Torsion group Z/2Z, rank = 19

Elkies (2009)

y2 + xy + y = x3 - x2 + 31368015812338065133318565292206590792820353345x 
         + 302038802698566087335643188429543498624522041683874493555186062568159847

	Torsion points: 

O, [-655364911965298267755181, 327682455982649133877590]

	Independent points of infinite order:

P1 = [-499155234006326082923757, 402509376386904307636088023311932246]
P2 = [14139901902190764472167779, 53177370026792370019660919624681843910]
P3 = [165026138566397083648829, 558309596396209485460849837556760960]
P4 = [463343337635697262499219, 645016881525945325912024782026024790]
P5 = [-428490311544140084738931, 458176166275251046654351925125281840]
P6 = [-3076708833879670305775, 549492732729622717403028037016638716]
P7 = [-37665731401560276357421, 548455893205160937812792765224762710]
P8 = [-589425676522172250643765, 280659706984671022310703064556433246]
P9 = [-481732375371853545253165, 418490225997586738600806619185884118]
P10 = [3690858926941989311074375079, 224228684581316592254479552957274125288710]
P11 = [6130049174458433978294529, 15193625860788829982804926312716459660]
P12 = [99629044314032316202835, 553310835513576760020037678256777046]
P13 = [-336069400109872546513581, 503527960099926164391149483607861590]
P14 = [3296316187302021571885259, 6018489996489383086719697427657451870]
P15 = [239450610550684059490919, 568576446830597022058144468592457990]
P16 = [1116036406771517906484819, 1314196172527374653201729069765173590]
P17 = [1104492511976272577147219, 1297713008801587828896903435227547990]
P18 = [-556915090457934898225581, 334424588793955899397684278466715990]
P19 = [142518206539016399870550419, 1701397854372553501423223969798389683990]

Elkies - Klagsbrun (2020)

y2 + xy + y = x3 - x2 - 5402916719086617828375837827547110441856966557762x 
         + 4833725859886565634383924531696717238724057019566476908693058963652612161

	Torsion points: 

O, [1346849829812568356183681, -673424914906284178091841]

	Independent points of infinite order:

P1 = [1336029600818931024308321, 6982484452074243346987552859255199]
P2 = [1630926883548284909109581, 600085698640165416761663370054568059]
P3 = [786615965542165440298961, 1034618520128380805345711459365818399]
P4 = [1353258908712003226771181, 20415869217081610498319216938503159]
P5 = [1355148419151889572147281, 24561709531635368236158281650671759]
P6 = [1145987795332272568193381, 383485712083352528350867755591748359]
P7 = [1396596533826252282615281, 109851390417013090094142637486054959]
P8 = [1348132837440840404135681, 7537547675555604912269657249988159]
P9 = [1411876165006009074652481, 141075971817791097581854810619114559]
P10 = [1370098423316701523847681, 55726239232128811357373652069156159]
P11 = [1128034573609557710890241, 417648334357021838786139121897798719]
P12 = [1067704454245305073516481, 531209003211532081789617478275016959]
P13 = [1351340422064499097757441, 16035496391810410639288149386712639]
P14 = [101431820565704004177431, 2070444820150954977072985628719278159]
P15 = [1510136400035377410685481, 344192907362529271265323346605808559]
P16 = [-1269076212698534526624319, -3105885159866903190847789391243843841]
P17 = [-2315970644293850285352319, -2219122405863341885580517167833963841]
P18 = [1655529684705243828561801, 653052122387568178405611813153584519]
P19 = [1334719710439428308798081, 10885471619868597645004968593786559]

Torsion group Z/2Z, rank = 18

Elkies (2006)

y2 + xy = x3 - 26175960092705884096311701787701203903556438969515x 
         + 51069381476131486489742177100373772089779103253890567848326775119094885041

	Torsion points: 

O, [3183040297775561251987262, -1591520148887780625993631] 

	Independent points of infinite order:

P1 = [3231737970618117409726910, 477734049899522560689163862493530849]
P2 = [3273309887687276930053886, 677805198733135867174443509568209441]
P3 = [3241000828313547371069168, 526142335107247006178138422111656119]
P4 = [3255153282123996886918526, 595229162470140060497670577715082401]
P5 = [26966585148660027255767774, 137677903994541133602151567271381542145]
P6 = [4770216163266413128311686, 5894953964627833789313924429835166673]
P7 = [2549750315144935427762366, 950643850306503428886497351231138273]
P8 = [3713349702880881629511998, 2252141359101383750330981276127632993]
P9 = [3542121340287734605297214, 1671112741117758577475984222816297825]
P10 = [3195043262517282313487906, 228081804454697230002446209771949321]
P11 = [5646805757967450691937630, 9127716726638497548695728027642334081]
P12 = [14331333023247963581855678, 51180113307318927046718773937933570273]
P13 = [97191985119716082916503194/25, 354969759255330273188266145971062270037/125]
P14 = [1185147271535670890597935886/169, 32017173765694036331237894920457649821237/2197]
P15 = [98739463791232711776641098401842/38278969, 199867994868228186007608230146203388221790785839/236831981203]
P16 = [2294824481268463496752138910, 109931747845168723937902307597670194926241]
P17 = [-52959420769695630752203586/9, 31331086291021542344530429579191837787/27]
P18 = [154432285705268244684426598052/44521, 13312631160178214785941322691372196088408619/9393931]

Elkies (2009)

y2 + xy = x3 - 1718612993735110076283239582307203184558215x 
       + 445677626128337788660554947611110167094039534522619288819463817 

	Torsion points: 

O, [-5700969771220616529329/4, 5700969771220616529329/8]

	Independent points of infinite order:

P1 = [-916413066082020853346, -35369782405684521707886952377707]
P2 = [195434116396250243974, 10828966775531818886070739823413]
P3 = [1265034698502036374374, 17205341075829552264529317189013]
P4 = [2216840056561938704974, 86776618821766613189523105183613]
P5 = [1317460353165617357158, 21637731566353513111501700533141]
P6 = [-419919197918370459176, -33065253185351621643390087304037]
P7 = [-29666703514651498703639/64, -17307761259547457289873127491657319/512]
P8 = [1028534464393349854573171/4, 1043092047443803329899021606077145579/8]
P9 = [-4727498668121314310834/9, -936668010323115521156024630441249/27]
P10 = [2529716865202204892214, 110846353150164494211027781928133]
P11 = [1199344199314248064924, 10470797020157142702308988437263]
P12 = [5710166898431918122165966/9, 13644960301239082757781340351692685151/27]
P13 = [-1338652300506182722676, -18640047007082369619825194657537]
P14 = [5372757156747175085983246/1369, 11786893726772068452866617397651512729/50653]
P15 = [29128426914241943990086/25, 624790324363217559708520261779569/125]
P16 = [4983719710548842292787296/1849, 9864984392366637148101983568300087321/79507]
P17 = [10589515239193964535623854/961, 34220949959199862455549906395740174723/29791]
P18 = [1023941243985123630141565744/259081, 31035258051713148261108384857840848626527/131872229]

Voznyy (2023)

y2 + xy = x3 - 131092767138360259739530662694875901594863x 
       + 11513825206543517171066572416002846205241167788788151682092217 

	Torsion points: 

O, [-399859298727796783098, 199929649363898391549]

	Independent points of infinite order:

P1 = [93922761628601831142, 172536183142846547019651383229]
P2 = [-50129317073713395258, -4237858386924835972521216331971]
P3 = [-85586222512760289858, -4701769957935207215670356805771]
P4 = [-112226086720247238258, -4981204691390384388312280789971]
P5 = [-6382114264687965138, -3514287164324372791040569133331]
P6 = [-61975801758421286388, -4404583464940048579421718953331]
P7 = [8805951679868879506902, 825658977348831750165246207555549]
P8 = [1063693026478103739858, 32796024716695803287365470950325]
P9 = [39058033423837004262, 2540311738090645849720634292669]
P10 = [306172033454233460742, 279024851751328167924122015229]
P11 = [-190899016575756710598, -5438977902059130788276281233951]
P12 = [2058431396010984516618, 91997445485354914650555923853105]
P13 = [-268567728817069704177/4, -35788685082941237533491020134023/8]
P14 = [350084920332270917759742, 207138045545955430308281145901442229]
P15 = [233038728147301046705862, 112497177953178712068114804246204669]
P16 = [523312432158494847942, 9285663592140230654731106188029]
P17 = [402009359485387238802, 4876746000213639259008862651449]
P18 = [5764113665374889509776198/11881, 10205816958752115947930462213486633025/1295029]

Voznyy (2023)

y2 + xy = x3 - 15084248699780772863935958932958691919487759038x 
       + 712998263524553933194323224272640402753488391782195083964735452378692 

	Torsion points: 

O, [70317727086699237217052, -35158863543349618608526]

	Independent points of infinite order:

P1 = [68790207655603411764572, 933434788606925260277495740318514]
P2 = [75146818077639206122268, 1955090501051966617107495670220402]
P3 = [71552178910534363959836, 118810273295578069452033898236530]
P4 = [79800174118214287627052, 4176782161160112807869494478045474]
P5 = [-26056625866204193392228, -32990177338448883370413673896591886]
P6 = [57822733371906922185272, 5840741403435611920296626522574614]
P7 = [46930402575736468274972, 10413974265337900102865233550528114]
P8 = [-1271412283523693576595716/9, -134140753111277735447168562497402362/27]
P9 = [71577645911288207847452, 145793855395096034170020490415474]
P10 = [-80040057074407483958344516/1369, -1891916031284604976258850678740365806998/50653]
P11 = [110120016426075878074652, 19679479165460978760227805583132274]
P12 = [26181801390794993273786492/361, 4782345477531878202967108940414849126/6859]
P13 = [1395508116955203707018390356/3481, 49926688837204336670502912175839738092270/205379]
P14 = [69214241858097938020652, 729351269806999870661158587057074]
P15 = [11837072424848177728759288/169, 641065220897527508798007288064028878/2197]
P16 = [3445552394613504550097468/49, 3125038929087975249545667774770462/343]
P17 = [128724695954406137506765532/1681, 181567994172562764032885249291630909794/68921]
P18 = [3530946993452506014985448/49, 156909097600250596650752037262744382/343]

Voznyy (2024)

y2 + xy + y = x3 - x2 - 2699166037133059619746778252673978061861652482078x 
       + 52919898978595790008822015260251263804547347101931081116667651611487895 

	Torsion points: 

O, [265027423168051987069299, -132513711584025993534650]

	Independent points of infinite order:

P1 = [334581050338157547723891, 8088241463126298598147681649755462]
P2 = [-57843514467119276805573, -261417839761086621066877625966771330]
P3 = [359463968919995465153853, 48399448427940440583769370161368784]
P4 = [-305499721237981262035443, -326905235268768720085718956888410638]
P5 = [-527518638431214678464901, -220250328160074602563345372593638330]
P6 = [-490141652624759664067419, -259742578928982538343250381704372174]
P7 = [263184120359160619945971, 10574264840945801235291065551450822]
P8 = [532282378579463914867827, 245064689755386537323872624472966470]
P9 = [41845350889648587877482987/121, 40705380065354338388939161393280093810/1331]
P10 = [263598160057427760062835, 9286053224329114133805517162086214]
P11 = [-2687166343856213880595749/25, -35507591017105816237934271734495029714/125]
P12 = [8692611443376873726662798859/4489, 783794346714304489585027465259065243024738/300763]
P13 = [69158968190749168228860843/361, 622676397430399117696620979197668491906/6859]
P14 = [85403188608826412065966473/256, 5955305135441125227604405874951692147/4096]
P15 = [10250526059681186328896307, 32777165430585451459118775138509525830]
P16 = [1841455699300358411790913, 2408356571955820957393446870665476002]
P17 = [13444667179332654268257230979/34225, 548649918344762445536547231169829991853238/6331625]
P18 = [141059273172122075926924697583/3721, 52973892369005597684945948438538093655178254/226981]

Voznyy (2024)

y2 + xy = x3 - 5683314401210621492911632703706655785381168445x 
       + 164890848036318916388498198309479413985191764686997097959363364445041

	Torsion points: 

O, [43921119967229347350882, -21960559983614673675441]

	Independent points of infinite order:

P1 = [44641631922248734923714, 378977676133996348694765099006991]
P2 = [50921387038993434827874, 2743560436171297731192250474593615]
P3 = [-33686530052573969395230, -17835781763719108530351825468439089]
P4 = [42619799571493298954082, 292827379736122777599526074533199]
P5 = [5838847854036662207298, 11485029333192609885941978850009519]
P6 = [45248121238865553802986, 610091741742590528419332548432031]
P7 = [20432612029373596300830, 7569434220951625743173570363936139]
P8 = [-20379955995558953084190, -16500057012036585501568720282449201]
P9 = [37893141641450993359290, 1985598283050941174197688196727359]
P10 = [90893593185053575522434, 19981106231077783825926363388226031]
P11 = [37466689610256728180226, 2133036097413924302478261733769583]
P12 = [44597741180131259968938, 361829443357404721375545820385823]
P13 = [-53358687949900149432606, -17782713002210366978203433940336945]
P14 = [17692097214605877674682, 8359360374675174943088135065445439]
P15 = [83600785812042225095106, 16554601482925895999528983275399183]
P16 = [60360232761624133109747832, 468949438496772093487913290891082734449]
P17 = [44174705372674583511906, 186632952809786713542510794511183]
P18 = [12746151116772493790784930/361, 19690792123555484120569621125453221301/6859]

Voznyy (2024)

y2 + xy + y = x3 - x2 - 430296049749789761073413883308424711159706580x 
       + 1337861518400904123211779594356237371160319164544826734391001349047

	Torsion points: 

O, [-22151565406308899719131, 11075782703154449859565]

	Independent points of infinite order:

P1 = [873341970000860051749, 981189094633168587223120852082925]
P2 = [40976084134658725604389, 7246135315482990654209935387546605]
P3 = [-16238645765279695485675, -2010785771521054795196584427009459]
P4 = [186157749475626434264221/9, 30630131514051509241337847707151455/27]
P5 = [-21891963223217084862569/49, -424270030304775177193822692320192405/343]
P6 = [19131661320670698340869, 328881129964964528137837548063565]
P7 = [2282014423776644986149, 606468071280179215918647357177325]
P8 = [-268703181750331275531, -1205596962221235940220111463291635]
P9 = [22235290403974145546725, 1662351481790006522368357346311533]
P10 = [2670653688648746419269, 455782769080264504930749909387565]
P11 = [-19007695562649592551531, -1627716241666041460378231827921635]
P12 = [33367936973584629247119, 4912460924767910735506967614713565]
P13 = [-21954066498294463339611, -450739278772134641492262871413395]
P14 = [-1048519079571925373955819/49, -296533583052853272345509825387065205/343]
P15 = [62997732739415569840861/25, 64898451573140343591068169309457401/125]
P16 = [-317043130564298354002979/729, -24306039494028980739685529387681032025/19683]
P17 = [26787688505450614202085, 3005585023511496593979237417202093]
P18 = [779265679529900402837563941/10609, 20906230266920000324852067226367531083675/1092727]

Voznyy (2024)

y2 + xy = x3 - 10363846234372609474021228275773377224259738x 
       + 10412633142849975752506070356136680338076754827045078931231445092

	Torsion points: 

O, [-3636882190631092911148, 1818441095315546455574]

	Independent points of infinite order:

P1 = [-2607430220370914397748, -140387047515681414866483277225226]
P2 = [-1605621491785584326188, -151372793043869629484835629808106]
P3 = [-2819922555961640428588, -131201968173035899303243763491306]
P4 = [875074463835213331412, 44873030649530301538628591068694]
P5 = [-2467740801703347504172, -144775716117584701878214589749738]
P6 = [13315637656440444494452, 1494441905162102144306674307907574]
P7 = [-1762195702769915024758, -152327124138187809062915466865846]
P8 = [-3041170932937489746148, -117490087567011259916929625833426]
P9 = [193937709055224344613248/169, 12175020573097089290719700040789038/2197]
P10 = [1137909325716961985492, 9639692990949146169233800248854]
P11 = [3675715656247791166436, 148257394272207471703227166795334]
P12 = [52674857918538925070492, 12067240814424463070666174122025654]
P13 = [24178122670442307993524/25, 4496666863426713185668843068346558/125]
P14 = [3043510109618488310996, 84036038998028036136847099902230]
P15 = [1003524686553582969812, 31982322815500336822454512655894]
P16 = [673212038823402740957972/1681, 5481850155437583218016483153847046374/68921]
P17 = [644529864811619733766772/841, 1317924596196559752853144019460116206/24389]
P18 = [22583923428257353747412, 3360790983252352570792019048207894]

Torsion group Z/2Z, rank = 17

Elkies (2005)

y2 + xy + y = x3 -  957089489055751752507625259831765957846101x 
       + 351598252970651757672333752869879740192822872602430248013582348

	Torsion points: 

O, [2541668599439235342183/4, -2541668599439235342187/8] 

	Independent points of infinite order:

P1 = [1037048102780198794447, 21779881979625846052436063081576]
P2 = [640151922319155456727, 1116379497785052017163204160436]
P3 = [8215515531545032362283/4, 671712937153262899818205610666563/8]
P4 = [-252494436924143857397/4, 162335292364600094400633862613143/8]
P5 = [3033356276097950346763/4, 62943339550041852920918618404183/8]
P6 = [-697039650804322492943, 26077977524885678965262644558346]
P7 = [11414518769372982291382, 1215170223607965741833261815562846]
P8 = [891674633090402503696, 14392420123651702644251835214211]
P9 = [94919125996596744048847, 29242036615099659730101568678875176]
P10 = [636565095929048595313, 542487929999796513742831489802]
P11 = [4202001410067480893647, 265563310660870839720550898955176]
P12 = [438987621400369262071, 4005643151170292277973367502092]
P13 = [-1055345243070301537073, 13647840402839172835783080260936]
P14 = [-1120995419674665243803, 3976668559063776088092945926576]
P15 = [476001270991734096802, 1968115763191782636541113312386]
P16 = [639949947842762264623, 1091505880400660592954070253744]
P17 = [45374293429909818890233/64, 2776529523851458968917039502401287/512]

Dujella (2009)

y2 + xy = x3 - 1243378215801409573671681394724148505836465x 
       + 533568551747456170418786926292796873632980274337049541031491817 

	Torsion points: 

O, [2549822399914115274671/4, -2549822399914115274671/8]

	Independent points of infinite order:

P1 = [295909366620588641274, 13840224417503771788066682779563]
P2 = [635444448565646044074, 238026802184285253010435263963]
P3 = [406841929406614922574, 9749398968236802857137233294963]
P4 = [-498536763048246361848, -32086329206297967537307675521387]
P5 = [365329877709573516324, 11317439122188943552599543969963]
P6 = [653658047088929911074, 334802329486502314680260310963]
P7 = [390116221121923660074, 10386461778331482325086438819963]
P8 = [4686357172719668406771/4, 209378289880549899790913148373779/8]
P9 = [620651162007351845724, 971661597627620215237774115163]
P10 = [-174087993049324255086, -27290103511304743453323169025397]
P11 = [601743991009112691324, 1806148426566753856090607319963]
P12 = [-69410472226008425466, -24890512532673385235973153079977]
P13 = [-334709979328169335446, -30203341402018178778521393923557]
P14 = [628923493523439835074, 588364888705804863742467594963]
P15 = [594390299829369312882, 2124756989643788803088946333003]
P16 = [659600354729670357324, 640233767104009049626213294713]
P17 = [137924634886574871255456/169, 17355263577043625203177043015047311/2197]

Torsion group Z/2Z, rank = 16

Dujella (2009)

y2 + xy = x3 + 88871190402766374892305201263009054x 
       + 3984685924354438849515723880588291198007040526340420

	Torsion points: 

O, [-175542362809146145/4, 175542362809146145/8] 

	Independent points of infinite order:

P1 = [151973772990544676, 144916412062834947325089374]
P2 = [2483151276492131324/25, 14679826610543776415004288958/125]
P3 = [1610418222555057704, 2079336080580622560199851146]
P4 = [4634585828316182444/25, 20475216698846556208892216662/125]
P5 = [-43256174748154756, -7715030657930259201193330]
P6 = [72902402348883620, 104168459661214206318188990]
P7 = [452835459272043074, 370252792228077611247142466]
P8 = [153321526455960346904/25, 1900732161197395082302431092182/125]
P9 = [2134230041464174184/25, 13803142047956961346950385942/125]
P10 = [82891046930330024, 109182645833355896465324810]
P11 = [375401087875922171036/1681, 12888190018226387298012343424614/68921]
P12 = [196347242398027736, 170305387431896979433767194]
P13 = [271776890222171386, 219572290075495322173230370]
P14 = [234450949350981596/25, 8677330466865166648614606166/125]
P15 = [11767892998547671020716/289, 1276614337651341056305878640548910/4913]
P16 = [37857943848339470264/289, 656844213086979152886012631450/4913]

Dujella (2009)

y2 + xy = x3 - 17849664414856321688532880703583568631426320x 
       + 29026120563785158608387957657788008917376822051452774596151718400 

	Torsion points: 

O, [9781726730442585255679/4, -9781726730442585255679/8]

	Independent points of infinite order:

P1 = [2543446417655415598340, 8961853916063213924060160145280]
P2 = [676322932174900255490, 131390037265339897550946875294930]
P3 = [-3997541813463081560740, -191046645807109461774605026744540]
P4 = [5218440445433960191106030/2209, 677018033704234550041753683384889540/103823]
P5 = [5831781158482772369635340/2401, 83257184732236633493571470017111220/117649]
P6 = [2461528428452813029676, 1834591258355264730181101873152]
P7 = [145775886315926345410430/49, 16284864524308066505985606229638890/343]
P8 = [68156294726946833251964/25, 3127918397470140498764192626284052/125]
P9 = [22161083471480601997715744/9025, 1105826078492419349835381946024352032/857375]
P10 = [119869942753025897193260/49, 101144849080247509831232689149440/343]
P11 = [93571017415623282191776/25, 15129951832994498291133009095470784/125]
P12 = [52971755060363114908123535/64516, 2001901260611376836110813068960571309795/16387064]
P13 = [532055598851487973712330/169, 139553955995261808837218634853391900/2197]
P14 = [342927708908745063881721020/142129, 117627027781800271227250936982152289920/53582633]
P15 = [2462336530293270134840, 1906663238979426296193238372280]
P16 = [121175500588940324940207526340/33651601, 20881325796189599676675229762719172392586780/195212937401]

Dujella (2009)

y2 + xy = x3 - 471959138426677420722309989289772596091750x 
       + 124751636856485490330319407549080294592546759914600508504125156 

	Torsion points: 

O, [1561735252151625340063/4, -1561735252151625340063/8]

	Independent points of infinite order:

P1 = [1615032476127549501731/4, 986346104104098864407375459875/8]
P2 = [409085542964731061972, 375291317854821617968120161794]
P3 = [180397342138991640296, 6744046979310659962103361215438]
P4 = [27947009757763988386622, 4670603555799874617291512532950324]
P5 = [1871140381510906872428, 76110600653371332335223760400234]
P6 = [7460282688357852771491264/49, 20376449515187704099682843432716586618/343]
P7 = [383373560129883900860, 401771825006915827383000708986]
P8 = [390413367202296657710, 17317252241368176315001812686]
P9 = [-16901742139619897986306/25, -1451387178086920644335362027445132/125]
P10 = [3625247527076520542002/9, 53709487180276833359886427418/27]
P11 = [28408205856250265992046/49, 2326291776873931331388306256937090/343]
P12 = [90779982592867689872, 9091496730293459632997464912874]
P13 = [2997284890348609921855499/7396, 132770326962741315002814782761343785/636056]
P14 = [-198613117743760590998788/529, -192001372317931671100953771453561722/12167]
P15 = [-3154280500565445833425/4, -20486601688580156443679414733347/8]
P16 = [7718438389637469958924668556/326041, 677818251107899626804657478524702368574718/186169411]

Dujella (2009)

y2 + xy + y = x3 - 28204247479665028137881824355126641095631x 
       + 1607628613312482130477520396860594598897534891797451337504758 

	Torsion points: 

O, [273169178426675086663/4, -273169178426675086667/8]

	Independent points of infinite order:

P1 = [47104689038013888877, 619350165040615817417427973796]
P2 = [13295687003414404091467/4, 1531160323050173785039954221042451/8]
P3 = [123173221335374522017, 48586725760711590936863664146]
P4 = [48094084679947110697, 602008916445967252186792134476]
P5 = [65330517064045065967, 209442555468631298752182543446]
P6 = [212861500502964569533, 2291023499970126181431567386852]
P7 = [128559997894086388018, 326325344217922637245334459357]
P8 = [716753399338596395052, 18697961334653137187462221675126]
P9 = [-6157876375856838190991/64, -948321228946683456980815301363573/512]
P10 = [-189763261767436243662, -355479153948820264624263195683]
P11 = [214375732344458024617, 2326666758850242263706410133836]
P12 = [5431072074149288882592, 400057850875175075993028090431821]
P13 = [-136448137674797588594, -1707524923780667599464904974604]
P14 = [208820172499131385183, 2196314395484531398162474612514]
P15 = [2941684732204891847404192/22201, 1467575989549454706096178683935864329/3307949]
P16 = [21947239135578171989355715777/172843609, 616551354963568249218769235719787123519582/2272374927523]

Dujella (2009)

y2 + xy + y = x3 - 51671229331059644891666297654483243x 
       + 4520596773662388877346447309051182845388785311959658 

	Torsion points: 

O, [528240160300186247/4, -528240160300186251/8]

	Independent points of infinite order:

P1 = [141619764967775934, 6578584744791410297700985]
P2 = [99864500008570989, 18878977611252925518992410]
P3 = [248238803992676919, 83611537644002554260799390]
P4 = [507266594870876331/4, 21686667772091179044642155/8]
P5 = [-248205283317232896, -45329551958008032415871930]
P6 = [179703173729305164, 32222800996699387743315625]
P7 = [-897824974045715049/4, -554849767967179778496192655/8]
P8 = [8527070458458717, 63879672597508782542481130]
P9 = [-257763946075387032, -26705050136250711582795047]
P10 = [132204028175118294, 318698988584720949558640]
P11 = [-255454636170693771, -32404173939906937257012680]
P12 = [129912028384611264, 652241277633523846496185]
P13 = [-122005078189427481, -94914036770170655800132910]
P14 = [77761220204880781509/361, 399061991814514109741444454760/6859]
P15 = [144584763577150887, 8499011128039330574109490]
P16 = [132062728972984404, 41787089121228963105250]

Dujella (2009)

y2 + xy = x3 - 579352424306143750269326367254022350x 
       - 57305844527587581171925109677515882551564446162252284 

	Torsion points: 

O, [-2823218609333774817/4, 2823218609333774817/8]

	Independent points of infinite order:

P1 = [4068219982994569252, 8057076720692148470663852794]
P2 = [-159476824589571716, -176157568737903201199725614]
P3 = [-209853749376245894, -234588510714978626702493824]
P4 = [-107903036268023300, -62862699807490056665190254]
P5 = [-407801248649888348, -333371702260952310503250566]
P6 = [1613028824672285860, 1790268242183837943924354274]
P7 = [30137928799613156340, 165398321581137978397389526626]
P8 = [-506128365115627052, -325987747254270204992027702]
P9 = [-217463635196806404, -241657382008399231119213582]
P10 = [-88925497540480809020/289, -1488795305143131800163175187782/4913]
P11 = [35980501480598807236/25, 180710978447160746595995035226/125]
P12 = [-108649531186230838766/169, -488497210480488264517264360904/2197]
P13 = [1872997724883320479900/441, 79716688493077586388902961013994/9261]
P14 = [-11948308108048013246/25, -41536210844661615551058892402/125]
P15 = [15772717897243037206, 62567722337928961199276631718]
P16 = [437004697917082731616/25, 9126719659481798690782010500346/125]

Dujella (2009)

y2 + xy + y = x3 + 267853229754852595376917238570941410963001621467x 
       + 170558547185604460032465298983507283645349525870236517451642935548238068 

	Torsion points: 

O, [-1596879202112581735196569/4, 1596879202112581735196565/8]

	Independent points of infinite order:

P1 = [-93937115844369725183611, -380221342287750978250850929228593570]
P2 = [454190456407473836539139, 621216073204930772322173900240574180]
P3 = [352065545058916201419431/4, 3531036092929254190907269368236297565/8]
P4 = [636006084975152784372914, 773422052507182042616573840046084330]
P5 = [773504119391079470208514, 916808763117865818936625260081563555]
P6 = [-343302262873018080512461, -195303721107982212098273111372640420]
P7 = [-395812681740205941959251, -50277110359467698750277165196768290]
P8 = [2811928370827030870017764, 4812223480355689844861652595373742555]
P9 = [791437258468947025647164, 937167248014828072578023898184619880]
P10 = [1259024220948617982966989, 1582252953486408745065916110566280030]
P11 = [-376548274808658326743147, -127705213964969629340049056471235042]
P12 = [3326170937835288273581459, 6153071373523880008067027618538326400]
P13 = [-397262119239232884674611, -38155125306164524385849082378129570]
P14 = [940793091628917567947343731/100, 28902916890531186391583918875443253426899/1000]
P15 = [1099592650337942372697921164/3481, 109966776751825341843596607673237351936680/205379]
P16 = [534846851477536307808578081/169, 12566376695950918945008717628793213997870/2197]

Dujella (2009)

y2 + xy = x3 - 196465475161695260241191786153619014545241225x 
       - 60082143680753989869605925276848496067056532671061605793936509543 

	Torsion points: 

O, [-55444516013008681325009/4, 55444516013008681325009/8]

	Independent points of infinite order:

P1 = [-1497658521656061826526, -480413186461364527564610882292557]
P2 = [-4778682187312818125009/4, -3326733356081824356287603382324991/8]
P3 = [-13697703884770375349846, -246948204267127388270486026110077]
P4 = [-9745736913117242264846, -963833264795990323850500371180077]
P5 = [14807862441906464957254, 526920713735721989487956218326223]
P6 = [-4661382333011726714846, -868581472282353633984437347680077]
P7 = [-11472383996660965607666, -826982822452510409691316592528837]
P8 = [38208792232080565692154, 6943678860999439430041833280841923]
P9 = [-4933859517396924414996, -888338965632311702251386163344477]
P10 = [-12662774894518816789802, -630311280803222476586894719333109]
P11 = [14974643236439775326974, 596515347015693517166377958724583]
P12 = [-492025459154574925616, -190957476853921086991225327062437]
P13 = [14397848551667513397154, 309650651989956093433880451455923]
P14 = [-11116903086607467285326, -866093006857162389735566578916357]
P15 = [-6233989099837585680696182/529, -9569514905994996585295943620524324859/12167]
P16 = [-3777451381839863530589276114/8334769, -4088219787593087500133978348842993611600911/24062478103]

Dujella (2009)

y2 + xy = x3 - 1778561648285876253264864713065168662962870x 
       + 1330436329617472863597139221866207954812165565920030448022583716 

	Torsion points: 

O, [-6453726948192281497697/4, 6453726948192281497697/8]

	Independent points of infinite order:

P1 = [-285105104812091797700, -42595053573075704325197926514246]
P2 = [-1290980955228846588212, -38404890280735531589576938220102]
P3 = [-1175330680438284452276, -42393749590184529628417401895814]
P4 = [777696124065308718076, 20435635617458747553847432731466]
P5 = [-1575944124006496573796, -14809978662619626603336986372054]
P6 = [-430056358240873306010, -44897436552136445084489871111266]
P7 = [3865853312852211459676, 228537233061001881878161879940458]
P8 = [574662431263670517532, 22319016873237823416258449738554]
P9 = [240166587402047398990, 30284287251739936532031988252276]
P10 = [5792218581397653419548, 430530336726132150130063724025658]
P11 = [10636427275689136727794, 1088921505900686665770751938046576]
P12 = [14393520313672903688182, 1719792314018873182907110195380574]
P13 = [13088983993003440215056/25, 2912175124610212530180406712350514/125]
P14 = [1002685899839688001744, 23562194378519002208020788293530]
P15 = [335314922786732946682, 27780560994595378646025402304894]
P16 = [45151965295099679571865612/29929, 236189220918648296821706523363928906178/5177717]

Dujella (2009), Aguirre - Peral (2009)

y2 + xy = x3 + 22461831362529182584186836961913400462x 
       + 99681757298539603818055720843145922688167002101080034692 

	Torsion points: 

O, [-12420185912395920417/4, 12420185912395920417/8]

	Independent points of infinite order:

P1 = [-1358524569007516818, -8164528737748013886919624416]
P2 = [-2234784439901270892, -6190582217455428383109349650]
P3 = [-1719872229735609948, -7480839738870867968220829026]
P4 = [-2421703974282043098, -5575249272923012681190735726]
P5 = [4231171480173269172, 16446017312171818470098786814]
P6 = [15697285123146446172, 65727903547114136654157542814]
P7 = [4753799047628626452, 17716941567651211752862606974]
P8 = [8993675336684768628, 32080529334009684664407115662]
P9 = [5188680690708476132, 18865863426485978882291779934]
P10 = [545331864463205172, 10587402145483296857892164814]
P11 = [11407511585843734272, 42899765798045991708660610914]
P12 = [-3062673106784277348, -1469945280631395019745063226]
P13 = [166035287329211386452, 2140337097540651803430540296574]
P14 = [16145622916781092777632/841, 2127123673299157394083356331211286/24389]
P15 = [-3075974597614047348, -1219029401147576527512488226]
P16 = [16066442368585324293/16, 710513502944173007902940368005/64]

Dujella (2009)

y2 + xy = x3 - 53380463151031517892334218440352731688495x 
       + 4746640874350051847809461015538184892459778801618641227879481 

	Torsion points: 

O, [529639515084352914383/4, -529639515084352914383/8]

	Independent points of infinite order:

P1 = [135137681567325064758, 28970030993970514070088064989]
P2 = [241446388019810023518, 2435891212353678105320088509013]
P3 = [131484644767132564674, 32619439963935506065623247125]
P4 = [-8470929521410582951738/289, -12317923150226589680054266250525843/4913]
P5 = [11530161688603228697052, 1237845840258412159273670972087469]
P6 = [19898709999237165695027/4, 2803992704510651900237464467416539/8]
P7 = [8715921962875241752362/169, 3207017999197835672735086161974421/2197]
P8 = [-3053016388045269528193050/26569, -13251851342923008357837429795269842977/4330747]
P9 = [873626673105123281208, 24997690042072074978641798724453]
P10 = [37839750237165375626741814/277729, 7881101962721907323193859085265136323/146363183]
P11 = [95079553062581197706403210/591361, 257389122693282059452644878131536713349/454756609]
P12 = [1212163602426927342166/9, 456262679057994358648562204975/27]
P13 = [130478877625482406647537/1024, 3831396559198536956794717435809447/32768]
P14 = [253861781230406405317071018/727609, 3318814225238694631379612388920978073153/620650477]
P15 = [834452325027139035411735605766/6086652289, 34089366612444515161489793824393147182771645/474862351630913]
P16 = [385989097281121251320169045630/39150049, 239742125758694771341949110056649028375379357/244961856593]

Dujella (2009)

y2 + xy = x3 - 30082139823936559483905935102688940491458934663x 
       + 2614705158611963590952856462176361058450781199585405595471549728071817 

	Torsion points: 

O, [-826859069206865753847217/4, 826859069206865753847217/8]

	Independent points of infinite order:

P1 = [4279651346255234015668563/4, 8745917746666196356470139664724180087/8]
P2 = [221408747528263959139502, 82511326555826084839043639463049949]
P3 = [161927027426760738122682, 44602454968330326501752915788496409]
P4 = [-18966915264973367162874, -56377720103358612152894833453015995]
P5 = [152956987066091815288422, 39899735167643805093963854957027589]
P6 = [102034875909190711734702, 24649029873565520289089405276370549]
P7 = [-134804803783127613130398, -64963097558593324795462949036598051]
P8 = [140609025064871202877752, 34129920724338098538459446817250299]
P9 = [-199463092173919885201618, -26062193288232395628636960614065291]
P10 = [4598519189780656759560444438/34969, 199728958238766472006520740700289734946447/6539203]
P11 = [8313811928104438453598300478/16129, 721495512431610143979717821021993194320147/2048383]
P12 = [68159272183066803527999219542/19881, 17772358574313347743644413305351940398883689/2803221]
P13 = [266895230482472058568305314192/1190281, 109754982150971423770786856687763068561753089/1298596571]
P14 = [-460038102279188358862162278/2401, -4313858620742668944672305018512482899139/117649]
P15 = [46804129918217080471255963302/3418801, 296864559583129472867770078056689560596064701/6321363049]
P16 = [3952831689914422660492554911166/7070281, 7532760779516368484247403408282857972907389495/18799877179]

Torsion group Z/2Z, rank = 15

Dujella (2002)

y2 + xy + y = x3 + 34318214642441646362435632562579908747x 
       + 3184376895814127197244886284686214848599453811643486936756

	Torsion points: 

O, [-55741267008740887705/4, 55741267008740887701/8] 

	Independent points of infinite order:

P1 = [-5955399047526089895, -52619192486073556789679851928]
P2 = [-10883488374931039920, -39009259582579792447480800428]
P3 = [25617164053798897605, -144480091250102706688189014428]
P4 = [-10819998365744200320, -39323416370158251425370822053]
P5 = [104461756233244297605, 1070832856583711138856374116822]
P6 = [-13178335910050336770, -21058433294831012498764155053]
P7 = [-8109021285488360520, -48712125024735484500144150053]
P8 = [-13641790592099985510, 13322871549061184750149766947]
P9 = [17051811768980000730, 93421745224403634416501304322]
P10 = [51413108001886672605, 375299141884454862856563616822]
P11 = [-9527137759746081954, -44639433008625651474894783026]
P12 = [-674553190484964645, -56222064156796770815845330928]
P13 = [60487341240781250730, 475989858966422000049387054322]
P14 = [44737088527034836586505/1681, 
      10440384606973435833942470793114062/68921]
P15 = [3423934952363100338459817/36481, 
      6360102793003685525437050804199384514/6967871]

Dujella (2009)

y2 + xy = x3 - 44983303148372813062091588735006222790x 
       + 113817052678905764015135842208733506900505149372185755492 

	Torsion points: 

O, [13670258741780008607/4, -13670258741780008607/8]

	Independent points of infinite order:

P1 = [4310210790883112544, 65365365737680503958746198]
P2 = [3256139879023839684, 1366812206363889258442661898]
P3 = [5606214825113296074, 6150799258812661160218467438]
P4 = [24740932855465046124, 118933399713162424765457508138]
P5 = [115043084731737275724, 1231878170189110085685888799338]
P6 = [6084305921271097704, 8084457212260904108353542318]
P7 = [814735121550003833076/169, 6591145014838387448887374359946/2197]
P8 = [4325066798743811724, 408458629406023762754275338]
P9 = [-6887211948173828136, -9845848358426608735316715222]
P10 = [1565261985677118444, 6873235096567408584547967658]
P11 = [616492241812365224364/121, 5469682223035425660234155027838/1331]
P12 = [2143543503151209224, 5219434221398996545403197838]
P13 = [-4942390918231726236, -14676961940075347315520232942]
P14 = [4823556538171617775944/841, 162676940434775957768151444511122/24389]
P15 = [-3224165652616605156, -15011152001960539717353346902]

Dujella (2009)

y2 + xy + y = x3 - 9787472643107005523075719618421934671816478x 
       + 1666408105881456642404124109941261415712089105209504669167254756 

	Torsion points: 

O, [-12841521034486825188905/4, 12841521034486825188901/8]

	Independent points of infinite order:

P1 = [-6176007349090217626405/4, -915553551467723487022948702104849/8]
P2 = [-3129727543028407345720, -40524570541991864371797835504653]
P3 = [3461438776471679393555, 96234617652133597957415588750097]
P4 = [-304569520786114509444805/4489, -14518337791411701360968690696166211989/300763]
P5 = [46749918438362505836941130/3721, 309717635823882664652843137775449108032/226981]
P6 = [-121760299909016401445, -53444630640731736532288009219903]
P7 = [-3878023321719040442905/4, -809706755031980940882066233773599/8]
P8 = [-650904952869654088945, -88098518147939984998018731159903]
P9 = [3211833539877933133055, 57996099141689105147032333358847]
P10 = [-279627254130111308410, -66192052084066431198211238763528]
P11 = [4778427566087150721680, 252992655387344035936908771921972]
P12 = [-22549528799987020100995/16, -7201356571428059433520262702341917/64]
P13 = [-41484235392297509524075/16, -6275050846011773962948320830988897/64]
P14 = [11404299380469664557060755/3364, 16838047702372204271654455398073697139/195112]
P15 = [2032370808462899194583150/529, 1753546464147333979091664135941424159/12167]

Dujella (2009)

y2 + xy = x3 - 38064598122520711827608887857833864769365x 
       + 2856369890490724644127902394897782785656508815105789929216225 

	Torsion points: 

O, [440616430188382357359/4, -440616430188382357359/8]

	Independent points of infinite order:

P1 = [154978462370139206530, 824317835312651521651728277735]
P2 = [101211988731799110310, 201440640099151015743920851435]
P3 = [-138339729063805884254, -2339804876291888838641359535273]
P4 = [107195862460181729490, 88233073199137259807678945175]
P5 = [118199632472186128210, 92377192999174562695465598935]
P6 = [109228167835768103350, 42687234750831717124370829115]
P7 = [1606735493653863109090/9, 35725359320226464578835504931245/27]
P8 = [319346546500341238540, 4823716478183218456447348148125]
P9 = [1632745931431399908160/9, 37427654249574472129716075752725/27]
P10 = [2968406979076876830646, 161387128120275934793381147733307]
P11 = [50435845020951603864809650/458329, 4266112332467988872880575035369208795/310288733]
P12 = [205650416099455169679121330/1874161, 71005882980840361899501165201016633615/2565726409]
P13 = [1020136311332667375161410/9409, 56764307939951866079331723615072775/912673]
P14 = [112794531630621535030942506847930/358368652321, 1007521941982262938831142487558547877562152870065/214533451656791119]
P15 = [166817185151770979365206811379605/1169624946064, 725173124355794556504624330436224982365418744135/1264940022168647488]

Elkies (2009)

y2 + xy = x3 - x2 - 47377997631934616131259094x 
       + 122064326885475393485584567015835076600 

	Torsion points: 

O, [13690851677475/4, -13690851677475/8]

	Independent points of infinite order:

P1 = [4500895301116, 17895577089353792]
P2 = [-7879047179700, -2496274582710240120]
P3 = [-7791526340259, -4266631333507969158]
P4 = [-7816770890871, -3845470103309695578]
P5 = [-7919982209319, -712375905043009743]
P6 = [-7861912714884, -2933213810436686208]
P7 = [-7921327767924, -563899328680245528]
P8 = [-7679614164996, -5743906466119247676]
P9 = [-7898698253999, -1869092036434260498]
P10 = [-7858400307321, -3014687899238193876]
P11 = [-7918000894850, -886766356327884100]
P12 = [-7916835300134, -974847693981397408]
P13 = [-7902140608214, -1735516496710803088]
P14 = [-7787026675214, -4337047328172214698]
P15 = [-7830443686839, -3595099957696460463]

Dujella (2009)

y2 + xy = x3 - 51106946802276227168271274508580303280x 
       + 127511987670191066099774598999351078737626128769504582400 

	Torsion points: 

O, [12201452815734744319/4, -12201452815734744319/8]

	Independent points of infinite order:

P1 = [-1061885199303113614, -13438166396821930695965658238]
P2 = [-7666539769156859440, -8289642574162821016677436480]
P3 = [5327609713098541790, 2539671936713653217982114140]
P4 = [2121832221529656080, 5350184553451769539475041520]
P5 = [5414518803419738660, 3087067553587538601612319520]
P6 = [2971945364209190060, 1369131240754368751222356020]
P7 = [12351298213903036280, 37155373829220331124571333200]
P8 = [334910154445166820860, 6127654170575785131355608617120]
P9 = [383695833739961228042, 7514597468793306339059329316492]
P10 = [33358723601631155032400/6241, 1309109399402868291804733819563920/493039]
P11 = [25353117800631553103349140/2968729, 90626337615556563707815779579029001440/5115120067]
P12 = [-37586223841485458708832415/6431296, -245504475872683240459449484023333477805/16309766656]
P13 = [16133503992634579813816940/2601769, 29388420857173821336387613744337139940/4196653397]
P14 = [-42488636178521660416264260580/30144946129, -73413294831371932452287754304542939817378660/5233855981755367]
P15 = [3721034315210006396548746764/1233765625, 38949376234014353810787505789687574666912/43336017578125]

Dujella (2009)

y2 + xy + y = x3 - 64190352133650606480221565034283908x 
       + 6257960443183058651654529269954235645237394699230806 

	Torsion points: 

O, [593026323000703735/4, -593026323000703739/8]

	Independent points of infinite order:

P1 = [92338140108743590, 33437230162544640827674142]
P2 = [45888040397788840, 58386796260042877248838517]
P3 = [118327323094807465, 17867031305490028104556517]
P4 = [148513842036805465, 692517542067274218021017]
P5 = [172149125104789465, 17588124111363414361101017]
P6 = [149362658107740550, 1575048851474566204300382]
P7 = [90809930693882340, 34317604453788783447746017]
P8 = [6531891904200723337, 16681550828050656824367212513]
P9 = [5304900745641500410/49, 8242351588161896607817145081/343]
P10 = [4057118166162754000/289, 359676992652357454978580374546/4913]
P11 = [-185551513370317493, -108536430701784246475738951]
P12 = [149177412176249215, 1410348578248129087948517]
P13 = [627880883076175465, 462045788287109723538216017]
P14 = [149175332254831465, 1408451932124928738328517]
P15 = [605045413439684339815/5041, 6016697840023330549800351640987/357911]

Dujella (2009)

y2 + xy = x3 - 216076975581241605290593269610764674033899535x 
       + 1221571297586610208346770805381771300462584021696247498228323684281 

	Torsion points: 

O, [34721934576424668841423/4, -34721934576424668841423/8]

	Independent points of infinite order:

P1 = [4692903629994832126114, 557580763456975389323748176870521]
P2 = [8288446428985899019896, 5604164256594277256921533635621]
P3 = [8700586735426579176976, 14528214339738708570436531898491]
P4 = [22705352275707976579462, 2832106340117461708951431179695429]
P5 = [8193139110687444322474, 34752799654833052215511638885985]
P6 = [502402501312525829364193/64, 48848246885900464467124744730118083/512]
P7 = [61388615253376870516486, 14808906533995279836662980833243781]
P8 = [292357223612325742950424, 157881679366676617068936044541587941]
P9 = [4440032215280265638736, 591365246082499749905575665561531]
P10 = [8142403554903633974920, 44904613685916539885100584832499]
P11 = [2001394459242343545502096/225, 195341032088543406641027339833689211/3375]
P12 = [2687520667923576749984896/361, 1096518199227105225096259946807930329/6859]
P13 = [-8316833945593347319097852822/564001, -464252352972379857781225887150917555638757/423564751]
P14 = [342403128920447282841426394906/6115729, 194050302246661180174450433586268407945564457/15124197817]
P15 = [-2559913076084793246254107406/619369, -696896633242884930073039942313463606139277/487443403]

Dujella (2009)

y2 + xy = x3 - 3832688764917421379334667773551764790415x 
       + 86844083576319836701329199109169248733271425836097421944441 

	Torsion points: 

O, [116261070514296540623/4, -116261070514296540623/8]

	Independent points of infinite order:

P1 = [6656130641062791966, 248250075852381303705305793261]
P2 = [24604175590483337310, 86246473587761149782907043949]
P3 = [27475413199124217894, 47754786650656801972471953885]
P4 = [-1118406126934827749139/16, -7356599929840944470824732652991/64]
P5 = [864255000994287004186/9, 20989213088703740811945773672935/27]
P6 = [-2414396542189864554, -309973611472605928026653192019]
P7 = [29050499342882413116, 4380977783221578307523092023]
P8 = [4106644802324513308689291/62500, 5382975137837119935597024106198350411/15625000]
P9 = [19434682709766691812774/841, 2512806449311780423862273924090625/24389]
P10 = [83242223929544333598966/3481, 19338975761480061820170171610980567/205379]
P11 = [290946951036997215911874/6889, 10016373364503557655929323347725607/571787]
P12 = [2073000081140995042435014/46225, 713605275654931885916906200776066507/9938375]
P13 = [115990700919341267419913898/1760929, 810070169470718030513694205901520253407/2336752783]
P14 = [374646133052716543292351379456/3423069049, 198099616279654496082477371586481353129471153/200273500849843]
P15 = [-2831668517610672068255879188050934/56078036629729, 
      -163521824048832949326475644095384985976592019308897/419941891408714619183]

Dujella (2009)

y2 + xy + y = x3 + 5951426409500892217936031442603949x 
       + 168382775057670806272015446735529656531537361718498 

	Torsion points: 

O, [-102020260065396217/4, 102020260065396213/8]

	Independent points of infinite order:

P1 = [-12424791682630248, -9618703592421505339970714]
P2 = [649064467008298733772/5041, -19828579149516242400501194545849/357911]
P3 = [-13817377740325239708/841, 198388696185516223761294953909/24389]
P4 = [267406725077795883/4, 235289186437254982731428663/8]
P5 = [7680740308109173692, -21287595448562703322767645134]
P6 = [33177298623841114783167/22201, -6051323485016661599273862091339666/3307949]
P7 = [4688944416563397926493/54289, 460739875476188684038560118520672/12649337]
P8 = [3476158666388532782148/11449, 212059593079260656203889309661923/1225043]
P9 = [20918078391406449524457/151321, 3547831924489188990973401942779054/58863869]
P10 = [42731990257498192073103/344569, 10729050986786556651175311836767418/202262003]
P11 = [-3534030474178283434347/146689, 186482162185567453519589074939382/56181887]
P12 = [180314539432342509037818/49729, 76585254534124261290293631017874172/11089567]
P13 = [-11296619573965647, -9985498106090620778112026]
P14 = [162430145824668823775955423/222695929, 2082134835367473153917387197736713666402/3323291348467]
P15 = [-607297056212820021753/28561, -27399578274434621895741420849626/4826809]

Dujella (2009)

y2 + xy + y = x3 - 1845405794077345534197002132615516017x 
       + 964836926172330152442989919849549759511718286466193960 

	Torsion points: 

O, [3115203349441793703/4, -3115203349441793707/8]

	Independent points of infinite order:

P1 = [377232811201533739, 567777484966206577250824784]
P2 = [240220266122144494, 731707012381939466824649426]
P3 = [25593867136891148734/25, 48180068099861572701196566538/125]
P4 = [230055802634309182, 743280884246136620278228991]
P5 = [1799380166907405457, 1862854700132552784079187396]
P6 = [1028418916861582507/4, 5698391196106618483711120339/8]
P7 = [19224634837106858161/25, 2731533966235473453779595394/125]
P8 = [645874988828094241, 205827933489236149819383284]
P9 = [845472178947190390, 94661509291150249920590879]
P10 = [794758098965046565, 13677627110943926048205554]
P11 = [-5664717206176434197/4, -6872667962844103726423989377/8]
P12 = [94070119515168716830/121, 8363542567184594681618226550/1331]
P13 = [344815710000483208, 607873236483237593958414368]
P14 = [-1123616547360931634, -1272707203719137051217594766]
P15 = [51576640452005053219/25, 304614140019074310163794180712/125]

Dujella (2009)

y2 + xy = x3 - 1191804730500424033925604503925418545x 
       + 631829803982594793008749008719966270203629849711747561 

	Torsion points: 

O, [-5183611506357375057/4, 5183611506357375057/8]

	Independent points of infinite order:

P1 = [861407141938567194, 494352075703123642302887835]
P2 = [918439928425639128, 558535703339782296632701443]
P3 = [3990520294451192010, 7708564099020598545996069051]
P4 = [956241737300303274, 605443769694831855482381595]
P5 = [-1159505055649479030, -674414229196683649544657541]
P6 = [-1183724535013522422, -619644266423586806790276357]
P7 = [1117087283917683210, 833351811529088132299379451]
P8 = [55261675943408932506, 410725937876108594719488514251]
P9 = [-1264503621414418422, -342006715751146159765609221]
P10 = [2248663936346095370, 3053228956455997385505067259]
P11 = [-1119777581831190774, -749863227610776343713163269]
P12 = [5808073305897428482074/5929, 290315134276388068122765020013783/456533]
P13 = [-1027318273748523996, -878623075427420577555378645]
P14 = [809655060417532253551290/19321, 728290247372252363902684632032551809/2685619]
P15 = [-44598679156783280198/81, -771885934254687294880060767389/729]

Dujella (2009)

y2 + xy = x3 - 1573649343823368540876031311163x 
       + 759700447776441994545662848372757124914524817 

	Torsion points: 

O, [2867454628160783/4, -2867454628160783/8]

	Independent points of infinite order:

P1 = [736514034219422, 458051495820921115889]
P2 = [762611160455882, 1770332236107660810509]
P3 = [241155905932406, 19855233918376765321505]
P4 = [194771754151600022, 85956748191903474189783689]
P5 = [612475617028382, 5063037998649968258609]
P6 = [681223001784722, 1955995370438330716889]
P7 = [713586963578522, 357500952850315853789]
P8 = [731750663034422, 63240180691528105889]
P9 = [-1090062926727778, -34348564992167678404111]
P10 = [198536812179296486/121, 67803436219902817183508299/1331]
P11 = [18330212232534656/25, 29680366770573301551739/125]
P12 = [731632950881882, 13316104610295872009]
P13 = [-529228154016012418/529, -444176165192718284305398761/12167]
P14 = [229711193000672, 20256771678786941459639]
P15 = [241584278923634357/16, 118344255883242245864080061/64]

Dujella (2009)

y2 + xy = x3 - 2360001638573495470166776973829890x 
       + 44062209861456503824552700986268012124494211867396 

	Torsion points: 

O, [115715265331868383/4, -115715265331868383/8]

	Independent points of infinite order:

P1 = [138695773158732088, 48834041585953407884183434]
P2 = [-21427735520031344, -9208322426930304955308494]
P3 = [122024281723192576, 39661280154856350066892738]
P4 = [29242915451430202, 236442760796635738944484]
P5 = [27013575629484486, 151102416796596076503138]
P6 = [27147999645803296, 36590914487122413608866]
P7 = [27064561308150808, 119725915735084111653694]
P8 = [325408935966906376, 183668087126791093681170238]
P9 = [32346505156149730, 1252372313833603977888796]
P10 = [8017811252386926064/169, 13699439601885268151273553082/2197]
P11 = [25919578616563216, 552604042585419645044146]
P12 = [58444300755232240, 10284156882845797880482366]
P13 = [5297168817039049090/169, 2065916661763672627482293482/2197]
P14 = [42396309523743608085952/1212201, 2768805689186555149986676959183254/1334633301]
P15 = [27689547135677436230486824/2809, 145704773233526650421493285148485147026/148877]

Dujella (2009)

y2 + xy = x3 - 29839290725011012608171999345220110x 
       + 1979236691612664032853709351618739821303730471684100 

	Torsion points: 

O, [382942867905233439/4, -382942867905233439/8]

	Independent points of infinite order:

P1 = [104055539767636020, 979951939413316844260290]
P2 = [-77910922428754800, -61896004229566068154716990]
P3 = [-158634451561350630, -52160883831840971076503610]
P4 = [136380331090699116, 21127309924083585418274082]
P5 = [103704076736092770, 264148683676886896418040]
P6 = [103891595223881600, 731658946815154839409790]
P7 = [78542926598100360, 10959110452891654057310550]
P8 = [22249040735911952220/361, 132699329269172752257790177110/6859]
P9 = [77962943459291520, 11258495475392498916401790]
P10 = [2892044005014469440, 4909633704758863831341920190]
P11 = [29702537616691646700/841, 759365459976651459041874766890/24389]
P12 = [2253185823247335540, 3372510043584688508852607690]
P13 = [60794880538044868620/289, 347792255535348172218586768770/4913]
P14 = [43840086636328260, 27483416717952599595420090]
P15 = [120303314488017510, 11428361550061020438054900]

Dujella (2009)

y2 + xy = x3 - 52047907302382016235549131295090894646019785820x 
       + 3765690091100200058431161279696704551339371810396491596556107365008400 

	Torsion points: 

O, [334240738101248507823679/4, -334240738101248507823679/8]

	Independent points of infinite order:

P1 = [-226726794406241886345710, -62541550125497679750178354043322320]
P2 = [80660418899939250341530, 9605680241206220455533159406048630]
P3 = [-78503787017029986138824, -85836130403386795200338467574987948]
P4 = [18060892589840047442770, 53212308875250653079279662542846000]
P5 = [286846533297908224584790, 111525462986250228094538136374449930]
P6 = [-161903632726418085382748, -89154304634803075355145476587033388]
P7 = [6248194206770294705387134/25, 9975699567650320102952960556495876842/125]
P8 = [45683444076070057473711385/1024, 1282766964613917190418072190307433353715/32768]
P9 = [183067127590016104869280, 19304475800265167800102660259717380]
P10 = [68283633159716705800240, 23022877219974364688898122570810380]
P11 = [17927790054625059635730, 53276150661689532034466985454173630]
P12 = [223487691292636503423859036/961, 1939610640296642172955445080027985450092/29791]
P13 = [230439101875043256443380, 63313787355496990080418298872886740]
P14 = [-113500218737183810275040, -90614541472246002278350760031709220]
P15 = [165744198177068383243645360/121, 2105599790468472939249034142714170830860/1331]

Dujella (2009)

y2 + xy = x3 - 4562085945883852510841543387549451275x 
       + 3745932842931265406265852327213395046483588868755572721 

	Torsion points: 

O, [5073086876276604943/4, -5073086876276604943/8]

	Independent points of infinite order:

P1 = [1185670516548425254, 60290420205775826394371881]
P2 = [1554321264148312594, 640385095371248235429151561]
P3 = [1293507567454295806, 95329079037031587947012161]
P4 = [1194410272462791934, 29920057751113875403314625]
P5 = [1765415189937321430, 1092799287332515989409668049]
P6 = [1359944139997096630, 238530608278523772792626449]
P7 = [1268274168995901694, 803407511955856542413761]
P8 = [793112856142726942, 791564288933005478426171809]
P9 = [-2463270085030832162, -192872978664982906262683967]
P10 = [1195935897826785646, 21747727978699644235464433]
P11 = [5906688287408888524, 13523215707481836000826510705]
P12 = [3249716208080624692, 4820744892134994527136441259]
P13 = [1146058813103733988, 151016246821093755237086683]
P14 = [-257979112036754762, -2214878412585172045518930671]
P15 = [777239190765714276539326/483025, 253758777295151476729268215096353191/335702375]

Dujella (2009)

y2 + xy = x3 - 895188084269145089286863460663926876363x 
       + 174411902397937497301876066491132779199450021157173123695217 

	Torsion points: 

O, [-244790903976707730417/4, 244790903976707730417/8]

	Independent points of infinite order:

P1 = [-56208049714625469098, -217136054543780599865255218151]
P2 = [263136744223006025758/9, 11237704697306115895520358615163/27]
P3 = [210692298707136365902, 3055928019781625445774620416849]
P4 = [1382244946363664051992, 51379526527706257051508409423679]
P5 = [471378523144860711118, 10222116651064412893780823047777]
P6 = [197633088076739262862, 2777915007465310417538696769169]
P7 = [-39332470236945751688, -385710811174441890323945181281]
P8 = [-60001773959891724458, -110025524956517462086701436271]
P9 = [305708133622801442062, 5335864709479243900715927647969]
P10 = [-54715317696554955548, -244105603226975437432020345701]
P11 = [41465211393216032206, 456712733375870970748217284705]
P12 = [-68126312633788247805572/1369, -15671728840767178720272032268898643/50653]
P13 = [3542390282687699337238/49, 239493942123094121816986612422367/343]
P14 = [-375671919223128356804348/36481, -2976988205974255215147869803725661441/6967871]
P15 = [61998940850057486597939962/72361, 487945961159791356629605295302613872961/19465109]

Dujella (2009)

y2 + xy = x3 - 13397943136358263756130318190185x 
       + 18870818293000775719167980823166925265792205401 

	Torsion points: 

O, [8340799720431663/4, -8340799720431663/8]

	Independent points of infinite order:

P1 = [1029022500230176, 78572591474967918603931]
P2 = [1578163880681536, 40709276641363021726171]
P3 = [-4141305136555478, -57712347640134375649421]
P4 = [2772428055260890, 55098615113008600208131]
P5 = [2082907841381770, 918540150707067712339]
P6 = [2054126279090674, 4123475144428102233115]
P7 = [115634161138496260/49, 6821596742053021577949397/343]
P8 = [-26892431106076454/9, -4846927644106656067145023/27]
P9 = [3487894012418428, 120713935554030864221923]
P10 = [784680557315050, 94025842467281956796899]
P11 = [2074435621130440, 2128765595701496186731]
P12 = [2085104685677122, 183713608378515394219]
P13 = [344467348644442930/169, 12089068728914504633365327/2197]
P14 = [709694235667821055/196, 366416357361358895030672471/2744]
P15 = [962081214366697076323522/421768369, 115631260259264430062170152953273099/8661856994153]

Dujella (2009)

y2 + xy = x3 - 26203137369313475904909479991597350x 
       + 1632588248343784552178712665324524152998828231119332 

	Torsion points: 

O, [373285797610436767/4, -373285797610436767/8]

	Independent points of infinite order:

P1 = [59549633938477024, 16833700528201574270280118]
P2 = [142046582091770104, 27868062533359288629172798]
P3 = [93274704391961212, 64696982221012348829530]
P4 = [78145765592565948, 7882988374248474895119786]
P5 = [684958047878659231/4, 372393506811855101207034689/8]
P6 = [67681777904086624, 13005828409820242938903658]
P7 = [18545044388765704, 33956264357289240390706798]
P8 = [93878451789280234, 210818795047112930964238]
P9 = [-92860659540334376, -57140895283433808760604342]
P10 = [44759254234233748, 23439830203467504321316906]
P11 = [93314292004238524, 23697769720367464594858]
P12 = [109253370530755312, 8595816756811177577059558]
P13 = [1463036831810415877/16, 67986161922212409371476357/64]
P14 = [11355408569171190402484/96721, 397347003746862898704297622297838/30080231]
P15 = [53034961459735260724/1521, 1636729460945517094620676211342/59319]

Dujella (2009)

y2 + xy = x3 + 13842139136873585658473535883368685x 
       + 2310578587702287143012929957420435535344485058013217 

	Torsion points: 

O, [-393203196144086129/4, 393203196144086129/8]

	Independent points of infinite order:

P1 = [122297614621067374, 76371517653697877352456313]
P2 = [-83732000697566876, -23759198445595187766047687]
P3 = [25441067662683214, 51761028418949259675488953]
P4 = [73953816612765874, 61145100990660665734144813]
P5 = [34832022390612950254, 205575107269815996538774839193]
P6 = [40055275609337374, 54122961609888925621386313]
P7 = [41494881996289582, 54372819039684046901077753]
P8 = [-41972894336652626, -40689547714679739179783687]
P9 = [3136354086645978414, 5558520651891938736366377433]
P10 = [-82923898375968626, -24341709003753460397711687]
P11 = [-82532657984748626, -24616403601647205397451687]
P12 = [-5623744936084986, -47249931938065315398104247]
P13 = [62724008442088794946/529, 912025929019355834260539572171/12167]
P14 = [665259823510317866494/121, 17162848762624869194438013238523/1331]
P15 = [6421783216109867310766/10609, 526871501011269788489694652535551/1092727]

Aguirre - Peral (2009)

y2 + xy + y = x3 - 14820294086928440424633522968703528226x 
       + 20765370987006393364428714101869184104544076455919147848 

	Torsion points: 

O, [7138903811934943383/4, -7138903811934943387/8]

	Independent points of infinite order:

P1 = [1142687090237852047, 2307045166112381109556799501]
P2 = [8538340000747454752, 22730978781324680005318100936]
P3 = [-2938001851485078368, -6240754507140851573712826729]
P4 = [4519718638237366132, 6790432653435836534972724896]
P5 = [-4399782995495761643, -894456200716891484237546629]
P6 = [1167203606452177252, 2248827862185965551133374811]
P7 = [-4415257613906420453, -357139516675029881971205299]
P8 = [2829152545920864871, 1217098931080161959291845661]
P9 = [1602776380021527877, 1062597429669885420210475811]
P10 = [144259304021613728053/49, 558492855415512636309518549093/343]
P11 = [-329828490410340974781/100, -5810845574934199698547692173573/1000]
P12 = [3450371693097114133, 3272116507099433546478160379]
P13 = [23983607481083649847, 116021611445599271376426720701]
P14 = [84128017524799962919/4, 759472289952908112284550429361/8]
P15 = [10186146099222737998/9, 62983720860821152551957010052/27]

Torsion group Z/2Z, rank = 14

Fermigier (1996)

y2 = x3 + x2 - 1692310759026568999140789578145x
      + 839379398840982294584587970773038145228669599

	Torsion points: 

O, [809823326908353, 0]

	Independent points of infinite order:

P1 = [866442291552879, 4852554862534554468168]
P2 = [643619051198181, 4097833397957401859316]
P3 = [310789314615903, 18532307930418477983880]
P4 = [935470575993669, 8654920131154858324092]
P5 = [988927329611391, 11530632350958995292984]
P6 = [832699306754277, 2752675553616194984436]
P7 = [2252513103656559, 91957939555201321662648]
P8 = [690291245594778, 342430653544628328855]
P9 = [2191409680250085/4, 70052106447307921537881/8]
P10 = [681925764652050, 1568465432141985518043]
P11 = [244337019116010, 20987431811752700667807]
P12 = [982479697930607, 11183605599461162465976]
P13 = [75293021661996670215/22201, 610918230634190643034903681368/3307949]
P14 = [1177083061299989778618/1261129, 
      12096101176020871187811506551077/1416247867]

Kulesz - Stahlke (2001)

y2 = x3 - 12980282175768890811438819732x 
      + 116802985717915987899448766677826872704944 

	Torsion points:

O, [-118188654139412, 0]

	Independent points of infinite order:

P1 = [6607378832738, 176990975394487960300]
P2 = [-103557136527662, 591987135009508933500]
P3 = [623445113629378, 15308407213006350954420]
P4 = [-655755381332, 353998013583629010960]
P5 = [-54341822899562, 813450641210644821300]
P6 = [-101353861608362, 625489006156183529100]
P7 = [-71527319807162, 824198245522092094500]
P8 = [-52956155250062, 809741315448326067300]
P9 = [-18026547302282, 587311513851766998060]
P10 = [-69415283384042, 826653910581533974860]
P11 = [-7975654090532, 468851667964437988440]
P12 = [373258347587308, 6875669199226331967840]
P13 = [148248807617938, 1204433799812463413700]
P14 = [579564746423857/64, 139391042715474957225/512]

Dujella (2001)

y2 + xy = x3 - 7372911492530406268416156245x 
       + 243594391906613268628507257344604677608161 

	Torsion points: 

O, [195391032383343/4, -195391032383343/8]

	Independent points of infinite order:

P1 = [-72376481830226, -630940588803637101569]
P2 = [56312693537242, 83547350623177255879]
P3 = [50545746944914, 7938107321308587511]
P4 = [-24664074799982, -640653456150957147401]
P5 = [48768170604178, 4243475038421673079]
P6 = [44275623883186, 62841111181852200343]
P7 = [44033644751050, 65709829875594008719]
P8 = [48781448921950, 3856666655607214531]
P9 = [48831932859328, 1852759677330985393]
P10 = [226433646572535934/361, 106787838011896189595371765/6859]
P11 = [153942078863442, 1660342552186148579319]
P12 = [2829817753498450/9, 145424908163363854584413/27]
P13 = [6692769349018554/289, 1434645063716592596334423/4913]
P14 = [270782451612808972/1849, 120702043132790721191878453/79507]

Dujella (2002)

y2 + xy = x3 - 9468594009199910821775026235x 
       + 391555244342706113038825183927385153742225 

	Torsion points: 

O, [-454561868024561/4, 454561868024561/8]

	Independent points of infinite order:

P1 = [47837672254570, 219256739278969879465]
P2 = [159012385189570, 1704860597983625569465]
P3 = [113203019208730, 877707099875585260105]
P4 = [-379785557030, -628610550798257040035]
P5 = [150694553832070, 1544923707786326053465]
P6 = [4423977031795/4, 4938562614739635671195/8]
P7 = [-105239107838570, -471667325486574870335]
P8 = [-97378850096330, -624649787995923803135]
P9 = [2781894749213470, 146638885030002257302465]
P10 = [5956132655951830/169, 700376526525629066927605/2197]
P11 = [5727420806916370, 433387520147639397982165]
P12 = [2510868216033430/49, 69378911457566195617495/343]
P13 = [29411611466070, 372170566570883535465]
P14 = [189299897497282, 2320045014085200589957]

Dujella (2002)

y2 + xy = x3 + 3316490747528662771547963488767495x 
       + 73682323027772693525742362632573935085905483165177 

	Torsion points: 

O, [-79425459402809553/4, 79425459402809553/8]

	Independent points of infinite order:

P1 = [42094543239920394, 16966966004633078487992403]
P2 = [27540919289973114, 13634932178069643502918323]
P3 = [44598680591423634, 17615393735713734372514443]
P4 = [-1136456995004838, -8361328012699544626237965]
P5 = [-15098621421260856, -4490643229989030974701347]
P6 = [26579506093367994, 13439145664988645954960403]
P7 = [-1917696386868006, -8204587024706744054523597]
P8 = [419077623404760282, 273979011551621447610165555]
P9 = [-2044470545809506, -8178833031796563463824597]
P10 = [359645054924887740306/169, 6822943308980403701468300739351/2197]
P11 = [207192901970717874, 98261888491687585278481443]
P12 = [196062307481841535386/49, 2745594468228521388878051373909/343]
P13 = [282299098535186380866/289, 4751544447032516633024737563339/4913]
P14 = [65052368021618394, 23763779112715350509257203]

Dujella (2002)

y2 + xy + y = x3 - 12949314925486190388475166345996148x 
       + 567175248136512872178139054853895538293674461867078 

	Torsion points: 

O, [263129338838302711/4, -263129338838302715/8]

	Independent points of infinite order:

P1 = [65601277223770979, 23563368510169401694305]
P2 = [66125889214142084, 185860513983389743561770]
P3 = [-69485744108634566, -33637363010212406099385505]
P4 = [-32331867075002041, -30855350764246689879332355]
P5 = [65800723636725209, 25822487830178626473645]
P6 = [65788305691643459, 14208407210362871438145]
P7 = [63871447749001739, 807017461103066030534475]
P8 = [66025536242433209, 140081934594192315807645]
P9 = [64736942716038959, 424751832934349364408645]
P10 = [-14167608711707416, -27345791928090461105989230]
P11 = [2020573482310072484, 2867722481686210471818712170]
P12 = [-43599334996233586, -32386396874479931764271565]
P13 = [23541087505805298449/361, 1465209842401319333313932055/6859]
P14 = [39933036650693051/4, 167598351724390091167288575/8]

Dujella (2002)

y2 + xy = x3  - 199429807965769527099340083105123887569092655x 
       + 946696238553698249107052023781560988843839015226125020059567966777 

	Torsion points: 

O, [-64290689047140226735153/4, 64290689047140226735153/8]

	Independent points of infinite order:

P1 = [5639318228208776052212, 37271684216749719028429712708303]
P2 = [15704314119697504774094, 1299181253016152729254527327109253]
P3 = [5646086610056830399244, 26189293677432863920539989800103]
P4 = [8483687132452927799891/4, 5841982001348824946858354165397079/8]
P5 = [5291742343771787729174, 198865004663386643794432850951933]
P6 = [563809874246061125624, 913474120253834186871652935806243]
P7 = [986165512420371070374946/9, 971508041876787699448435768073304131/27]
P8 = [2129108697489953593600229/16, 3089765187069780494937336263780777717/64]
P9 = [55517454259089667567694, 12688186520170214767232133089825453]
P10 = [12733217275021471264502, 686885056742081034745356367894925]
P11 = [87980925084778734722696966/6889, 
      397287764237169029978161387104794075311/571787]
P12 = [820513627981586695423544, 743129902037346668451025626696015203]
P13 = [5258429421462479540535254, 12058200726631987221580325174355239213]
P14 = [2872756878358176252959674442/508369, 
      4912881888067244704270816163064058926397/362467097]

Dujella (2002)

y2 + xy + y = x3  - 1773871677446826525005545991723918613373997023x 
       + 28749498729292324150415916003880104290244501502154076094544626253078 

	Torsion points: 

O, [96051482732372697840711/4, -96051482732372697840715/8]

	Independent points of infinite order:

P1 = [-47044310997606458664291, -2843086997644656346080364015494980]
P2 = [23745203486730985504984, 130093056208578535670863801614170]
P3 = [205573821123733735733881/9, 10414838935169185953308935885141790/27]
P4 = [15696202411860401264209, 2184842169148806945167348397048020]
P5 = [-17291536024932555789791, -7365619021860070584720462749450230]
P6 = [39131903091467280157879, 4388329507640944379855417135264990]
P7 = [20079751914859584086119, 1107555842610401088236193721385750]
P8 = [24010761905126646071959, 9651119797335609647441543876270]
P9 = [31504114780415394538839079/1156, 
     31628049196167576342016172027834709605/39304]
P10 = [26921537270076604490689, 711369417084865847526978127961300]
P11 = [95284429954576796577751/4, 842207664122997953807518180209025/8]
P12 = [23195498903484427434279, 289070198352919962487571429038390]
P13 = [116445120400296998088803386/5329, 
      252612413972703463025231084884895504840/389017]
P14 = [8327200301669504405477307229/281961, 
      218023730294084529820717977462112475769460/149721291]

Dujella (2002)

y2 + xy + y = x3  - 26363867662083075045300295608x 
       + 1621855500711191032644827748500946408874618 

	Torsion points: 

O, [335995856219831/4, -335995856219835/8]

	Independent points of infinite order:

P1 = [-13523214151261, -1405669456443029816745]
P2 = [108064574225729, -186623470209939903855]
P3 = [-9283400340886, 1365943554420666161130]
P4 = [45091038864014, 724403525277098828655]
P5 = [-39381624677386, -1612150715652115017870]
P6 = [103202418965714, 14921148085177587930]
P7 = [229522556724614, 2768056987261476921255]
P8 = [196487519758739, -2006874802546559401995]
P9 = [248201700083864, -3220021411044645365370]
P10 = [121414876687139, 459059783092694170455]
P11 = [105113501512604, 109727698460088223125]
P12 = [-88622695886761, -1806170337626894748495]
P13 = [-152427507622741, 1448762069584790066925]
P14 = [82158932261969, 102021930719234171685]

Watkins (2002)

y2 = x3 + 402599774387690701016910427272483x 

	Torsion points:

O, [0, 0]

	Independent points of infinite order:

P1 = [17715373576525779, 3562569314711466369088086]
P2 = [2626434695669379, 1037072601415883504491614]
P3 = [2569230493256067, 1025344316293086716196318]
P4 = [235538747268099, 307962520197557881526046]
P5 = [72777729441003372, 20366017444893924849237282]
P6 = [208383733118864688, 95565185470960061947766676]
P7 = [36178079522739, 120686925577870348570566]
P8 = [103189419061250643, 33768487838255557704513174]
P9 = [1751414347117072176, 2317991574180462284959749972]
P10 = [306104494367228425/4, 175082211930567255911081155/8]
P11 = [54693351931994304/25, 118007688830447299097189592/125]
P12 = [2696555916804876, 1051304226981395145047478]
P13 = [2842774711299072, 1080497092155012281695968]
P14 = [46439279877409015377/1681, 391130341466321391183789029622/68921]

Aguirre - Peral (2009)

y2 + xy = x3  - 364003597619839345303475845x 
       + 2661752594229761591647083926409872269121 

	Torsion points:

O, [10425279415922, -5212639707961]

	Independent points of infinite order:

P1 = [8843705675426, 11588270988956470823]
P2 = [-8622686155982, -71828530978734086777]
P3 = [-384019630966, -52929013493014332745]
P4 = [4037474716010, 35467066700728688759]
P5 = [-15484349407750, -67716351166827878761]
P6 = [10407391606610, 829899092205015431]
P7 = [10208626601660, 3111039289244693309]
P8 = [-17158466998714, -62095246818053375809]
P9 = [-5262124352014, -66569335769569265977]
P10 = [6398763865059122, 511849395123434923792199]
P11 = [38581505585459/4, 55507478604745283059/8]
P12 = [206949572689130, 2964893429706509319071]
P13 = [-15809709094798/49, -18082196507376854582143/343]
P14 = [13018891934150, 11376338678435580539]

Aguirre - Peral (2009)

y2 + xy + y = x3  - 61921000404140250035010966476x 
       + 5493922843641638281057255866260479093623098 

	Torsion points:

O, [110535006781577, -55267503390789]

	Independent points of infinite order:

P1 = [276709309010457, 3089804955456605283571]
P2 = [-140803625339604, -3379511618361877054658]
P3 = [-242605053208503, -2497441255528243176149]
P4 = [-176570164560918, -3304904144947723832654]
P5 = [186197514016122, 647891768238453001651]
P6 = [175403497429593, 171156787111345109539]
P7 = [267212553335622, 2833286220206723715151]
P8 = [-266079063701403, -1769723283772507723349]
P9 = [-114887262677778, -3330382886331318018374]
P10 = [98591391228357, 589389009871923343471]
P11 = [176648880552456, 260662906790218798726]
P12 = [628592122188957, 14661011011598808671071]
P13 = [-282921058183374, -605353164381882698558]
P14 = [65747283047932997, 16858293431372459634667851]

Aguirre - Peral (2009)

y2 = x3 - x2 - 509950789086030314489955920558837608x 
    + 140130321779001521948352158126853977618474636223309712 

	Torsion points:

O, [417597273365813017, 0]

	Independent points of infinite order:

P1 = [421784425516995336, 8795276442738182984128828]
P2 = [216718354653222922, 199482338162078619253026750]
P3 = [228939740140161472, 188100589775514770047943700]
P4 = [217059290797782778, 199166905584440511664138434]
P5 = [-264846618079782888, 506568587352219088674584300]
P6 = [432320713782075936, 21663163441240902215944628]
P7 = [2208923136415295173/4, 1312767005054781857676596325/8]
P8 = [406945271068122648, 457123088292887774269204]
P9 = [405467167559798122, 4721385460575752676403650]
P10 = [448466352960979698, 40386041195382624441426254]
P11 = [52791858740879247922, 383540208837412775340971459250]
P12 = [45468296293167051792, 306555968637434846759613213700]
P13 = [-188565259121537888, 479149805925427707694869300]
P14 = [85142953638912842512, 785611516955525651270791899900]

Aguirre - Peral (2009)

y2 + xy = x3  - 171200986856092494838171586102348100x 
       + 27265121712499053058689490946092296820255657246754832 

	Torsion points:

O, [238809532287939848, -119404766143969924]

	Independent points of infinite order:

P1 = [229878017126722824, 7578252134422291705612668]
P2 = [46046772421044032712/169, 63899629510414279194638881452/2197]
P3 = [-467820873188353848, -70504886426713749456023172]
P4 = [225232613354477184, 11448393809244239374788228]
P5 = [238544735139573384, 282153082748039443144188]
P6 = [12820346464911239976/49, 6710717361735586272666743844/343]
P7 = [271904260473719304, 28587582628424813436660348]
P8 = [238739776817239304, 105967530714749090516348]
P9 = [69199360871748022536/289, 2295721301593011509773590204/4913]
P10 = [4778690007204254297034/19321, 19310615287905564698504927539512/2685619]
P11 = [301739044508233224, 55492059141156736059283068]
P12 = [2149259858956761976/9, 487342124480143465911956/27]
P13 = [90787496504972068670712/201601, 18438964379691870018093443817104892/90518849]
P14 = [258024326194706315325384/8281, 131054784166053045654354134426350068/753571]

Aguirre - Peral (2009)

y2 + xy = x3  - 1509728080370551903948467456595x 
       + 699861599603435695418146285237400317340485025 

	Torsion points:

O, [789403541630990, -394701770815495]

	Independent points of infinite order:

P1 = [901203265748942, 8439049844516759607737]
P2 = [847459673233190, 5391030562491286056905]
P3 = [8153094929272670, 728252172911546180927705]
P4 = [1589603835165710, 48131768013432489280505]
P5 = [536414048510990, 6661083956191151680505]
P6 = [407148514203470, 12356011630808400704825]
P7 = [8141986371716470/9, 232981045327907647187755/27]
P8 = [890735173845430/9, 634018628763684261869035/27]
P9 = [998059415789276750, 997089780595240903063354745]
P10 = [-34289610585213646/25, -1724349355117084566220727/125]
P11 = [1311303328338062, 31224312726348506905337]
P12 = [566062728872270, 5161645962821658275705]
P13 = [174308857896364750/289, 14483902246919906242614185/4913]
P14 = [-32634001782859802/49, -12879328857736723109531609/343]

Aguirre - Peral (2009)

y2 + xy + y = x3 - 101715916348577317389705969215206393x 
       + 12481057169848342962649256704133118757859512528137008 

	Torsion points:

O, [724255796041028647/4, -724255796041028651/8]

	Independent points of infinite order:

P1 = [136568358231527974, 33719527062689548014258455]
P2 = [187460167224703009, 985462304309209428366260]
P3 = [84617872792264474, 66932445540503951848140455]
P4 = [192224114804057089, 5613148301631764005909460]
P5 = [165023898509353369, 13768707447013446039987740]
P6 = [9563353724439859, 107280876786316688598199580]
P7 = [148064320915294819, 25818202469507788980403940]
P8 = [33974734236243240229/121, 103592716910054585002802003920/1331]
P9 = [29820429356099191243/4, 162697028115897090160900464715/8]
P10 = [35025833700458628886/169, 38207960747516643883506845930/2197]
P11 = [187583266015553539, 1198379442955705370665160]
P12 = [-6642979716088253999/64, -75804610470633667452249427715/512]
P13 = [208606508319737059, 18447674834055244897274660]
P14 = [41126650109180847961/169, 101626662169245451435447956980/2197]

Dujella (2009)

y2 + xy = x3 - 91850566882818096919315x + 1037306571339910255836508005644277281 

	Torsion points:

O, [-4170082397297/4, 4170082397297/8]

	Independent points of infinite order:

P1 = [-996479609134, -373306111797408307]
P2 = [1931413067938, 2839851910855975069]
P3 = [2368432972490, 3755718401298815621]
P4 = [-22038014750746/25, -82278434916377213243/125]
P5 = [-45431381814754/49, -195668853202643488417/343]
P6 = [15929753656846/9, 68410268470418517715/27]
P7 = [120539589837944, 1323406612061547270311]
P8 = [-76374786569194/169, -2182139658362122909315/2197]
P9 = [4322187601621/16, 65022456752560397389/64]
P10 = [-1042515559102, -3995834311749247]
P11 = [-656482032314, -902596833950329079]
P12 = [142736460327974/625, 15844097570647185301457/15625]
P13 = [-959497727296, -492024863758482385]
P14 = [14049252923996084/11449, 2039761707301937603588713/1225043]

Dujella (2009)

y2 + xy = x3 - 54577758097861548710739028530x 
       + 5829104169635539327474318664633772807972996 

	Torsion points:

O, [-1100953370271777/4, 1100953370271777/8]

	Independent points of infinite order:

P1 = [-116302822057212, -3256301401692409369986]
P2 = [48820560870036, 1811338882476833939646]
P3 = [-82006214698800, -3123031522331208597486]
P4 = [53696637658020, 1747365743628206652126]
P5 = [-58958495358780, -2973546808099445601474]
P6 = [97000590691524, 1203211931607552057150]
P7 = [-197844308014524, -2980420643943555580482]
P8 = [1451728618080468, 54645568837094816108478]
P9 = [164930874869964, 1146310672974976323606]
P10 = [-25683631451820, -2685873590703554670354]
P11 = [1272270665166600, 44674165801264507888314]
P12 = [555267179583012, 12112999111899305672574]
P13 = [5082185543349252/49, 388688014340518164369042/343]
P14 = [1377885568827204, 50464219610883673426110]

Aguirre - Peral (2009)

y2 + xy = x3 - 1987692401077923895199708829309x 
       + 1075883914107800804285521609739811088223454705 

	Torsion points:

O, [780221277132770, -390110638566385]

	Independent points of infinite order:

P1 = [-6252531406974, -32989570755456660464817]
P2 = [774912962810082, 960660275395742000655]
P3 = [778342175367138, 558257464266854218767]
P4 = [778673993483586, 505389880145837919951]
P5 = [780071218471602, 155822187196530342063]
P6 = [510535849964298, 13934318811473071081047]
P7 = [878608181042498, 2779342419882922353647]
P8 = [6941008438579170, 567168762820334418324495]
P9 = [4597815053077056, 298553522737307073390873]
P10 = [929930438817762, 5625368006425945052175]
P11 = [-1038003055448094, -44952395985144102073329]
P12 = [2352743404413186, 97070762501062975717551]
P13 = [543932534071266, 12475681836520517925903]
P14 = [-131210337134664812/81, -4896776800349876932543387/729]

Dujella (2009)

y2 + xy = x3 - 47847763372758290648644402243255x 
       + 127351524490807893375157005788342713513098443177 

	Torsion points:

O, [15742887693283151/4, -15742887693283151/8]

	Independent points of infinite order:

P1 = [2402192630678294, 162092266368711928387253]
P2 = [-3391843101653806, -500621445843756363450847]
P3 = [3898541733166694, 8216220130453507683653]
P4 = [32377754126076766/9, 1138429748985801612624391/27]
P5 = [390366006792027974/121, 107844827632800665778236143/1331]
P6 = [-163904684517556, -367681375287588486702097]
P7 = [4075783435005734, 6431233972466766702293]
P8 = [4280103056359694, 31089897478920261972653]
P9 = [16470707761625651/4, 96727117093963215845599/8]
P10 = [9925993664878474364/1681, 15518946541291953916348858663/68921]
P11 = [19820967570789886694/5041, 828900104352225901270695523/357911]
P12 = [3933675401213972, 1693998224614066185845]
P13 = [4431526619262194, 48384960945654700025153]
P14 = [487580757398702435654/841, 10765620460399382973566818211017/24389]

Dujella (2009)

y2 + xy = x3 - 7563016932293571961417207451x 
       + 386369359779887273958016110137382888086481 

	Torsion points:

O, [-423545465356529/4, 423545465356529/8]

	Independent points of infinite order:

P1 = [66767376437326, 423140231789716881937]
P2 = [-9144873957554, -674364453464665338863]
P3 = [12529961180047156/81, 1245305883208100001392323/729]
P4 = [-104289251220674, -202076618783126154863]
P5 = [-101540199122414, -327716768598151710983]
P6 = [-47091677018864, -798807075201939840953]
P7 = [17546944193347186/289, 1909121817951638820440069/4913]
P8 = [6496704677251840/49, 449100315418851513581233/343]
P9 = [-105826098639194, -39625584501587663903]
P10 = [256380787837048954/3721, 99553155072107759480970913/226981]
P11 = [41025161952201947614/2518569, 2067236229026733299084170388891/3996969003]
P12 = [255111346692991103824/16834609, 36237644966030676192257928030959/69072400727]
P13 = [39628940233241058646834/267878689, 6939397994014654564678230871020311/4384370502863]
P14 = [17246400470544478/67081, 10772216401655188406489710603/17373979]