Torsion group Z/7Z, rank = 5


Dujella - Kulesz (2001)

y2 + xy = x3 - 3871874529581532682991685x 
	   + 2932443695831973034287157248711276225

	Torsion points: 

O, [1171933025970, -66562907187908985], [1137976122990, 3199206958195395],
[1910775530370, 1584461941569375015], [1137976122990, -3200344934318385],
[1910775530370, -1584463852344905385], [1171933025970, 66561735254883015]

	Independent points of infinite order: 

P1 = [1139468193570, 6113353595217015]
P2 = [423997075362, 1169189107911863031]
P3 = [1157854869570, 40341192423477015]
P4 = [1137065493270, 1069297314954015]
P5 = [1137272072370, 1646036791995015]

Elkies (2006)

y2 + xy = x3 - 801634269837107139166772851280x 
	   + 315710247481803582042676623278248394848262400

	Torsion points: 

O, [1131186190931680, -29263601581724789037200], [430440545011360, -7099716846165341836880], 
[-561233063314040, -24265928141999279774480], [430440545011360, 7099716415724796825520], 
[-561233063314040, 24265928703232343088520], [1131186190931680, 29263600450538598105520]

	Independent points of infinite order: 

P1 = [85526630898592, 15740863331343335618992]
P2 = [290385834223569760/961, -299500046651904120799989680/29791]
P3 = [-178019446528040, -21278513390150019041480]
P4 = [-81372900992864, -19503915948192485780048]
P5 = [-437834763635540, -24140442806878317303980]

Elkies (2006)

y2 + xy = x3 + 17189192408099124368974280x 
	   + 14347563590500778387882617467320974400

	Torsion points: 

O, [13227279881840, -50556618967055108920], [2286184756880, -8099031927845206360], 
[-454714844560, -2537195715703556920], [2286184756880, 8099029641660449480], 
[-454714844560, 2537196170418401480], [13227279881840, 50556605739775227080]

	Independent points of infinite order: 

P1 = [-733027479160, -1163415328491323920]
P2 = [-683839158160, -1507690912971332920]
P3 = [1495149953554160/1849, 426501021351985991673560/79507]
P4 = [55827804602887280/2209, -13373046199076994518617160/103823]
P5 = [2543774259440, 8633260650255723080]

Elkies (2006)

y2 + xy = x3 - 1644173544974177009215399260x 
	   + 29144075820496678960101949181880262179600

	Torsion points: 

O, [50748118673640, -276406650897190527180], [19543376894520, -66901727956450562460], 
[-25215304199880, -233602705412996604060], [19543376894520, 66901708413073667940], 
[-25215304199880, 233602730628300803940], [50748118673640, 276406600149071853540]

	Independent points of infinite order: 

P1 = [18840522713400, 69675800769119471460]
P2 = [-5279882261448, -194108035447655037084]
P3 = [28556991474360, 74025000283910777700]
P4 = [14185096013112, 93142882933735615332]
P5 = [-16480379716140, -227518256916697261800]

Elkies (2006)

y2 + xy = x3 - 239247306678234007210828097520x 
	   + 45246626407933026379552521501618249969926400

	Torsion points: 

O, [-148947654166560, -8807808260645246196720], [393999910993440, -3485133109850043996720], 
[267568080668640, 622574473646697227280], [-148947654166560, 8807808409592900363280], 
[393999910993440, 3485132715850133003280], [267568080668640, -622574741214777895920]

	Independent points of infinite order: 

P1 = [46074969993440, 5858423537724469003280]
P2 = [275652423665370, 492718372260784145100]
P3 = [138768613071840, 3836513831575606436880]
P4 = [297508887793440, 633557750590112003280]
P5 = [169967679183690, 3080992491904517095530]

Eroshkin (2009)

y2 + xy = x3 - 11181845072095618101356644660230x 
	   + 14391914697117329050689039214352461501292556900

	Torsion points: 

O, [1986637187437500, -4284940246971133320870], [1928016592364460, -218287646293676691030], 
[897878946226860, -71244855727391880665430], [1986637187437500, 4284938260333945883370], 
[1928016592364460, 218285718277084326570], [897878946226860, 71244854829512934438570]

	Independent points of infinite order: 

P1 = [-50212338713940, -122283501274174214105430]
P2 = [1494991187264172, 31881939944292796642986]
P3 = [1933393961761860, 230632595187600474570]
P4 = [2937317706484836, 83005881436952963158602]
P5 = [469571691228966885/16, 319772096187718923698671605/64]

Dujella - Lecacheux (2009)

y2 + xy = x3 - 23029452969111267963793629026710x 
	   + 43247274604914893171276548913972152943570776100

	Torsion points: 

O, [-2026713362963980, -285651033709562007205510], [4404650476318220, 165121071122022034846490], 
[2534623395651020, -34051511381888809345510], [4404650476318220, -165121075526672511164710], 
[2534623395651020, 34051508847265413694490], [-2026713362963980, 285651035736275370169490]

	Independent points of infinite order: 

P1 = [-2346860782356820, -290462146379303405728870]
P2 = [2850183100882700, 27617093411134421129690]
P3 = [2758937068611020, 26660034889979335294490]
P4 = [-1201537965455980, -263027344254022693525510]
P5 = [-5139499726938280, -160779489389448463993510]

Eroshkin (2009)

y2 + xy = x3 - 19970723901492180991598876405614595610x 
	   + 1128216419636366078345077292747293694901309237422300864100

	Torsion points: 

O, [27699579731035398420, 147743024764975177294792323990], [27699579731035398420, -147743024792674757025827722410], 
[4234627545077060820, 33460177546079624864074621590], [-8213766415332397140, 27168026339294265704253226590], 
[-8213766415332397140, -27168026331080499288920829450], [4234627545077060820, -33460177550314252409151682410]

	Independent points of infinite order: 

P1 = [-2703095212592975148, -34094697795764678945874029418]
P2 = [44901815012942018820, 301266196829776702902849541590]
P3 = [44605145162873126520, 298302971098885510345090573590]
P4 = [15097279409901820820, 65328425588859962336358621590]
P5 = [7179393227630076720, 36808845915857031738953928090]

Dujella - Lecacheux (2009)

y2 + xy = x3 - 36180559909936665984616479270x 
	   + 2653605664924418914307133525288436083708900

	Torsion points: 

O, [105804676040940, -99886935778126468470], [-42659775320220, 2029636825097341138290], 
[142595695818540, 627604708716620443530], [-42659775320220, -2029636782437565818070], 
[142595695818540, -627604851312316262070], [105804676040940, 99886829973450427530]

	Independent points of infinite order: 

P1 = [47596634272620, 1019490087452772331530]
P2 = [65357521331220, 753734338701716054250]
P3 = [37071254323980, 1167601425603747441930]
P4 = [110821323250140, 71171122159540704330]
P5 = [20835879745863744/169, 568498652465192600946354/2197]

Dujella - Eroshkin (2009)

y2 + xy = x3 - 2989806201437063120537582346x 
	   + 62923591421774788114221127970660801865252

	Torsion points: 

O, [31499319107676, 761568248418148038], [11931636316404, 170143891921344990054], 
[32852997138612, 12584684220719275686], [32852997138612, -12584717073716414298], 
[31499319107676, -761599747737255714], [11931636316404, -170143903852981306458]

	Independent points of infinite order: 

P1 = [6853784163492, 206770538800519125222]
P2 = [30065337157044, 14520823416137528742]
P3 = [32052598075764, 4730940164143391142]
P4 = [30446686071732, 10862750159321762982]
P5 = [18923480796347904/11449, 294994843954559765609898354/1225043]

Eroshkin (2009)

y2 + xy + y = x3 - x2 - 81998483989093847324602383387x 
	     + 9039662557314583503984236650851472967245899

	Torsion points: 

O, [191882826583267, -608686499672848318814], [162720369372107, -73045620933554030854], 
[-17238856037493, -3232352015313135149254], [162720369372107, 73045458213184658746], 
[-17238856037493, 3232352032551991186746], [191882826583267, 608686307790021735546]

	Independent points of infinite order: 

P1 = [120758100624827, 947965475556972223546]
P2 = [-117778126528243, -4130799992267648976004]
P3 = [166003611484257, 47038619859647754246]
P4 = [292645587321907, 3178955262932679668346]
P5 = [-95474599855473557/289, -1331648350736416603324902/4913]

Eroshkin (2009)

y2 + xy = x3 - 12151449801116771364158721464095x 
	     + 16303853171210911871908176340222708651618600025

	Torsion points: 

O, [2013059167335440, -35199376003741729045], [2696250702242090, 56050108202283692852705], 
[2029966459194590, -1352774570748645034795], [2696250702242090, -56050110898534395094795], 
[2029966459194590, 1352772540782185840205], [2013059167335440, 35197362944574393605]

	Independent points of infinite order: 

P1 = [2012780061897290, 9918904791182773505]
P2 = [295193067596090, 112882913713614812821205]
P3 = [2797902037885640, 64868942660403853981205]
P4 = [2005584289115840, 543238680070107868955]
P5 = [521254825746693017/256, 7516252265355007774821851/4096]

Eroshkin (2011)

y2 + xy + y = x3 - x2 - 273298230287404986977345675193402x 
	     + 1763992752893124742187852765930832732626192628729

	Torsion points: 

O, [-6753079378194263, -1817038635834474322965369], [14916706572653387, -1003180850734141911526369], 
[8774156170053237, 203757145601492595687131], [8774156170053237, -203757154375648765740369], 
[-6753079378194263, 1817038642587553701159631], [14916706572653387, 1003180835817435338872981]

	Independent points of infinite order: 

P1 = [2917519700212787, 995727611790608931699581]
P2 = [9749082105993237, 161813140897747451659631]
P3 = [16971589375305737, 1419188683076734957659631]
P4 = [-29969163375951083/16, 96411464282442301352179509/64] 
P5 = [105832944850010347003/1089, 1073950829336930074855988831717/35937]


Dujella - Petricevic (2021)

y2 + xy + y = x3 - x2 - 17907983402610796845301737584278827x 
	     + 918615712609867556949586469889367324426713965667579

	Torsion points: 

O, [82951061106410987, -1976275127363926549108694], [107043849878983507, -15107149179874203677173694], 
[312782438932060587, -160989787726939064719374294], [107043849878983507, 15107149072830353798190186], 
[82951061106410987, 1976275044412865442697706], [312782438932060587, 160989787414156625787313706]

	Independent points of infinite order: 

P1 = [-20871881575755721, -35823127855862706963836978]
P2 = [25341438484441387, 21933436410138535072241706]
P3 = [44711474814624107, 14398152203503904068564586]
P4 = [39152434506895787, 16658086489089121799358506]
P5 = [33906769712321365268476627/544708921, 85358880162279388691036806552516251614/12712961507219]


Dujella - Petricevic (2021)

y2 + xy = x3 - 1179738992808013649201688520831270x 
	     + 20341741017663928259054974393093749054248510588900

	Torsion points: 

O, [15952185076191980, -2362565146295245279521910], [50609019531184940, 9500516559571041538875530], 
[-24141328549476460, 5895129440562658323404930], [-24141328549476460, -5895129416421329773928470], 
[50609019531184940, -9500516610180061070060470], [15952185076191980, 2362565130343060203329930]

	Independent points of infinite order: 

P1 = [11535103066584440, 2875443410585745355316030]
P2 = [11987700592944440, 2814618137603239479699530]
P3 = [-157905432994864866336860/6859161, -106731975354189938714972385345292930/17964142659]
P4 = [-10429750881708749637318580/331640521, -30995734403475544523315273036231515570/6039505527931]
P5 = [137922235446201087916288940/33651601, 1619706199365298827922155566381362361530/195212937401]


Dujella - Petricevic (2021)

y2 + xy + y = x3 - x2 - 53654574142929228694167821760024057x 
	     + 4785338664028031460084060425095105105184396047278489

	Torsion points: 

O, [131170351381553447, -2078925339028892298521524], [158479233871421167, 16202302676235643822482156], 
[-22183158125596953, 77231149171026458759854476], [-22183158125596953, -77231149148843300634257524], 
[158479233871421167, -16202302834714877693903324], [131170351381553447, 2078925207858540916968076]

	Independent points of infinite order: 

P1 = [107989472814371047, 15828870937931229162542476]
P2 = [119816576668103047, 8758965941338307086654476]
P3 = [14468122984476889983/289, 231730967643429660375450436588/4913]
P4 = [2069138649123976633188793/15944049, 179265251517760895377532602680292982/63664587657]
P5 = [3795828026213312594732703/26450449, 870548298911626352933180920188495732/136034659207]


Dujella - Petricevic (2021)

y2 + xy + y = x3 - x2 - 153589324870014604074433676903748x 
	     + 742021601843466503362801323651925035161079536103

	Torsion points: 

O, [11041389806035141, -626309113895788093288067], [6601144218190529, 125705487269559403805413], 
[-4931701839593067, 1174534407616595453471949], [-4931701839593067, -1174534402684893613878883], 
[11041389806035141, 626309102854398287252925], [6601144218190529, -125705493870703621995943]

	Independent points of infinite order: 

P1 = [6860715799010129, 105918910549412145638057]
P2 = [-4223058747553951, -1146875476348138945008007]
P3 = [29460168865547329, 4667523993212221528049113]
P4 = [119601134681835373/16, 6896780319858766620612073/64]
P5 = [69472733627579516270954386217/368275418449, 18272857113738350970677395747309805089843981/223490515613704793]


Dujella - Petricevic (2021)

y2 + xy = x3 - 89853212251485817694781304087091815x 
	     + 10436674438209609349697425142822012692015543267937225

	Torsion points: 

O, [250168069757608730, 60123240286726993759631885], [-101773201667434570, 136114579102870769867714885], 
[162508209917556230, -11245256732136583808403115], [-101773201667434570, -136114579001097568200280315], 
[250168069757608730, -60123240536895063517240615], [162508209917556230, 11245256569628373890846885]

	Independent points of infinite order: 

P1 = [94737922187911730, 52673205740712375316246385]
P2 = [147906924518856230, 19556119825483557164096885]
P3 = [128062654486223030, 32094651579935959890478085]
P4 = [-105678791251849270, -136938058305663834997210615]
P5 = [26016357816574554315005790230/181645587601, 1740515703527419715173274857672752233374115/77417167789958599]


Dujella - Petricevic (2021)

y2 + xy = x3 + 15993630692363832287530647849724279250x 
	     + 8084571165211855368609505912896196727654986513985562500

	Torsion points: 

O, [13067444468960253500, -49481840171844696256040722750], [2359335637100803580, 7678025294571082264579872770], 
[-186032235010395100, 2258938268260929318122464250], [2359335637100803580, -7678025296930417901680676350], 
[-186032235010395100, -2258938268074897083112069150], [13067444468960253500, 49481840158777251787080469250]

	Independent points of infinite order: 

P1 = [357427249035638000, 3721127978222812410370249250]
P2 = [3140149591273002800, 9448308470741529934626140450]
P3 = [1321999409463321080, 5615921708860791367715555270]
P4 = [2183490639358638394844/1849, 425331354585250679485515500339174/79507]
P5 = [9775075924081383428/49, 1152148241929742543831997021518/343]


Dujella - Petricevic (2021)

y2 + xy = x3 - 205961874661171633417509140632649829040786636x 
	     + 1140460666073155509458651792768519434207350324748379175417096240272

	Torsion points: 

O, [7944374253747867586136, -74942629594186233110130938866252], 
[10995674719117027034672, -452991642404924067503781331188004], 
[7944374253747867586136, 74942629586241858856383071280116], 
[-3589416773467166871016, 1354067184841265364664911638157812], 
[10995674719117027034672, 452991642393928392784664304153332], 
[-3589416773467166871016, -1354067184837675947891444471286796]

	Independent points of infinite order: 

P1 = [8291862345189438439784, 52535628672749764234348028460404]
P2 = [213271493137093433539544/25, 8165249972489444785209067908328612/125]
P3 = [1753161790747535493259281657656/213656689, 168720372356186561784514695538665332193094292/3123019823113]
P4 = [95732016661591368158357107115635544/1473147795289, 28951753557008746593938135376148237330651680137293732/1788008093019503837]
P5 = [202416987812938966451533340440430706584/24531789393870529, 
     202906346176238992996504708397170843784211092392408355956/3842322742782870001808417]


Dujella - Petricevic (2021)

y2 + xy = x3 - 115622311899313072951091649881515042240x 
	     + 482699978073801087413569916568779663002986741070291865600

	Torsion points: 

O, [-3900690837002273920, -29569517109017744809660143040], [9201457540189236080, -14066426049470419327307493040], 
[5791076149766065280, 2708349167246258449331984960], [-3900690837002273920, 29569517112918435646662416960], 
[9201457540189236080, 14066426040268961787118256960], [5791076149766065280, -2708349173037334599098050240]

	Independent points of infinite order: 

P1 = [6196436620726422400, 2042292258422140941266213440]
P2 = [6634886241812585060, 2763723161587537540396036880]
P3 = [360469403177123860745/64, 1631350563817018781460635214895/512]
P4 = [1418404204199315800596020/214369, 268989707593956622556210782616127620/99252847]
P5 = [-5599673048913880570, -30895984843646577223583849140]


Dujella - Petricevic (2021)

y2 + xy = x3 - 18708808092249102134844156946089008169080x 
	     + 1297973789068237390285141073869973936158531467688333502990400

	Torsion points: 

O, [-96756449156877963440, 1484033723006317607134444231720], [63422149911664376560, -605415769231990961879741308280], 
[-96756449156877963440, -1484033722909561157977566268280], [203493239852980395760, -2432572889203502153475108143480], 
[63422149911664376560, 605415769168568811968076931720], [203493239852980395760, 2432572889000008913622127747720]

	Independent points of infinite order: 

P1 = [-75812756293997484320, -1510165775396254758356585212280]
P2 = [-132995392699033863440, -1197399914497794982112895868280]
P3 = [10511984782312250440653424/9, 34082157752170007246414866787999272024/27]
P4 = [-17959052046459974537360/1849, -96684345226750490340632924114729960/79507]
P5 = [139606293180734861394160/961, 38219854145292529480746442790310520/29791]


Dujella - Petricevic (2021)

y2 + xy = x3 - 1377820803344637211579216383238890816922370x 
	     + 743998244439833798717712321871231193227157137944012197218632900

	Torsion points: 

O, [555771423229035167140, -12243877442535555215621305583570], [-772079835363765636260, -36708902174517707693853483597170], 
[1575422313076769927140, -49834492336204554660051099383570], [555771423229035167140, 12243877441979783792392270416430], 
[-772079835363765636260, 36708902175289787529217249233430], [1575422313076769927140, 49834492334629132346974329456430]

	Independent points of infinite order: 

P1 = [-1350996389092171995110, -11815345758945944659592731891070]
P2 = [-489999236916532706300, -36076043800795541074009284974930]
P3 = [50803476694566890617540, 11447889589088230874675075502298030]
P4 = [65318779243663253864143084971460/60548968489, 337481043574455836891715068921671111421682796090/14899103029182763]
P5 = [-6699118075543513028511058981271789799209870/6898116050727872182969, 
     -19564632952704888705388158980572980588791114885247186076475782150/572922323695418548427415533946797]


Dujella - Petricevic (2021)

y2 + xy + y = x3 - x2 - 391242185070640375240837276550158296236607x 
	     + 95479764698939515140521266715914513384217058559373840567620839

	Torsion points: 

O, [332499390121787134547, -1466876825555050648085426156074], [-252639532273880828853, -13349076795731503916930264732074], 
[561262975782789575827, -7259263121742264604085094842474], [332499390121787134547, 1466876825222551257963639021526], 
[-252639532273880828853, 13349076795984143449204145560926], [561262975782789575827, 7259263121181001628302305266646]

	Independent points of infinite order: 

P1 = [74226254508017033107, 8176079438219227254310287274966]
P2 = [5574037288764043097299, 413641651805281478485973097374038]
P3 = [23682732847472414296147, 3643323706241561444792342725267926]
P4 = [272820241187688881757, 3007861221783256180864293296066]
P5 = [6491835160588561439034963/16129, 3671001606869767973619311823147247658/2048383]


Dujella - Petricevic (2021)

y2 + xy = x3 + 7277061617690468036766843700447533254310x 
	     + 2170395305007409286933667399487826007666114216620875605344100

	Torsion points: 

O, [387608695252715248980, -7951450942591655568502901624490], [54204460726647744180, 1650485961419257158283415972310], 
[-84645676519828111020, 973625437882791424883283975510], [387608695252715248980, 7951450942204046873250186375510], 
[54204460726647744180, -1650485961473461619010063716490], [-84645676519828111020, -973625437798145748363455864490]

	Independent points of infinite order: 

P1 = [76833976858036588340, 1784126452302940907471087243510]
P2 = [22647573000550201621620/169, 5176812090900963363850517535475470/2197]
P3 = [-137064690116217555959448780/1315609, -800509880704693792577753630663165046270/1509003523]
P4 = [9202045438822385641465674630/119006281, 2320694519604590356044280551785470231115040/1298239519429]
P5 = [2433902669716049086511255802762320521620/14976429976707768529, 
     160254079395732325278800251503469161194857215946103357741670/57957874536195868674570539417]


Dujella - Petricevic (2021)

y2 + xy = x3 - 1855628644686280702792353193428311788466094670x 
	     + 18115623398178620834089480532070307448527787064967838439894336944900

	Torsion points: 

O, [246364361716069333257740, -120474636428090830130079458115661870], 
[66778451928858613541180, 13856005275509395708828717064514530], 
[39326803309716802273340, 2441805627966974127084973215426530], 
[246364361716069333257740, 120474636427844465768363388782404130], 
[39326803309716802273340, -2441805628006300930394690017699870], 
[66778451928858613541180, -13856005275576174160757575678055710]

	Independent points of infinite order: 

P1 = [7678873296328893351740, 2078285746658848561616699149948130]
P2 = [63918053701949647314357248315/206116, 16008061634767249437292398997574921212564445/93576664]
P3 = [-3826147499684861512022660/81, -444258543015177485153223206917374830/729]
P4 = [-16274570504731173178536246966340/348606241, -11269287050696988190790220020160435724269377090/6508827125711]
P5 = [30339237664481242294203160585441340/1050568794925441, 
     144717177803044687788686084274676141643766904130499015070/34051539003576162978239]


Dujella - Petricevic (2021)

y2 + xy = x3 + 28934267683831835064426859651659481490x 
	     + 126197007971554693087737153226059352663091351422668052100

	Torsion points: 

O, [2587215086238348860, 14777488846035849183322592450], [-2423989410796411780, 6466680380768958415845770690], 
[17808726447974634620, 79306558336395920947448714690], [17808726447974634620, -79306558354204647395423349310], 
[-2423989410796411780, -6466680378344969005049358910], [2587215086238348860, -14777488848623064269560941310]

	Independent points of infinite order: 

P1 = [2444530349746180220, 14544261873217196961710090690]
P2 = [-412057492435262380, -10686648790468757277125040310]
P3 = [8749997565960475580, 32392793881142723744781717890]
P4 = [73233206625661473916, 628492118932761107389302511042]
P5 = [78298505297148528499745180/76729, 692845286313085774129903695084776665370/21253933]


Dujella - Petricevic (2021)

y2 + xy = x3 - 810792386114073513747228940886523400x 
	     + 281005051809319098968356653671663871284733730875560000

	Torsion points: 

O, [545030164878202640, -31689897403385341582625800], [518390997074896400, 2095156436167279519307000], 
[170785151070060800, 384076996281072535416302600], [518390997074896400, -2095156954558276594203400], 
[545030164878202640, 31689896858355176704423160], [170785151070060800, -384076996451857686486363400]

	Independent points of infinite order: 

P1 = [-140390387929901200, -626151331915580188957275400]
P2 = [-121238937901237520, -614428663783258114792001000]
P3 = [497253402180126410, 28055765059788611585853140]
P4 = [1750146716496193925/16, 28161888665558678054868436775/64]
P5 = [8515783801667944299680/17161, 65903681764230241766506021178920/2248091]


Dujella - Petricevic (2021)

y2 + xy = x3 - 2624072431622429725423386569042315586456x 
	     + 67869752984781371426649184581366550790317236811261591075392

	Torsion points: 

O, [-36134636648215405776, -339865016410974205530250853016], [75888091484836236312, -552967998605972101676767301184], 
[23769134440020188016, 137574387524308323847276847976], [23769134440020188016, -137574387548077458287297035992], 
[-36134636648215405776, 339865016447108842178466258792], [75888091484836236312, 552967998530084010191931064872]

	Independent points of infinite order: 

P1 = [-4101299749567101648, -280290695570043789438428588184]
P2 = [140749901161132849656, 1576978952012604033585324446688]
P3 = [305429624480626746576/25, 24249518982740390846068363756584/125]
P4 = [-101397424316703799310544/12769, -428534401999287153780399257436284952/1442897]
P5 = [4130618238590661802389694128/351649, 265471844202757692957269587067207706878184/208527857]


Dujella - Petricevic (2021)

y2 + xy = x3 + 39480823857257291749892179216018633223790820x 
	     + 24280599600327280676573359696182806472317896177020489863095856400

	Torsion points: 

O, [3820022837127337306360, 480460420964395611493840176371620], 
[-132768828626054183240, 137972593194760921917087604403620], 
[20790833387383131692800, 3135624266872797093129754915120420], 
[3820022837127337306360, -480460420968215634330967513677980], 
[-132768828626054183240, -137972593194628153088461550220380], 
[20790833387383131692800, -3135624266893587926517138046813220]

	Independent points of infinite order: 

P1 = [147260183801722964152, 173487020834330954403550670504356]
P2 = [7093970805417583030750/9, 6383079025412560419953737366419910/27]
P3 = [1543282654020305669560, 298138121466673265209511182662820]
P4 = [129985986139860965662483072135/106276, 46865206351062509432319397035374696213411495/34645976]
P5 = [3626467749438645772154116009720/111915241, 7037042504241119584509150442382286374344659340/1183951334539]


Dujella - Petricevic (2021)

y2 + xy + y = x3 - x2 - 62795666246210832061948614703945509487353x 
	     + 6968363897937466448633681286676453037664022073020728793789593

	Torsion points: 

O, [120159346105764849639, -1075997490836551302098570831988], [-158371555957029513497, -3597388943469256133994245239668], 
[319736982081517765751, -4424650763001078408709609839172], [120159346105764849639, 1075997490716391955992805982348], 
[319736982081517765751, 4424650762681341426628092073420], [-158371555957029513497, 3597388943627627689951274753164]

	Independent points of infinite order: 

P1 = [-74719806535816755481, -3353099991532049915746804015988]
P2 = [-31717024876593189301, -2988000877068472272733305305912]
P3 = [3983890412962979671254277/11664, 6344467831997292322976251929327516619/1259712]
P4 = [371969191848230286317311/225, 224416870060248204144325699134978196/3375]
P5 = [4766946237593874599482406701/9265936, 296927258108328609424272173934108867218745/28205509184]


High rank curves with prescribed torsion Andrej Dujella home page