267054543],
[314507707695394, -680859139221893105297], [314507707695394, 680858824714185409903]
Independent points of infinite order:
P1 = [7623182390607544/25, 36551064280788524433293/125]
P2 = [424230835442381554/961, 145512410300383937698370593/29791]
P3 = [847472570714184226/1369, 579650496863870030350456099/50653]
Rathbun (2022)
y2 + xy = x3 - 933450552229139506293892380430x
- 346949119899898380964449835765729115066031100
Torsion points:
O, [-547543665375364, 273771832687682],
[4285503697519520, -272687264375734035165730], [4285503697519520, 272687260090230337646210],
[1292208479022860, -24588035090066648515630], [1292208479022860, 24588033797858169492770],
[-566045264003590, -247271038673797107130], [-554586500505100, 397366842460873529930],
[-554586500505100, -397366287874373024830], [-566045264003590, 247271604719061110720]
Independent points of infinite order:
P1 = [1201665472130060, 16326677304909354575570]
P2 = [1530493537821199700/961, 1399194883566968046222591830/29791]
P3 = [30393541675980392587202/24098281, 2597198487437530868170803498954014/118298461429]
Rathbun (2022)
y2 + xy = x3 - 50990749716623265606902237465x
+ 4424532211302347932780364862745551337959225
Torsion points:
O, [504087939603759/4, -504087939603759/8],
[260797494721450, -2977331308864032113885], [260797494721450, 2977331048066537392435],
[139071350025430, -151448391297483956165], [139071350025430, 151448252226133930735],
[-130398741286370, -2975967598785308853365], [101194568659210, 548463394695417246835],
[101194568659210, -548463495889985906045], [-130398741286370, 2975967729184050139735]
Independent points of infinite order:
P1 = [21888286191242955430/151321, 16152651357831104773537033715/58863869]
P2 = [-28658160276250102685970230/114400209361, -47036129021368561984368396957112945915/38693697212380391]
P3 = [485944739514306379751160925523806616838040/2725995500085280241875951801,
142296206940975751698549603263109821894492196858223139736939775/142327133247813187337820048065664327013549]
Rathbun (2022)
y2 + xy = x3 - 14177824164609889207611422615x
+ 670968148773316077297987405840294839769417
Torsion points:
O, [-551947461412529/4, 551947461412529/8],
[81818295706624, -242226207617643479837], [211383396451594, 2668190893028696026033],
[57382982462524, -215298382463735681387], [57382982462524, 215298325080753218863],
[211383396451594, -2668191104412092477627], [81818295706624, 242226125799347773213],
[-15070562621726, -938729496372061542887], [-15070562621726, 938729511442624164613]
Independent points of infinite order:
P1 = [171745422241060264/361, 69138445477703999516700217/6859]
P2 = [1037891062044886908/6889, 799406245297359182881140135/571787]
P3 = [3754821848506912125064/16248961, 204355118418129723398892279322133/65499561791]
Rathbun (2022)
y2 + xy = x3 - 759312261767826374607025811330x
+ 254211225813421281729881845005124352297862852
Torsion points:
O, [119578752471544, -12850038142562188829522],
[468666744668644, -1135242763070154264722], [537913229909044, -1188551269528168079522],
[-1005987326340956, 502993663170478], [537913229909044, 1188550731614938170478],
[1016745308699044, 23092549880986808610478], [1016745308699044, -23092550897732117309522],
[468666744668644, 1135242294403409596078], [119578752471544, 12850038022983436357978]
Independent points of infinite order:
P1 = [818916294221092, 13475268743651551807918]
P2 = [1004138726789668, 22454932507982414223406]
P3 = [860646409843646958436/1530169, 4260926958964631341621490337334/1892819053]
Rathbun (2022)
y2 + xy = x3 - 553155555966463542957403280105x
+ 158345469816530432780403858579348265180319577
Torsion points:
O, [431346174239994, -215673087119997],
[434993128329994, -188622220222513099997], [1808662697567674, 71235390221090843433283],
[459829034639494, 1102721870791629637003], [459829034639494, -1102722330620664276497],
[1808662697567674, -71235392029753541000957], [434993128329994, 188621785229384770003],
[607698199897594, 6827518894340234953603], [607698199897594, -6827519502038434851197]
Independent points of infinite order:
P1 = [133506974941705715194/25, 1542609242408923722026508555287/125]
P2 = [1626374783890617276312394/122124601, 2070938555962184824205093016509196953/1349598965651]
P3 = [68023649134266427281984954/10087992721, 557757525212133875386879957617744761877/1013227900904519]
Rathbun (2022)
y2 + xy = x3 - 3636435703025862488261121550978x
+ 2643739994795650564197214626204840659224847972
Torsion points:
O, [1253356219101248, 7408794596809391961590],
[2769072461053706, 117502234513096913903474], [2769072461053706, -117502237282169374957180],
[1253356219101248, -7408795850165611062838], [950870548256072, -6759775183901265730426],
[-10197465419698, -51776648802168705439246], [950870548256072, 6759774233030717474354],
[-10197465419698, 51776648812366170858944], [-8798492260031777/4, 8798492260031777/8]
Independent points of infinite order:
P1 = [10096208314676527376312/66049, 1014387332613767747246060157895330/16974593]
P2 = [-22394916484943739513571112542884613/10589201967325581604,
-1019339985933050026725116364561937321027248885033089/34458379324743202590368224808]
P3 = [20597966835091340961715121736820495220494497573266581436787129377736618052189/20362882818090083818956128497462659889047025885898177586315024,
54994266724974526227802658408713924497454191969035025576072664632598915340219744464015215864551387421344948361385/
91888019915150655479787524491336408923539888027756053894257664925512956812057778309316104768]
Rathbun (2022)
y2 + xy = x3 - 10359453160683201662616515812800695x
+ 405838608527437906064656071809779711263839986496937
Torsion points:
O, [58764025843867414, -212875734769951063307],
[39372047640785314, -7681056269406345232779407], [58746098362529494, -7313656024304722238027],
[58746098362529494, 7313597278206359708533], [39372047640785314, 7681056230034297591994093],
[58764025843867414, 212816970744107195893], [59362675667115814, 251995230311335760377093],
[59362675667115814, -251995289674011427492907], [58763488496225814, -29381744248112907]
Independent points of infinite order:
P1 = [73742227929811714, 6550840118159141905992493]
P2 = [84584230717157164, 11608162669698474982280143]
P3 = [692919473494613879591750703338469733801720441394956414/11788453326391412175781158764482330081,
271727580615850927867192663707346190304585933336383369932277188841760110523667/40474849495575904684102579257048277433197316892060674479]
Rathbun (2022)
y2 + xy = x3 - 220390483813928768312607548857370x
+ 1220144097979683444549311154610384685976750732900
Torsion points:
O, [29220564615702879/4, -29220564615702879/8],
[26056253354950420, -3628763249017661293087850], [26056253354950420, 3628763222961407938137430],
[10526247966172540, -258045448877666550769970], [10526247966172540, 258045438351418584597430],
[4089586720077460, 622282323812872518326230], [-11413648843458260, -1499577236015604103227170],
[4089586720077460, -622282327902459238403690], [-11413648843458260, 1499577247429252946685430]
Independent points of infinite order:
P1 = [467348123393810260, 319333241917541577168974230]
P2 = [61750079853408320112657940/5528071201, 160293422141247925927448115167459537930/411017621865551]
P3 = [103328332243700245149580/6205081, 22757566041798977710477999504616290/15456856771]
Rathbun (2022)
y2 + xy = x3 - 13497464227081791660959597455190x
+ 15769601628243927128921337366518633060070733092
Torsion points:
O, [8982171540219724, 786898542493575923995738],
[3123386704734604, -63891623276386913722022], [3123386704734604, 63891620153000208987418],
[8982171540219724, -786898551475747464215462], [1111723741172044, -46240270509303522501542],
[-1237910215710476, 174874955947768383953338], [-1237910215710476, -174874954709858168242862],
[1111723741172044, 46240269397579781329498], [-4158118464039092, 2079059232019546]
Independent points of infinite order:
P1 = [-3259433076375476, -158542670690992820586662]
P2 = [7007635269082024366636/218089, 582913751005904828084127438179294/101847563]
P3 = [18813751279390672204, 81604308518704032124400946778]
Rathbun (2022)
y2 + xy = x3 - 9595101654169822845129538525030x
+ 11529530792170221956797911987470573262555175652
Torsion points:
O, [1980922251931244, -17193728286772730244022],
[1980922251931244, 17193726305850478312778], [46265569899644, -105288684018537858184822],
[46265569899644, 105288683972272288285178], [4376716280090924, 231026659120173660562058],
[1608543642779144, -16042357087126813626322], [1608543642779144, 16042355478583170847178],
[4376716280090924, -231026663496889940652982], [-3579905823390356, 1789952911695178]
Independent points of infinite order:
P1 = [-522016071916010164/169, -237607478695379428511613934/2197]
P2 = [6100818207266335222774529976716/3298191461393689,
1987028757100138879124488566282369361433617886/189414749739438576208387]
P3 = [1922271258148838473799437341623276/349585404108405529,
73085717681059720242991184691479266880695278675874/206694984029161287569390333]
Rathbun (2022)
y2 + xy = x3 - 290341365926893955858580556393025x
+ 1502834681162301583516579787950673729815279775625
Torsion points:
O, [43432318912608550, 8415574809811182583539475],
[14881991413181050, -691336537828937812595525], [14881991413181050, 691336522946946399414475],
[900047243191150, 1114559486514413179989475], [-14865811191078950, -1591780182060132213335525],
[-14865811191078950, 1591780196925943404414475], [900047243191150, -1114559487414460423180625],
[43432318912608550, -8415574853243501496148025], [23496969146918575/4, -23496969146918575/8]
Independent points of infinite order:
P1 = [-24262190871821402/49, -440120576598027323232171839/343]
P2 = [-76797721589658340550/9409, -1665191050328442159174586108325/912673]
P3 = [9059553999502442365909480/427538329, 19499014185143956802421470837536714375/8840210028733]
Rathbun (2022)
y2 + xy = x3 - 3426095658744800810344112808080670x
+ 77170786466425846496919278833745823684158124047556
Torsion points:
O, [136799858134327583/4, -136799858134327583/8],
[38141310748532124, 1407637971121681459621650], [179194946779081380, -72231087871608056438142606],
[55212344322963996, -7504497842005207270890222], [38141310748532124, -1407638009262992208153774],
[179194946779081380, 72231087692413109659061226], [55212344322963996, 7504497786792862947926226],
[34771136461516308, -284536551176766477967686], [34771136461516308, 284536516405630016451378]
Independent points of infinite order:
P1 = [52527626321966305404384/133225, 11913017371451047237223744547558918/48627125]
P2 = [72396761395488926912244624/1986930625, 74607979234218701540469874858261233282/88567432609375]
P3 = [224453808687095910877810716899644627568236445863435734/1791459439978222169066002246523746249,
96351358901768557278906852432523300172882510504258588937345614570275969649312046/2397786274029347216087523894930478598769202797427319557]
Rathbun (2022)
y2 + xy = x3 - 17242228237002206877333854061557340x
+ 871440914896576530012979639305465773385098604865296
Torsion points:
O, [89518311444208776, -6730769715384184145096412],
[74207334231510504, 762076144617378692346996], [74207334231510504, -762076218824712923857500],
[-11757440623198260, 32749657583702159836191444], [-11757440623198260, -32749657571944719212993184],
[89518311444208776, 6730769625865872700887636], [76009284035051748, -91568839116768580434936],
[76009284035051748, 91568763107484545383188], [303058281859704383/4, -303058281859704383/8]
Independent points of infinite order:
P1 = [292027044692611039558938703550484/1417283131406041,
4155808090334386250406929746431915760922880502596/53356204354362703845661]
P2 = [49719325235999730268038913514476362/240095204883941449,
9249314936936157611911466415909748665387152449032912/117645475607293812884490043]
P3 = [912740051381729988124356837973833311467746870/12031789357174210679214382729,
8610073342058353985582562686116534399346490163315599207491700192/1319761120317111875531501791927787486990683]
Rathbun (2022)
y2 + xy = x3 - 6764885347449940924390209877805853x
+ 205699980846692634430011297123771342100556986696497
Torsion points:
O, [219989112299022063/4, -219989112299022063/8],
[150528721878518898, -50972591793893420849476785], [150528721878518898, 50972591643364698970957887],
[59468830238837406, -3703264087998924234816405], [59468830238837406, 3703264028530093995978999],
[79169596083363282, -12897593205627680999477601], [571421185190271462, 427693566483198861104069139],
[79169596083363282, 12897593126458084916114319], [571421185190271462, -427693567054620046294340601]
Independent points of infinite order:
P1 = [13040024448609825644478/97969, 1250640033236755592680367047363683/30664297]
P2 = [862138870265505385189160625664391538/1420812984230929,
800508292416238773637972002864214075121475764279965863/53555660021754794212217]
P3 = [268335763248628698969884994275108639128615245463658983760930044688334/2038009938507090499736471073416702025521142529,
4395596689530990597323839755451186968551792859948875257381661109851182047650634400589512609074751172265/
92004579830038008433447024217746693688794985671333477774046329911167]
Rathbun (2022)
y2 + xy = x3 - 1535239713714526556731870431123515x
+ 23152964872265995965235374187045472044372251856017
Torsion points:
O, [30484980938146594, -2163779729953712781885767],
[22554311521004958, -11277155760502479], [21400712918705254, 314744322127347283157953],
[-10456110558997376, -6169475814699288932935337], [22831460632662574, 51797712913333598745313],
[22831460632662574, -51797735744794231407887], [30484980938146594, 2163779699468731843739173],
[-10456110558997376, 6169475825155399491932713], [21400712918705254, -314744343528060201863207]
Independent points of infinite order:
P1 = [1566048524367798133161130732174/401006829001, 1959683998668480647512761311006921921578076363/253937975471712251]
P2 = [644842428862656317719378132140286/19676944608368089,
7824719523650469198687758420719540934045216777981/2760174215805701576577437]
P3 = [1244189173971878845602161777959145061934216422859/253562020258800016004688806043556,
16017696450284273980560491242615267933082940205119991342207222130327740093/4037628014644183782484414185294999832082558558296]
Rathbun (2022)
y2 + xy = x3 - 121439171950857032870481084373354128x
+ 16288612126875476859576995529510417304573329358908672
Torsion points:
O, [803294253160683263/4, -803294253160683263/8],
[258396079609393776, 46496597592019385583785520], [202461402685013028, -940940759666680614573120],
[202461402685013028, 940940557205277929560092], [193027113493109712, -6296552914486860975989376],
[-73233364749800868, 157446027486527789695975524], [193027113493109712, 6296552721459747482879664],
[-73233364749800868, -157446027413294424946174656], [258396079609393776, -46496597850415465193179296]
Independent points of infinite order:
P1 = [793801491615388993564/1089, 20171909638948563040455900707648/35937]
P2 = [947987391821843248227176388287769924/4674972860230788025,
12103905925594928162881462273734978936810632931033408/10108079313869419910525553875]
P3 = [85397946657973355084030751707922645251213138736579/406680813168536482056917571607684,
56375491009834623339905229565414450715924043241149923982830144912437533135/8201258953655275656947476690809716126601517818248]
Rathbun (2022)
y2 + xy = x3 - 147582266931461807932911150726120758x
+ 1002582251282555006884114646304059103777013678580625
Torsion points:
O, [-52456657754622390, -40403025397510442764840635],
[46623060453789300, -20392487802150729287916975], [382341011091231090, -226389693749186286515496975],
[382341011091231090, 226389693366845275424265885], [46623060453789300, 20392487755527668834127675],
[-52456657754622390, 40403025449967100519463025], [111390052884879000, 27216940378713392544792825],
[111390052884879000, -27216940490103445429671825], [-587641695824713201/4, 587641695824713201/8]
Independent points of infinite order:
P1 = [67566611107860935160513210/656025769, 402954089891233327733640414380337163845/16802788021397]
P2 = [44447257558745345311107427743437891221422289200/1352488196438940784310913167521,
36990512820062891744294696464087140004999571090736736324899081422717625/1572896787293046200188188913228010567853229681]
P3 = [-1169140501499769942304558049550093206565605661284029915308064243732135756508493825/8540908026406369027061867777786463649888987351740434232333013636,
-16888430020512003738161307342906859681134953906745275359043144568939382117342317967106460339369258123985015526921088954075/
789325380676892453812133418270675482062458422404159880475026139695443184764529568292478738932616]
Rathbun (2022)
y2 + xy = x3 - 5020351996919968127252008383162928365x
+ 4329615953987801931683224442211327194760033035222646225
Torsion points:
O, [-2587238430043076670, 1293619215021538335],
[1178309814821166930, -223758326942308748941897665], [1178309814821166930, 223758325763998934120730735],
[1294495318731483330, 1752332359828514642338335], [1294495318731483330, -1752333654323833373821665],
[1292743315101089670, -1751542745572961133494205], [1412459649857187330, 237672096443775371663914335],
[1292743315101089670, 1751541452829646032404535], [1412459649857187330, -237672097856235021521101665]
Independent points of infinite order:
P1 = [31036773181791079388364/24025, 13001213098985781715286519943903/3723875]
P2 = [117324122106006039472290/6889, 39855022362593929334259366527617845/571787]
P3 = [12412203919363776889951170/7059649, 18165310798012266821735450061597110655/18757487393]
Rathbun (2022)
y2 + xy = x3 - 102136311052771139268683138562817555x
+ 26398300979665298868765656779270223625692337793017377
Torsion points:
O, [-408383691513241906, 204191845756620953],
[350095973025222494, -183169510573079312061591847], [350095973025222494, 183169510222983339036369353],
[-174687779930139406, -197254975716466491558246547], [-174687779930139406, 197254975891154271488385953],
[1295520346566510134, 1438208941590912808216527593], [116607848861778344, -126783153133496379029522047],
[116607848861778344, 126783153016888530167743703], [1295520346566510134, -1438208942886433154783037727]
Independent points of infinite order:
P1 = [1367591706783513344, 1563500551261041280714359953]
P2 = [1716744330717904844, 2216001874211324812875678953]
P3 = [50564722805065654162177358/157276681, 322853524072616022800814028572616445981/1972406856421]
Rathbun (2022)
y2 + xy = x3 - 32069010437070444727471013763259064090x
+ 69878283331141236222644293034563408249932491101726126692
Torsion points:
O, [-6538787674293704492, 3269393837146852246],
[3161038851898843924, 304174797241215883911383638], [1445850868063911064, 5151097544283742897161361558],
[3161038851898843924, -304174800402254735810227562], [1445850868063911064, -5151097545729593765225272622],
[5509124300818825684, -7772420691335189474886405482], [5509124300818825684, 7772420685826065174067579798],
[3378732195948330724, -311001399827313653880225962], [3378732195948330724, 311001396448581457931895238]
Independent points of infinite order:
P1 = [-518521546543686882991694/97969, -293075480714229774450133751204993564/30664297]
P2 = [375553232133264851899933864391461781796679216/116592140778010063512794809,
45095048184773087913074681372320193250481093883730384037532017774/1258936760140630805080889369407124887123]
P3 = [724608306851920436200501782528115650004/759423963347019296001,
132604783140436625275110156324263437191491430395379359299478/20927938265441483571750384944001]
Rathbun (2022)
y2 + xy = x3 - 243793445552461217885337288602518942785x
+ 1458609629586535796915044124605960501013389960426000953225
Torsion points:
O, [-18020418831413022934, 9010209415706511467],
[20397918792536750010, 70518058983474065093224827915], [20397918792536750010, -70518059003871983885761577925],
[8117385594335360070, -3809800962720587366015250585], [991674981069866730, 34897292177657442984417394155],
[991674981069866730, -34897292178649117965487260885], [8117385594335360070, 3809800954603201771679890515],
[9924278708164681770, -4073170564419010575475457685], [9924278708164681770, 4073170554494731867310775915]
Independent points of infinite order:
P1 = [29693131646109748770145920/3500641, 6483318911046398745701942635895207565/6549699311]
P2 = [-21218788748891696649369784454195270523030/1470678566491400985601,
-2504975903593827495142608355805807612949669891314664206919915/56399680618791662956822396761599]
P3 = [67327244578935465726128886686335174530/15091532795823790849,
1257109035365534972886982830653362227362379202427984818845/58627318081573226597484623743]
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