Torsion group Z/4Z, rank = 12

Elkies (2006)

y2 + xy = x3 - 1086750289534747727483801311783198679020964x
         + 435973165715323898311705750809969552813996511661336976727731984

	Torsion points: 

O, [608652855284830069192, -304326427642415034596], 
[765575145621101788360, 7258912294053670714797672847132], 
[765575145621101788360, -7258912294819245860418774635492]

	Independent points of infinite order: 

P1 = [667212090873280716424, 2811468741600154868659805081692]
P2 = [588300445738899279592, 496738531576486238655704034844]
P3 = [640878480652690741030, 1650227478438617514410537429218]
P4 = [594914072761535795656, 61252759091705020914823536412]
P5 = [638462258521963853092, 1543723151978346502319214760144]
P6 = [611110705367872899304, 267524019061985430016982751484]
P7 = [594950966257051623880, 53222697163458916334270893852]
P8 = [716616869926847885656, 5020041299716878281470542342412]
P9 = [627762722675286133960, 1069751374718071593281800264732]
P10 = [510340803979604535780, 3778525680405340851280110580752]
P11 = [617601639147843518920, 606053623188294616739131272988]
P12 = [610092172393399908808, 198061390862962920112854267676]

Dujella - Peral (2014)

y2 + xy + y = x3 + x2 - 204436185783252342785934887233210383183371840x
         + 1165977772244037776901948451219544033496456897571880326934385121505

	Torsion points: 

O, [8321256469951156635413, 202492403819802069202802590388693], 
[8321256469951156635413, -202492403828123325672753747024107], 
[-16576367231130988793387, 8288183615565494396693]

	Independent points of infinite order: 

P1 = [978748421021154077677013, 968189872097011478431309250996630293]
P2 = [40938350455374318726499411487/734449, 8034798036372727657292256069809358560313049/629422793]
P3 = [-1833858234229021806425707334957/129823236, -1643957467127684520633723817507798298370057463/1479205950984]
P4 = [466652543424944830571020577/104329, 19679459405477726600184522257021115789031/33698267]
P5 = [1855357476468407776750099333857/9048064, 2521230557158903421620671041761650894499866191/27216576512]
P6 = [-3057825789598843317991399927/474721, -486854952876376400114202289959672893443583/327082769]
P7 = [1316165334856113211967439783713/19351201, 1479078000627128774872361508989894420231052407/85125933199]
P8 = [1813152158641149066379817305273/226532601, 702396508269043497895380089462203516064428283/3409542177651]
P9 = [14504830996189006898486130877/4313929, 6440066697804847094677254799511744033478569/8960030533]
P10 = [5609636083108794972298867953144693/459099749761, 218252275733512453971818858150694480104231578525237/311071758345811009]
P11 = [-4174731052256571796429970002572787/492999175321, -523817741681937590070885889786485498002950586908993/346153947960711619]
P12 = [6380415804693738957573514663666885797/274098255263569, 13629281585957393563736821264699724609670040970930713421/4537946867595440433497]

Torsion group Z/4Z, rank = 11

Elkies (2005)

y2 + xy + y = x3 + x2 - 10920091632464590365831264648975539x
             + 437651494057993449247068775775947593191303103178481

	Torsion points: 

O, [63258054081367075, -31629027040683538], 
[96192118300939107, -16651818918278859993549458], 
[96192118300939107, 16651818822086741692610350]

	Independent points of infinite order: 

P1 = [12312962916337123, 17465954517603234702423470]
P2 = [67285511500842939, 2740790813470355147146630]
P3 = [45984212347729443, 5721494183071967029585390]
P4 = [63658075732213475, 681407101617676553902702]
P5 = [57081828073673891, 551746937417282363027054]
P6 = [46468625331642675, 5527304026709760117608782]
P7 = [113108473177593891, 25486327153555762916111854]
P8 = [-8906302459944157, 23112824697957639230384366]
P9 = [63489682889990683, 511303164918466268499686]
P10 = [-3704626064653973325/49, 9888282977010465021877712866/343]
P11 = [1685476156824117371/25, 350691194569447786722914054/125]

Eroshkin (2010)

y2 + xy = x3 - 615411322294732283803288785027250860840x
        + 5538719221187391635372324416383813743465156669756429313600

	Torsion points: 

O, [33031894622115968880, -145780032072398118828250407240], 
[17040500771125811280, -8520250385562905640], 
[33031894622115968880, 145780032039366224206134438360]

	Independent points of infinite order: 

P1 = [18053404313496660780, 17678035935154218667942954860]
P2 = [18328783455961838160, 20406585717086330830203665880]
P3 = [29608841568563327280, 115215822286141843190344794360]
P4 = [17294778830561783280, 8267224166145000557315682360]
P5 = [17083804568307863280, 3342124281341824097293734360]
P6 = [86478894245983532880, 773989414331611579789717868760]
P7 = [22441632017274878280, 55046282104980150351733662360]
P8 = [20595174804919271760, 39998625478512888593836472280]
P9 = [17624343157730840832, 12920054428777609733507610072]
P10 = [19406810773483363440, 30076980385559785010892114360]
P11 = [21533376366441332972880, 3159860490394902449468489594828760]

Dujella - Peral (2014)

y2 = x3 -x2 - 28988736544619415368095370719165120x
        + 2092184664137813418988486724511221531954993872509532

	Torsion points: 

O, [-198780831808763131, 0], 
[100472774249930694, -13923227690347515187963700], 
[100472774249930694, 13923227690347515187963700]

	Independent points of infinite order: 

P1 = [-89000242786181962, 62985827654559137516454420]
P2 = [321430220667349174, 161194476035051426899197420]
P3 = [378022639686402069, 212493865987873070406505700]
P4 = [-566101963637165587/4, 463734408645541734832665303/8]
P5 = [6573279977227087494, 16847251581507446314932887500]
P6 = [548360548631527693/4, 210833999252583711856628007/8]
P7 = [-168526343253234959/9, 1384243803975672042355038790/27]
P8 = [-445046372896160167427/24964, 201249458022639301328770506615903/3944312]
P9 = [118837756467477323337/961, 594649308054850367972835623386/29791]
P10 = [934144748087810038, 888916130445674287868810220]
P11 = [61137597239000642222229/3818116, 301403386312262003154014958582327325/7460598664]

Khoshnam - Moody (2016)

y2 + xy = x3 - 83598958924587909464854346830766301770x
        + 294558475635028689022196236625520239031964650641823108900

	Torsion points: 

O, [5280266705656745140, -594924624464385582083718170], 
[5280266705656745140, 594924619184118876426973030], 
[-10559122671197498060, 5279561335598749030, 2]

	Independent points of infinite order: 

P1 = [-376658071791198860, -18055283474071165325696694170]
P2 = [5126975891755967860, 845996987662141966273374310]
P3 = [3061243374503166190, 8205441734919964615103472280]
P4 = [1941917047927221472, 11812674654292737888137594566]
P5 = [620417310829718740, 15586245343508460341818496230]
P6 = [5301357312000892480, 601609041349147923620788090]
P7 = [2881859166491031610, 8807508921706068412899766810]
P8 = [4170532698807427752, 4294856170447441908261060786]
P9 = [-3328999758526185560, -23150952839357719761727450970]
P10 = [5122395271209196780, 858924728430079776471759430]
P11 = [860309498550198580, 14942363941257491522837379430]

Khoshnam - Moody (2016)

y2 + xy + y = x3 - x2 - 6733405851080577415475454221932585499304047x
             + 4800325455798548390824144090920449266363788590480449836501600119

	Torsion points: 

O, [-466406396651267428173, 88540213093604830382637677042086], 
[-466406396651267428173, -88540213093138423985986409613914], 
[2111993798863171867827, -1055996899431585933914]

	Independent points of infinite order: 

P1 = [612431631770882567827, 30104501132478688536678946066086]
P2 = [711816938318439197427, 19184340278585521798388646194086]
P3 = [4268560138861462087827, 232021827986848369563432827666086]
P4 = [556272770601756280827, 35026387726633526512811324981086]
P5 = [784176974198665091227, 1536340416191398554476259698086]
P6 = [2116726688248123095327, 5622008589229975369763987328586]
P7 = [-405612554541403539147, -86398769666485987658728130570312]
P8 = [342432162195579242827, 50346243685237300680925648066086]
P9 = [-1130345153944969017873, -104724297772201699033993373444714]
P10 = [272850750430950673227, 54620725748904290293131623468686]
P11 = [2121357868214022354099, 7925283056603117101549058856358]

Voznyy (2022)

y2 + xy = x3 - 16807300719676114741159074415663219985838088x
             + 26485415853243610398964585891912523713720572243019985442333257792

	Torsion points: 

O, [2437698274691638852112, -1218849137345819426056], 
[1427837930075778859472, -73472973105340461896652285110536], 
[1427837930075778859472, 73472973103912623966576506251064]

	Independent points of infinite order: 

P1 = [-4648750166642176469488, -64457619026540953139403339016456]
P2 = [-12115098394194783933440752/2809, -20384006038466890959973684924992509672/148877]
P3 = [-1194118111020657194453668/361, -1469300806972833957609372980866396204/6859]
P4 = [999593655487329402954896/361, 235280644078336487820336635919191720/6859]
P5 = [1409600760387461937270032/361, 979468891631966955668511059152061096/6859]
P6 = [478582565391696627582033408992/1394761, 331058278112161405758201104956985444966926024/1647212741]
P7 = [9510453474341142722298752/3721, 3399671379801898296092421848764945064/226981]
P8 = [828049328228405852971088/361, 9036721387786914249620879466468200/6859]
P9 = [134886982654478699683088/49, 11265432007040524997481242473003592/343]
P10 = [-2150008162113382697670774208/896809, -195518725900403925824370295148530122681944/849278123]
P11 = [5637427309363026547802095877648/1043483809, 10299726730852441124845858900570149562430126728/33707657482127]

Voznyy (2022)

y2 + xy + y = x3 - x2 - 65307967645295697830427336722134356346912165902774467x
             + 6776556666061653734253097820671526771886795499021732626074384890594739542801859

	Torsion points: 

O, [-296874251695587001057277733, 148437125847793500528638866], 
[149326371695000079245646267, 595053608798268266824311379377910514866], 
[149326371695000079245646267, -595053608798417593196006379457156161134]

	Independent points of infinite order: 

P1 = [-15858125931733047129277733, -2794321140690579614070730086127367361134]
P2 = [-137721076403273141509223220953/841, -88205278284985986104851460440149576681607126/24389]
P3 = [132493098645274713591385167, 670478429717454516206588749899851768866]
P4 = [151781528101766785431202267, 600583524471246770486322606417900158866]
P5 = [132150505971881036148502267, 673735793559147712567660276621042858866]
P6 = [-20147734915775975389991823, -2843270245932917435036374570949344156034]
P7 = [-258531502760718766083286726413/961, -65781715872798720159313938318819640124167994/29791]
P8 = [-174039969799769690972196877413/961, -106016438030311386542660255514033087028486994/29791]
P9 = [-4572719815037198399046212324661/96721, -93966312621561315228779896785261471579368287042/30080231]
P10 = [188979135046311233404995893294931/316969, 2392668038443781649937777079532998595697142560454/178453547]
P11 = [111517697825424830105842722979795587/1051640041, 34839344810465509114833153533834318500751625590630474/34103634889589]

Voznyy (2022)

y2 + xy + y = x3 - 25608438138583363750453644220110015973x
             + 48850271826555999667034974046685502042020878022915152756

	Torsion points: 

O, [13031852518377921639/4, -13031852518377921643/8], 
[761058421198939795, -5459081142391210440927616048], 
[761058421198939795, 5459081141630152019728676252]

	Independent points of infinite order: 

P1 = [3714957595181452035, 2232891675453869424154155112]
P2 = [52942253926750485753565/9409, 8310030562840609480525630480819646/912673]
P3 = [-1345845383538959330, -8993194126322818500991676173]
P4 = [136594593573114679885/169, 11765792953857756289686076177004/2197]
P5 = [33525830666154009430/9, 61255029266872647391477837154/27]
P6 = [-3412633787657997006074/961, -290378335563937316532841984514086/29791]
P7 = [5734295604847363066128340/2313441, 2734109536714773679614687066086811472/3518743761]
P8 = [26073998596261383583015/15876, 6701149472546673454267582436523907/2000376]
P9 = [4835510255543659655290/841, 233536810144194765033662425506703/24389]
P10 = [488738899328903792325838/205209, 108772538266988726031103049829145046/92959677]
P11 = [4361448006818835011738153245/2690185689, 475106929099042848174688263019971056373626/139531861131363]

Voznyy (2022)

y2 + xy + y = x3 - x2 - 253117693608320317481471859070333603713560604347x
             + 48928612825281236145946031275063726668034883245591529738101538876498219

	Torsion points: 

O, [300388533188292313369803, -150194266594146156684902], 
[432986116140324513506427, -143202981047792723394031543079137814], 
[432986116140324513506427, 143202981047359737277891218565631386]

	Independent points of infinite order: 

P1 = [3031870403766188323366827, 5210679739323119541483463355308626586]
P2 = [131556884977737904418296803/484, 154357129144781894581999707280826301583/10648]
P3 = [-43170655160157055133709634797/162409, -20429594220499370407107247991244769891025378/65450827]
P4 = [248971093945011165587659, 36640097734088184644611355826883482]
P5 = [252818540261333556288210819/841, 49120367480159889483654947157194016098/24389]
P6 = [-125257372932976394323491449517/597529, -140688518878789347105971176363589838925010638/461889917]
P7 = [11310260885931220076984443479/1681, 1199572406544815374922321074008132976892222/68921]
P8 = [16807048486007808650180560723/54289, 195423008109251813741470347172469954803722/12649337]
P9 = [439692609609097525705606803/289, 8768764205126377836536761605997492908218/4913]
P10 = [9923244519102466154616912929643/23493409, 15008985669597946494882137354352235897946094278/113872553423]
P11 = [594998768680892479540491397442853/923430544, 10988504905368161316238961268743000812759299857767/28061207371072]

Voznyy (2022)

y2 + xy = x3 - 101634854745305789909593544356506871024975808975x
             + 12471286206505690638915431397948987770853556352343302542131897789660000

	Torsion points: 

O, [184273670355417640439200, -92136835177708820219600], 
[199619745210754049497375, -11722564747058369862644546561381525], 
[199619745210754049497375, 11722564746858750117433792511884150]

	Independent points of infinite order: 

P1 = [147695786024769367617907, 26116833670524048667487732980486591]
P2 = [119250285500346189861280, 45245055192994025620439342759582800]
P3 = [183326482834983218947825, 521590709742404468274673661013025]
P4 = [184273813157271150694825, 5800120368805796787557314729150]
P5 = [117268676881033036606075, 46533572569932582885674160975109150]
P6 = [234776341502159072262475, 39378705841793305538511652158448375]
P7 = [381766883601170535357025, 171205849425833915557661294730171025]
P8 = [184475449406819022674281, 264642357067669586606439520528702]
P9 = [3418829721882733115742974425/23104, 91036076309745277299409530126868757048825/3511808]
P10 = [1681800404520858334418999425/69169, 1820460692458296876133777439970523846153175/18191447]
P11 = [40194609793224326407893008725/529, 8058383074893091975351883739864379760250650/12167]

Voznyy (2022)

y2 + xy = x3 - 1234140270416378250678088578402933925437564x
             + 527447606280303914796391760482999986982123024359861103558856208

	Torsion points: 

O, [653020238752531025784, -326510119376265512892], 
[440497237068337744248, -8323782120287706078552815728572], 
[440497237068337744248, 8323782119847208841484477984324]

	Independent points of infinite order: 

P1 = [3835407722965517628792, 228504301248000433460701865863236]
P2 = [800421217404316984151994/841, 357592581751334850718936215428924382/24389]
P3 = [1042482966150433380168888/1849, 261916528689335052190062060227055372/79507]
P4 = [-8638346270099840316816216/80089, -581973137012577697848855182784328429620/22665187]
P5 = [-2657308988904526189437066/2209, -1710062594654663285568572758865404458/103823]
P6 = [18779390259223821452763634104/128881, 2573413917211842125088416607016428228809052/46268279]
P7 = [124109078951801959056412663128/1138489, 43720272984384566451063222665058730163805708/1214767763]
P8 = [377497067519865683415814392/573049, 246700213804495007075372771521967091252/433798093]
P9 = [64804783401535186901758778242/104468841, 814885466607887455628930566582482991070806/1067776023861]
P10 = [-6576059757207854095972240224/8994001, -869404526623524049939971860682467344052004/26973008999]
P11 = [993910598494520311209918693678414/1275569206921, 8984443087288728057329356738484938248373090017408/1440641893557853531]

Voznyy (2022)

y2 = x3 + x2 - 98157972552649846551441608681894049x
             + 17173523831080699917850997782683206552726896135031487

	Torsion points: 

O, [-378805909904245639, 0], 
[197669397097277667, -74123347163736915087632784], 
[197669397097277667, 74123347163736915087632784]

	Independent points of infinite order: 

P1 = [128855060092964637, 81638432561593390605208164]
P2 = [-7938783333687338421/25, 15969799545743675692435201008/125]
P3 = [24817026840736474269, 123620432467089668380394853924]
P4 = [12309421217494150611/49, 31377430254863109626702062128/343]
P5 = [4557714551401009933251/16129, 224391997963421310525101749971792/2048383]
P6 = [1551372858474736219998651/64009, 1932138513456898568279766310524953808/16194277]
P7 = [1677453647094357397905987/261121, 2170065217864825235714208165103733424/133432831]
P8 = [107899012783006936461819/51529, 35077189914780926191611962760851760/11697083]
P9 = [-1414306374225384339701/29241, 738407823739449169949563410382256/5000211]
P10 = [-1034333775630154712091/3844, 37001289006451624962607023421785/238328]
P11 = [25439111806571211796699713/161086864, 153143561548162495891268778410148849033/2044514477888]

Voznyy (2022)

y2 + xy + y = x3 + x2 - 9616802040765253686519863489400032714x
             + 11458141648950677597857694544338957425465840088897243351

	Torsion points: 

O, [1851990373201879945, -925995186600939973], 
[2672236059890973113, -2200409385461146359569970229], 
[2672236059890973113, 2200409382788910299678997115]

	Independent points of infinite order: 

P1 = [1084146104289492873, 1518683309539256514245998651]
P2 = [1375161852338459147203/529, 24411918982693235834049597225355/12167]
P3 = [15422310165617800073, 59424785067732305697277231675]
P4 = [14591018719842282655/9, 9671991429426159057884111189/27]
P5 = [13841374557228493796289/841, 1601390214571428264506169246227495/24389]
P6 = [10405602055730261253, 32219128799494318875079868191]
P7 = [2749938751531443734567847/1437601, 428407644928952276034519608229665825/1723683599]
P8 = [57281960365991295632024633/3073009, 427884710327425088879593927830812916179/5386984777]
P9 = [-70551359216673824299171/303601, -618733463976659279322191600671118035/167284151]
P10 = [161949936045576405934466353/247464361, 9083669727279833423555403950536285817641/3892861862891]
P11 = [-955960764580198934391664725617255/493884441167121, -52432633421565222424864633837673543172412771585123/10975846311006366381831]

Voznyy (2022)

y2 + xy = x3 - 204612883217644162374401645935933337240x
             + 1126458801999575619505157608163376285898744251881550465600

	Torsion points: 

O, [8316639696921356080, -4158319848460678040], 
[6617638717645512880, -7887449354112646449715846040], 
[6617638717645512880, 7887449347495007732070333160]

	Independent points of infinite order: 

P1 = [8516689742361939760, 1258557746444139996430355560]
P2 = [87151157544487517830, 803265529207451947250387612710]
P3 = [1726456402245267089830, 71732928956835871254964242920710]
P4 = [89877195839939054896, 841876686600359771888361686632]
P5 = [4014405800817444147760/529, 39864065312678465090276882922200/12167]
P6 = [7353521281977893280, 4412476003028123558085446760]
P7 = [46219346744713441546960, 9936551405074724996120320013857480]
P8 = [990903204473409123760/361, 165968122228853630339350672422520/6859]
P9 = [1147807797564561615472/121, 8321895429390224494641744582776/1331]
P10 = [226000159585908090165664/10609, 87656215263243991410412542676632664/1092727]
P11 = [416445801148637774289040/49729, 5540488986506714228645753000442520/11089567]

Voznyy (2022)

y2 + xy + y = x3 + x2 - 21867223320112239016783671995123950489x
             + 39354506601874758642325518766562884477556802289319976926

	Torsion points: 

O, [2722011719392931145, -1361005859696465573], 
[2121328706960296288, -1585242091020863279049363579], 
[2121328706960296288, 1585242088899534572089067290]

	Independent points of infinite order: 

P1 = [24732512710203778780/9, 3301823666656208241591779234/27]
P2 = [1761921743490658633, 2509148111321239324296323131]
P3 = [163508330617070294453, 2089941357655756156848881887041]
P4 = [2298089380222767728, 1112823686752402012572175530]
P5 = [7602910627595664572, 17679946510704434260598732925]
P6 = [13018573601018243020, 44284362094015236647610890077]
P7 = [41516282021171101989/16, 18575917855584889611077597215/64]
P8 = [-18467972809008322938016/57121, -92984173365396273958232105339982330/13651919]
P9 = [345349833367586271490068/139129, 31532953016429304254615419069916134/51895117]
P10 = [8723565315738477727921996/3583449, 5021194902199967569996659253707031070/6783468957]
P11 = [277664718631328317393427830/104101209, 71735717309677383678351186541196567239/1062144635427]

Voznyy (2022)

y2 + xy + y = x3 - x2 - 595526764519545473538759784349237221738404650282x
             + 207404712817763552978197730613335214330524536966377034126822264871403881

	Torsion points: 

O, [-907749466601149462784559, 453874733300574731392279], 
[462104729225716126671441, 175747498503850620440840806083040279], 
[462104729225716126671441, -175747498504312725170066522209711721]

	Independent points of infinite order: 

P1 = [263385382871596577215041, 262341765293768874617852167469619079]
P2 = [13884044773743433733841, 446250007211976531142848021383046679]
P3 = [62696561667055960948425441, 496401252915531579828061889970166252279]
P4 = [319445922309616026821601, 223078905661425343002424117884506359]
P5 = [8546413940666077862815441, 24886905021942923687704829027612992279]
P6 = [27196947075306390843721041, 141777585068685928302001021901624761879]
P7 = [1484995076990113432880565441, 57225218845606403407155098116249028692279]
P8 = [5479172528132737704827241/25, 36956995456165990672720785116198003771/125]
P9 = [3585555444950117964152719/9, 4933137826348422574707936102681101533/27]
P10 = [6639774897237945165589163049/289, 540740160779152581570315001710356763359927/4913]
P11 = [20521987420448115281323587321/169, 2939817567270529944385336846917363859414627/2197]

Voznyy (2022)

y2 + xy + y = x3 + x2 - 2435109968648812284250327501767338349106208713x
             + 46251325990521754026689983318486396751949337631251172036297849383406

	Torsion points: 

O, [28537664503990119507945, -14268832251995059753973], 
[25694265591055000445680, 803863600647378612983197533500922], 
[25694265591055000445680, -803863600673072878574252533946603]

	Independent points of infinite order: 

P1 = [28249476777825481619230, 68966919135415511094965346852397]
P2 = [28684194095819223838170, 55009232057118016842353045253877]
P3 = [10096064279813987704021105/256, 13923404495257906311519264999806510287/4096]
P4 = [118122318351864384735080759020/109561, 40555577639978171877388947749543888328603282/36264691]
P5 = [16478998180802258531106430/961, 92000029541776379694245439517639283052/29791]
P6 = [302780580291955926869056645/10609, 4778808892731683510945250686753697519/1092727]
P7 = [758236476045213915905173770/26569, 10526662133379160210090443466088291959/4330747]
P8 = [-4498680646908684216518885348720/89510521, -5467757907824274947514756713939309406370537518/846859039181]
P9 = [2361629687316200258046809835834864/83030998801, 41859814819749868610714230562366067684859859347/23925465335506951]
P10 = [11960942584465581707124843631570/413593569, 1051547435015886751967540917226114385504903541/8411252412753]
P11 = [8330238964895550899659071373820970/270157734289, 97530833579632740061531859774175726099385705207136/140419075078190663]

Voznyy (2022)

y2 = x3 - 944350340701979900709096424316569452x
             + 351982210527405532452913727852239888857539342858675696

	Torsion points: 

O, [587981882605635556, 0], 
[283321839089223190, -327367893264950076421954104], 
[283321839089223190, 327367893264950076421954104]

	Independent points of infinite order: 

P1 = [38254916231980109305/64, 16777169165426102075826590733/512]
P2 = [-18750900605870873341295/21316, 2205015052135300753750914135675609/3112136]
P3 = [82535380295061133467062/22801, 22932283690078837935213080092568200/3442951]
P4 = [-113875989962068818524408/145161, 43196683471633451523632373497805020/55306341]
P5 = [688878499471005282902/121, 17832799164339424213464306070600/1331]
P6 = [301838641211894138055389/75625, 161311889604268215124849389013203787/20796875]
P7 = [482724803077483366159732/1018081, 106831406043053549774123781730277880/1027243729]
P8 = [1670497998040055352029060/3481, 2159076594773081080192801590570282896/205379]
P9 = [34077331595867471432087461/286225, 198922518214977527829310211025423289209/153130375]
P10 = [-255049975187481208364790218/821338281, 18463838919342848703883023541179689343880/23538733795179]
P11 = [-105635307959015288236949372/103286569, 522772318161554324725216926818096493600/1049701400747]

Voznyy (2022)

y2 = x3 - 71016450598376685828738822609116652x
             + 7262019996454072966062130364617906017922660966355696

	Torsion points: 

O, [160750617222142756, 0], 
[80091877996173622, 45694038820021232280733800], 
[80091877996173622, -45694038820021232280733800]

	Independent points of infinite order: 

P1 = [590570941802758957, 413881117676024094193872915]
P2 = [486460870147091782, 296367050257566784853447160]
P3 = [93068439245587659286/25, 895609680842394633167167157784/125]
P4 = [13633090461214947622/81, 6403866092638841715230090440/729]
P5 = [22832849567776951798/169, 25380126005861616020352158040/2197]
P6 = [-3945302181194111383/16, 6329408988650232042162538315/64]
P7 = [32669525469732318327541/185761, 1165818454502900530104418402049265/80062991]
P8 = [-65114466074481061191242/413449, 32056601099762566609947153300588840/265847707]
P9 = [3726052363107527062, 7174480684765838367651735960]
P10 = [-1662524697198869271565802/16104169, 7506976486515505378148934374734803240/64626030197]
P11 = [2504026697401386137958790/18412681, 863047192812114567750670212901106184/79008814171]

Torsion group Z/4Z, rank = 10

Elkies (2005)

y2 + xy + y = x3 + x2 - 178794778214407978859461188x
	      + 919419935068616719030140166742670899781

	Torsion points: 

O, [7902333519965, -3951166759983], 
[10825661583645, 15892163331274543377], 
[10825661583645, -15892174156936127023]

	Independent points of infinite order: 

P1 = [7991223717565, 973476603398652017]
P2 = [7157502138095, 2524594321090659027]
P3 = [6490090505595, 5691791551237981527]
P4 = [8260503930845, 2479531125255223377]
P5 = [7068765426045, 2961370070561940177]
P6 = [7986191049565, 940173095443704017]
P7 = [7906176561445, 182183392974586577]
P8 = [7447027420345, 963938571466557377]
P9 = [7536040864245, 36725312300251577]
P10 = [5577275134045, 9783604580829236177]

Eroshkin (2008)

y2 = x3 + x2 - 110907705551334904313030730340x
    + 14209200477703631816262785853057594833158688

	Torsion points: 

O, [195804468832796, 0], 
[131691564567386, -1373853819454733446830], 
[131691564567386, 1373853819454733446830]

	Independent points of infinite order: 

P1 = [7487174762891, 3657763636175745336240]
P2 = [66153929096078, 2676141294657606477702]
P3 = [-13347561044449, 3960703205400133720710]
P4 = [181718532279926, 236339226851902975710]
P5 = [129109836878846, 1429021260168509457450]
P6 = [145247830530626, 1079064641655703813110]
P7 = [88799390252396, 2249639192885701617000]
P8 = [-199927079309134, 5328358228788194289690]
P9 = [187628598971846, 71501205004095977550]
P10 = [68197418265338, 2638704196747226745522]

Eroshkin (2008)

y2 + xy = x3 - 1281493142199716912383484016491195x
         + 20908478821228455374087389955630487236070347099025

	Torsion points: 

O, [21486290540011990, 1814750762615772718487905], 
[21486290540011990, -1814750784102063258499895], 
[-42159575397842210, 21079787698921105]

	Independent points of infinite order: 

P1 = [-1884428609245490, -4828733727563649610956095]
P2 = [9999761497788040, 3015589736530490299309855]
P3 = [12200758408015870, 2662607223124380557977105]
P4 = [4933348790184430, 3834904647907043298422065]
P5 = [3519275753727790, 4054890671211978028291105]
P6 = [14461367628578290, 2323931548228764087838105]
P7 = [-2033604490069460, -4848310938042222755152895]
P8 = [8994062137272190, 3179655310614273671989105]
P9 = [16053683488503262, 2114984845243170564101137]
P10 = [26966762358435790, 2441547962033335259143105]

Eroshkin (2008)

y2 + xy = x3 - 760145319394626167366827836801635935x
         + 326380843415620023885693187007160075335038240252804697

	Torsion points: 

O, [-1036794707078723866, 518397353539361933], 
[533136652721679734, -269546737807367996487415267], 
[533136652721679734, 269546737274231343765735533]

	Independent points of infinite order: 

P1 = [9351912801440222, 565042342279830932298098525]
P2 = [213713389039346534, 416759679868093440475592333]
P3 = [393973467736036454, 296739590176255292862135053]
P4 = [406816171100407334, 290635968208203911412939533]
P5 = [234359676554991974, 401379509123341236684375053]
P6 = [400579344813463634, 293531629923125075348299433]
P7 = [-64825358359178866, -612686803147736648313213067]
P8 = [1554210922215654122, 1702722065578612070128963925]
P9 = [237074990359828634, 399367114886444437383304433]
P10 = [510752320135368038, 267158678585778218818603661]

Eroshkin (2008)

y2 + xy + y = x3 - x2 - 1438890788668364715460404815472111782x
             + 664238447429240521151735809720974728393274982519227189

	Torsion points: 

O, [699504630281583497, -349752315140791749], 
[869884777856821097, -266102711989934394825413349], 
[869884777856821097, 266102711120049616968592251]

	Independent points of infinite order: 

P1 = [520887678470565777, 236785302619335675555907371]
P2 = [710270859444232457, 23601426293735409770127291]
P3 = [647688470016257117, 63174492741286520948721951]
P4 = [709562420082172937, 22478274457271147570215611]
P5 = [702959263351471497, 11196955863283826439240251]
P6 = [711442588904296697, 25442532030235744453497051]
P7 = [699713582108187017, 2481405925156054230971451]
P8 = [517284388093930737, 241535268737908928011771811]
P9 = [702701713122958997, 10690728311934648509815251]
P10 = [-196617500442541171, -969303167941575286336924593]

Eroshkin (2008)

y2 = x3 - 2901413377029475814340493444042767x
    + 60112620677766830193510638729425884294374453937874

	Torsion points: 

O, [31760259820397783, 0], 
[42928470713286833, -3830178611508582492309150], 
[42928470713286833, 3830178611508582492309150]

	Independent points of infinite order: 

P1 = [9646618920345158, 5746431883465628287663500]
P2 = [22516670868944423, 2489661273896584110839880]
P3 = [-11731608543750967, 9619575762996283592576250]
P4 = [31932595197275909, 155981139952020471555390]
P5 = [32234760310611533, 284153673834028171923750]
P6 = [33132846938761673, 594386933433533810843130]
P7 = [14198652836651958, 4666790390939468272881400]
P8 = [32130881903267393, 243651479979758871850830]
P9 = [32807820520613813, 486179240037017139923310]
P10 = [11055368642843465, 5421035543526884598589062]

Eroshkin (2008)

y2 + xy = x3 - 469917050010248316855222453915732505x
         + 121700328613583346435162710697715924409177216507045177

	Torsion points: 

O, [767486105638297994, 461650993946261693920122803], 
[767486105638297994, -461650994713747799558420797], 
[438895821028911194, -219447910514455597]

	Independent points of infinite order: 

P1 = [-146286683898037306, -432796061234100100258416097]
P2 = [108038449934232194, 268686205122140342089930403]
P3 = [452441406303420482, 41311174649746778876836763]
P4 = [452695314206676944, 41752991757258929222247653]
P5 = [-253366593281982232, -473810970451121523534799459]
P6 = [442081176832193294, 18902908600673667767825003]
P7 = [227860822860174452, 162650862827172354406068323]
P8 = [85157260367825594, 286881543391818429188711603]
P9 = [449352484018106474, 35695023271699947299504243]
P10 = [-67833587645935306, -391489921725469422537090097]

Eroshkin (2008)

y2 + xy = x3 - 87362539812439413437833065426284x
         + 1241608478171540522727605890546080801398358040464

	Torsion points: 

O, [-13413637921750568, 6706818960875284], 
[7856399856190384, 1019889278393031984370684], 
[7856399856190384, -1019889286249431840561068]

	Independent points of infinite order: 

P1 = [12671735539611790, -1472857965505361554356272]
P2 = [-5742943676520860, -1246561784318309584428668]
P3 = [2138788584575050, 1031766535181282505457558]
P4 = [-6702171337531556, -1235342734384161373398716]
P5 = [-759249792205406, -1143460008124367165861378]
P6 = [-12995920712039624, -426652860429217686365708]
P7 = [28054933432416298, -4568601038777740126291424]
P8 = [1152874383209740, 1068841779862998610161328]
P9 = [-3563935899462440, -1227882379605974010717548]
P10 = [-12170113713276020, -708720448433330741811152]

Eroshkin (2008)

y2 = x3 + x2 - 18930547595582330633859100826042865x
    + 743333575262731208284792941763359206829310485395775

	Torsion points: 

O, [243395856800774595, 102736862257161790173215700], 
[243395856800774595, -102736862257161790173215700], 
[110458120688643645, 0]

	Independent points of infinite order: 

P1 = [20559514928248395, 19047862763645511972676500]
P2 = [39565101831733395, 7501975394540494976608500]
P3 = [28287947149303395, 15181023867991162550596500]
P4 = [-32685445410724035, 36430314859269554797617120]
P5 = [-11186576971152435, 30882061465346532434966280]
P6 = [118419368795569395, 12735866015645411612200500]
P7 = [124314225677221770, 17639517362720208634940625]
P8 = [182624320292371875, 58111756167727774877945580]
P9 = [110642430084334065, 1807888292870044459854780]
P10 = [23321632188969315, 17734906498764828289125780]

Eroshkin (2010)

y2 = x3 + x2 - 50491061391988204405194159029361x
    + 135663699587915859546796760459040265253947368735

	Torsion points: 

O, [4539034041928485, 0], 
[7903172670072207, -479851415254420547970060], 
[7903172670072207, 479851415254420547970060]

	Independent points of infinite order: 

P1 = [594879530959527, 325327708047053156882580]
P2 = [2884705001402037, 118393501187363110445880]
P3 = [-1520096210813991, 457058525564559582882036]
P4 = [2775663697578585, 130007938722486060873780]
P5 = [-1133633732800665, 437544521662602852957420]
P6 = [4540694038684071, 4338712096157000607084]
P7 = [-2587491423319143, 498984311740534566303060]
P8 = [16514120392102887, 1950773163564108331686420]
P9 = [3618616115188602, 18424847821955205003945]
P10 = [1321489924618677, 266923276622854745030280]

Eroshkin (2010)

y2 + xy + y = x3 - x2 - 28562016892450236469278130528841147x
            + 1855604032124054096684337837801147788788173909411371

	Torsion points: 

O, [141241169865718611, 25280448179887316452374994], 
[141241169865718611, -25280448321128486318093606], 
[100384705906350411, -50192352953175206]

	Independent points of infinite order: 

P1 = [-35654245600770339, -53184928493164853355793706]
P2 = [102663271430755911, 2319240609938111081641294]
P3 = [52673995966314411, 22299665827759615565408794]
P4 = [91736654652562531, 2727711406692375247325914]
P5 = [100595198949492411, 603919072698101752016794]
P6 = [-65816389876514589, -58739676675009736575030206]
P7 = [104943321056725411, 3736640023782459047249794]
P8 = [85100033778102759, 6424267594322106960581806]
P9 = [109620193709308971, 6472309265284227861714874]
P10 = [131809366710013161, 19516154123990917016704294]

Eroshkin (2010)

y2 + xy = x3 - 1034642810304700336989303292996335x
         + 27194354320720666208457979454230524027566043738297

	Torsion points: 

O, [-41172155077932666, 20586077538966333], 
[22473710859921534, 3910605563287108844697933], 
[22473710859921534, -3910605585760819704619467]

	Independent points of infinite order: 

P1 = [1963070251109334, 5017055188546855513152333]
P2 = [2685645541820454, 4943181282395407331179293]
P3 = [7997842751105574, 4408064167520510706622653]
P4 = [9767429295482214, 4245043305621547405927773]
P5 = [-5651061635916666, -5732427126985005778937667]
P6 = [16574454263852334, 3820853916529487973711333]
P7 = [7436414620847334, 4462236776055147090486333]
P8 = [19476238825878894, 3798842748743389505855013]
P9 = [-6605865818580816, -5808683381863099996969317]
P10 = [13748357584511334, 3945680279355505842090333]

Eroshkin (2010)

y2 = x3 + x2 - 1943429743722969114553996571920532980x
    + 14884792023408679915420022260951621825514385918921561728

	Torsion points: 

O, [-2722332069468628924, 0], 
[1782093082051715126, 4132927520396891255805415650], 
[1782093082051715126, -4132927520396891255805415650]

	Independent points of infinite order: 

P1 = [-427172584770742117, 3954367586298572428628234592]
P2 = [760257887621777546, 3721116398478610908210262290]
P3 = [606915923615763026, 3732137348465002791209459850]
P4 = [1068510370143712046, 3745417316748935152721248710]
P5 = [-839006221187752474, 3990581262430580122452759150]
P6 = [2022554584651863956, 4384953595030965159721878360]
P7 = [6639950657837281478, 17167671130294892638491378318]
P8 = [464669811929636006, 3752608357156476706290191790]
P9 = [-200110161257290129, 3907131791504323450172525190]
P10 = [4499207948473513826, 9859908154317940015940535750]

Eroshkin (2010)

y2 = x3 + x2 - 38396932203315800018086858812203832603560x
    + 2895935359083517194158307262550771514346143693455215925052708

	Torsion points: 

O, [113414196619751906611, 0], 
[127249216727992963336, -265370194766021422762990755450], 
[127249216727992963336, 265370194766021422762990755450]

	Independent points of infinite order: 

P1 = [113916758950557205111, 13500221026921276791248250750]
P2 = [113896389823119173431, 13096470814850457576925850610]
P3 = [113590449221455398496, 6656667623985127552184010630]
P4 = [30455989741818665911, 1324676853536502975722736519150]
P5 = [114142831910452099927, 17902270485010503247645720170]
P6 = [79428078175202623027, 589269244861500242748997345200]
P7 = [138439983835588620736, 483274323444600799593635175750]
P8 = [113987591930549406256, 14893171177371804903757972710]
P9 = [84735300792849385411, 500764667481151987168163808900]
P10 = [111510896511728917936, 29348679413717229219858354150]

Voznyy (2023)

y2 = x3 + x2 + 5365964600284239371851791x
    + 14610806763317668249280146321957009215

	Torsion points: 

O, [-1740415499715, 0], 
[2061308179779, 5867724792430860372], 
[2061308179779, -5867724792430860372]

	Independent points of infinite order: 

P1 = [-481561549686, 3451824108575669073]
P2 = [14226198513, 3832381364126005692]
P3 = [-876724802157, 3038493239492760972]
P4 = [1572849910698, 5190536505800612673]
P5 = [-1530696957942, 1676504493512744337]
P6 = [167896430085453, 2175725964008832334632]
P7 = [2291392442418, 6239971645725964203]
P8 = [2249038281533, 6168880912264161312]
P9 = [-577134290262, 3364771968584939583]
P10 = [2580925660593, 6756623848368234972]

Torsion group Z/4Z, rank = 9

Kulesz - Stahlke (2001)

y2 + xy = x3 - 791410724196656192877500062111x
	   + 270985332491881387056053084997768958465063385

	Torsion points: 

O, [448086509574998, -2516417112919062906259],
[448086509574998, 2516416664832553331261], 
[515072096254310, -257536048127155]

	Independent points of infinite order: 

P1 = [-74068218887962, -18143796961075289154739]
P2 = [511534686823160, 58470570596143399925]
P3 = [357745618823558, 5800567653253786719341]
P4 = [46172989499126, 15314763171500332546349]
P5 = [355981327890944, 5862491533929390068891]
P6 = [602281137752798, 3578629072947333881861]
P7 = [380819855348144, 4982804555495324973515]
P8 = [-703211300867866, -21903697871091460615219]
P9 = [487486341852188, 1015429697665547098151]

Dujella (2005)

y2 + xy = x3 - 166949722612780501168288982743613641730x
	   + 834840766609103026403820802333562999484076469013075040452

	Torsion points: 

O, [-14928863831425505756, 7464431915712752878], 
[7468975423264965244, -2135092766480393408286474122], 
[7468975423264965244, 2135092759011417985021508878]

	Independent points of infinite order: 

P1 = [-8820362216509922756, 40263932840798434036966781878]
P2 = [-782860091620997756, 31065402787828962844224056878]
P3 = [-5636143289585842256, 39959416553160222669625340878]
P4 = [9961806811829238544717456/573049, 24485557556804809925082322730120724154/433798093]
P5 = [-537544178655329825148656/39601, 193027647463604874596475787842840322/7880599]
P6 = [6904282448278329892, 3360620299363613882353063918]
P7 = [1741500512137540439760724/168921, 1004730397874305643252222751219816218/69426531]
P8 = [-11975077422549535854893084/840889, 13884475622003938729376902028644617014/771095213]
P9 = [6752874832387240284195425865364/14123183281, 17541877711551772567165400626439982280674660638/1678413224297321]

Eroshkin (2008)

y2 = x3 + x2 - 205496172578185251395440662829934785x
    + 11849852981876652616557426694362320162271429199181183

	Torsion points: 

O, [421139626921969361, 0], 
[-150331792760363809, -198355779911253887186223960], 
[-150331792760363809, 198355779911253887186223960]

	Independent points of infinite order: 

P1 = [-354190018494997279, 200502385826984101223443080]
P2 = [-437037439569393439, 134849804811372529303534200]
P3 = [-97475078008482769, 175938795101499865283688840]
P4 = [-144765896268442582, 196379244958849401511041903]
P5 = [-410120921945459473, 164760838222673865206745480]
P6 = [-416990865640816369, 158217988422627336188933640]
P7 = [-111756092132904814, 182810100770872307835777675]
P8 = [582484911105669551, 299636387842864495851517320]
P9 = [1904291285507941919/49, 21481588372636373466395144520/343]

Eroshkin (2008)

y2 = x3 + x2 - 246850542450447117600763943437460x
    + 2124703140418099231592606536930952455079436940608

	Torsion points: 

O, [9864754457609206, -805950219044077741466910], 
[9864754457609206, 805950219044077741466910], 
[-18947023375137164, 0]

	Independent points of infinite order: 

P1 = [-1880660411281574, 1606951619114589607243230]
P2 = [-1623386504886464, 1587815711394256785718200]
P3 = [53194260738466, 1453124997658357390638810]
P4 = [2524678293767631, 1231899847699778544207690]
P5 = [3083221020040426, 1180219570536845236882770]
P6 = [12040644818635588, 947671639507458641010312]
P7 = [3981613914031006, 1097707203286600656164310]
P8 = [7254218066499856, 846013666593435770097360]
P9 = [145648955101134916, 55280308365256034344100040]

Eroshkin (2008)

y2 + xy + y = x3 - 1742907593966990756845614x
         + 884438686985072950763948120250518212

	Torsion points: 

O, [3140269971671/4, -3140269971675/8], 
[1110774894341, -564764161159305741], 
[1110774894341, 564763050384411399]

	Independent points of infinite order: 

P1 = [-75449078194, -1007725103207297976]
P2 = [820809034388, 82740042886701567]
P3 = [411269065781, 487029241050481419]
P4 = [935988672731, 270356715099523419]
P5 = [263042753099, 666468018565637865]
P6 = [916824173531, 239061498026206299]
P7 = [2928006134039/4, 233685892742150397/8]
P8 = [738992386706, 3766605528298749]
P9 = [789721893716, 23342402566444524]

Eroshkin (2008)

y2 + xy + y = x3 - x2 - 176620653974058428143264127x
         + 903414674763811890417046406006315779751

	Torsion points: 

O, [7718659159251, -3859329579626], 
[9172083968451, 7419985594402839574], 
[9172083968451, -7419994766486808026]

	Independent points of infinite order: 

P1 = [7768993064691, 406346675232305014]
P2 = [4347401613651, 14755987046504074774]
P3 = [8207792508501, 2586575356972455874]
P4 = [249263407251, 29315611689872948374]
P5 = [4777788280851, 12985466545844741974]
P6 = [7865802003931, 902972932760584854]
P7 = [7808702553939, 615370768676079766]
P8 = [7721544259651, 79289152381169574]
P9 = [9142567814251, 7269385757356565374]

Eroshkin (2008)

y2 = x3 - x2 - 63101137631999143241257265x
    + 191341468112384598938400129107933347137

	Torsion points: 

O, [4922161372179, 0], 
[1826700164329, 9064767173835187100], 
[1826700164329, -9064767173835187100]

	Independent points of infinite order: 

P1 = [4046893030649, 1501755661273561980]
P2 = [-207449533823, 14297651626859442556]
P3 = [-325725187176, 14555429899070970195]
P4 = [3981277360529, 1795508458242684900]
P5 = [5946541104089, 5136700039591756740]
P6 = [809049061709929, 23011314698170406393500]
P7 = [37491752675879, 224778020445313965300]
P8 = [2264866538708309/196, 86996381245561229373525/2744]
P9 = [5807638191824, 4555957985766417945]

Eroshkin (2008)

y2 + xy = x3 - 3796945199097665047266867217657570x
         + 90053238757721148532503511375148048023191940383812

	Torsion points: 

O, [37810942192819364, -737721397592643487120882], 
[37810942192819364, 737721359781701294301518], 
[35598869204894564, -17799434602447282]

	Independent points of infinite order: 

P1 = [28976854476915914, 2088147659103842244510818]
P2 = [32835719065976564, 883614424636281921448718]
P3 = [31994009520868964, 1150364535137936227811918]
P4 = [19798347862574564, 4758197751976174562272718]
P5 = [35647438683607592, 22129387556019059551178]
P6 = [35610546243722564, 8467716416727238900718]
P7 = [35972156521606874, 129460455676705830809348]
P8 = [35607291607482724, 6984928715105109452878]
P9 = [36765729402447614, 390779703902764130106368]

Dujella (2009)

y2 + xy = x3 - 483725969460602178479334521365188x
         + 190358540102254190991536781247531330227214704382992

	Torsion points: 

O, [-60325983573810168, 30162991786905084], 
[41820709534592712, -15597179772769573766807556], 
[41820709534592712, 15597179730948864232214844]

	Independent points of infinite order: 

P1 = [-16645085583782268, -13921154095846610086268016]
P2 = [30569176457931912, 14287671347748000840206844]
P3 = [16638057761691912, 13671726629420585942126844]
P4 = [-1795117496287224, -13828271777700233522135556]
P5 = [38614274101441608, 15141205218230059828962300]
P6 = [134075838854196312, 50355676623093919804459644]
P7 = [20335183698911112, 13745213070611076417605244]
P8 = [-56432036076432888, -6159882060292563595722756]
P9 = [98489398436756232, 33137286223500682310303484]

Dujella (2009)

y2 = x3 - x2 - 16275673326928004830300499825x
    + 22374180470634970227928749712599947693981025

	Torsion points: 

O, [-301008832994949, 0], 
[204504054373925, 5253426414016928203980], 
[204504054373925, -5253426414016928203980]

	Independent points of infinite order: 

P1 = [-77014662931824, 4813611129563743070025]
P2 = [-106173766036725, 4785953101507739912520]
P3 = [31413536475375, 4679092135601877391020]
P4 = [96000948900701, 4657946180745108640620]
P5 = [540550068665225925, 397423806070678002049531020]
P6 = [230752447751901, 5559256565264735519340]
P7 = [-79459122953443, 4813080716618069800212]
P8 = [-65863763757800, 4812529297203127196605]
P9 = [11734315925224435105/2704, 40184485126455200520458751625/140608]

Voznyy (2023)

y2 + xy + y = x3 - x2 - 12595569846799730587572505x
    + 17205797813043188222391188752442437497

	Torsion points: 

O, [2049464139559, -1024732069780], 
[1976389306599, 179028516128616300], 
[1976389306599, -179030492517922900]

	Independent points of infinite order: 

P1 = [-1365084886601, -5644115121196512100]
P2 = [2050179682599, 2638919079368300]
P3 = [2048460936999, 909906266069100]
P4 = [-943982574201, -5315506132459837300]
P5 = [-1354803427545, -5637692797515722644]
P6 = [1600442612775, 1070845269289591916]
P7 = [63684624301863, 507447295857069989996]
P8 = [115404196615, 3969099734681083148]
P9 = [2043654754849, 13276177323863600]
High rank curves with prescribed torsion Andrej Dujella home page