Torsion group Z/6Z, rank = 7

Dujella (2001)

y2 + xy = x3 - x2 - 45123702275641081919424x 
	    - 1963535841750202515136116268762932

	Torsion points: 

O, [-185908156668, 92954078334], [344607416557, 153003436850034459],
[344607416557, -153003781457451016], [-75521527458, -31836073229860926],
[-75521527458, 31836148751388384] 

	Independent points of infinite order:

P1 = [-46184748668, -4687994158267666]
P2 = [-60161183646, -23095727833899384]
P3 = [-48542581178, -10606589957382016]
P4 = [-55854944093, -19559910217201666]
P5 = [-185253203193, -6173748038545641]
P6 = [-64106657393, -25801849446340566]
P7 = [-45896523588, -3287014604709246]

Dujella (2006)

y2 + xy = x3 - 31124678862448817636407940x 
	    + 66835225530144951377745363438177411600

	Torsion points: 

O, [3234077113480, 40624133358323260], [3234077113480, -40627367435436740], 
[2536040165080, -2052397774202172740], [2536040165080, 2052395238162007660], 
[3220528153480, -1610264076740]

	Independent points of infinite order:

P1 = [28959993461320/9, 268083677343528020/27]
P2 = [7671451839880, 16719376910549900860]
P3 = [-21698790966705/4, 69762015022586294205/8]
P4 = [3219393486280, 4790107476198460]
P5 = [7588642289980, 16360070989734833260]
P6 = [-2034896926520, 11033795763492203260]
P7 = [1858293133480, 3926015569011743260]

Eroshkin (2007)

y2 + xy = x3 - 841913947832430618894580x 
	    + 295136017837598326614751155711520400

	Torsion points: 

O, [667332397160, -174598124235145780], [-1058632940440, 529316470220], 
[667332397160, 174597456902748620], [401533787720, 147709535370407660], 
[401533787720, -147709936904195380]

	Independent points of infinite order:

P1 = [-66649549720, -592412943604904500]
P2 = [349723116710, 208500601797241970]
P3 = [116593882760, 445599531600982220]
P4 = [490218516062, 14855023338761192]
P5 = [168034756136, 398007187783655372]
P6 = [342150521960, 217092549535759820]
P7 = [406678659560, 141446471939830220]

Eroshkin (2007)

y2 + xy = x3 - 8034015051455135062999285730x 
	    + 289348572973066562201234135502825455736900

	Torsion points: 

O, [-104000906778140, 52000453389070], [31559939385460, -259287856260895148930], 
[31559939385460, 259287824700955763470], [76099405897000, 344478640455444367630], 
[76099405897000, -344478716554850264630]

	Independent points of infinite order:

P1 = [67148375096860, 229440835734440214070]
P2 = [-21739950377660, -673596907070996876210]
P3 = [-6632888557628, -585102965527994657714]
P4 = [-52920008223740, -752532224932127441330]
P5 = [28187521974790, 292036985720387317090]
P6 = [37197034000612, 204874522324991904142]
P7 = [43362951743740, 150024312364188466390]

Eroshkin (2007)

y2 + xy = x3 - 822259949983210124060751x 
	    + 286775782051582928617737165270930681

	Torsion points: 

O, [535079801286, -267539900643], [584705383110, -76780918112411619], 
[584705383110, 76780333407028509], [1274038014006, 1143314401264057917], 
[1274038014006, -1143315675302071923]

	Independent points of infinite order:

P1 = [160504431390, 398665542695590701]
P2 = [-115474044474, -616591949781999843]
P3 = [192070044378, 368686646528688837]
P4 = [541104466374, 16715448906014493]
P5 = [440598323286, 100106751037992957]
P6 = [539087782536, 13146152721528357]
P7 = [538400443590, 11811127630377501]

Eroshkin (2007)

y2 + xy = x3 - 51054993026763259730885310x 
	    + 140295994906362117844167089363816108100

	Torsion points: 

O, [16111853758239/4, -16111853758239/8], [4627603818420, 1769896228442004690], 
[4627603818420, -1769900856045823110], [56375302020, 11722539518574675090], 
[56375302020, -11722539574949977110]

	Independent points of infinite order:

P1 = [3522275931120, 2040851885423177490]
P2 = [2659435984970, 4829867772309556640]
P3 = [4234397012610, 179227639595181750]
P4 = [4222794188832, 45758176345977486]
P5 = [6671554403460, 9829966339234300650]
P6 = [9657738289782, 23409735015050279286]
P7 = [7358694486180, 12770040775324262730]

Eroshkin (2007)

y2 + xy + y = x3 - x2 - 45374649173740836605820102362x 
	      + 3720066318230759490581315479518302807124761

	Torsion points: 

O, [128336794962481, -102854390133902441241], [128336794962481, 102854261797107478759], 
[44278012708881, 1340811652622470193959], [44278012708881, -1340811696900482902841], 
[122348007122481, -61174003561241]

	Independent points of infinite order:

P1 = [-81706520877519, -2623356956662003561241]
P2 = [-62237678361039, -2510577534231057953561]
P3 = [115442739052081, 142831727702898531559]
P4 = [121158369112369, 32771575184217466599]
P5 = [108287374802481, 276331769484406678759]
P6 = [124251519318801, 21138819990513227719]
P7 = [124109673231201, 17914148013272118919]

Eroshkin (2007)

y2 + xy = x3 - 533024166437861795831860x 
	    + 150145561559705338985839395548651600

	Torsion points: 

O, [-843254960680, 421627480340], [353471641820, -76812672080584660], 
[353471641820, 76812318608942840], [493903097270, 85825911577001090], 
[493903097270, -85826405480098360]

	Independent points of infinite order:

P1 = [225881035820, 203151228866431340]
P2 = [-199633635190, -498596928696485410]
P3 = [379553028866, 50131880774897702]
P4 = [268669162916, 162270575082307472]
P5 = [329053583870, 101885757234320840]
P6 = [316093339430, 115076505790470290]
P7 = [-232169239720, -511256044385040460]

Eroshkin (2007)

y2 + xy = x3 - 3027369717001109222247250443030x 
	    + 2028817184758375459182141696978493700290404900

	Torsion points: 

O, [-2009255022303540, 1004627511151770], [896256825536460, 5954684828112112111770], 
[896256825536460, -5954685724368937648230], [1117198419525660, -6407493369462133642230], 
[1117198419525660, 6407492252263714116570]

	Independent points of infinite order:

P1 = [719144428256460, 14953932762832583791770]
P2 = [191272884896460, 38167541407197495151770]
P3 = [-263920449615540, -53003951094727421776230]
P4 = [95788311456540, 41709824304933169890570]
P5 = [775746301887210, 12131641521829168430520]
P6 = [-697452700998540, -61652212024596037573230]
P7 = [665290658317260, 17584134432951765506970]

Eroshkin (2008)

y2 + xy = x3 - 165622879312545076279689272890746x 
	    + 818377467155538128945404717298826491824235027940

	Torsion points: 

O, [8747576267131284, 197342405753318848488246], 
[8747576267131284, -197342414500895115619530], 
[-1055097540542892, -995967465143662385937354], 
[-1055097540542892, 995967466198759926480246], 
[7126469030754708, -3563234515377354]

	Independent points of infinite order:

P1 = [6097805914754708, 187556538864956915662646]
P2 = [7739550190564476, 11613251360835905805870]
P3 = [2300450906945940, 670480663392912136839990]
P4 = [8074157605384596, 86503689476159534451510]
P5 = [5686582350100884, 245840560739210811777846]
P6 = [5104993505865108, 325445490174819334094646]
P7 = [-3097342426993716, -1140900428066739076886754]

Eroshkin (2008)

y2 + xy = x3 - 7124549942935826931044066x 
	    + 7319360155313501266864951695617016900

	Torsion points: 

O, [617523082948, -1776308031346216754], [1598858413924, -124308508474598834], 
[1598858413924, 124306909616184910], [617523082948, 1776307413823133806], 
[1534675231588, -767337615794]

	Independent points of infinite order:

P1 = [1353468402148, 394833692638471246]
P2 = [-118478415284, -2856886785679150610]
P3 = [1379258899300, 341468869627858510]
P4 = [-200668339100, -2956509884462198450]
P5 = [2211778113316, 1543168340947208590]
P6 = [196629775204, 2434350708655533646]
P7 = [978986723668, 1132605317857492366]

Eroshkin (2008)

y2 + xy = x3 - 822259949983210124060751x 
	    + 286775782051582928617737165270930681

	Torsion points: 

O, [535079801286, -267539900643], [584705383110, -76780918112411619], 
[584705383110, 76780333407028509], [1274038014006, 1143314401264057917], 
[1274038014006, -1143315675302071923]

	Independent points of infinite order:

P1 = [160504431390, 398665542695590701]
P2 = [-115474044474, -616591949781999843]
P3 = [192070044378, 368686646528688837]
P4 = [541104466374, 16715448906014493]
P5 = [440598323286, 100106751037992957]
P6 = [539087782536, 13146152721528357]
P7 = [538400443590, 11811127630377501]

Eroshkin (2008)

y2 + xy + y = x3 - 4019175690941783130628x 
	      + 97050922917328246600400524493006

	Torsion points: 

O, [47323693630, 3582099886172822], [47323693630, -3582147209866453], 
[128914071400, -41488914336241798], [128914071400, 41488785422170397], 
[158454146295/4, -158454146299/8]

	Independent points of infinite order:

P1 = [-21470236145, -13169894998135303]
P2 = [6797578855, 8369247193969697]
P3 = [40568361277, 875555712946313]
P4 = [39706357882, 254801927431934]
P5 = [31943322940, 1122165893548322]
P6 = [-49413353270, -13228743202800553]
P7 = [24325376740, 3698212836832562]

Dujella - Eroshkin (2008)

y2 + xy + y = x3 - x2 - 82332276908073834616547402x 
	      + 287541668542010063173870439227562187401

	Torsion points: 

O, [5357890870801, -472504457312885001], 
[5357890870801, 472499099422014199], 
[5120414604081, -465418402990226921], 
[5120414604081, 465413282575622839], 
[-10477415138799, 5238707569399]

	Independent points of infinite order:

P1 = [1953110661201, 11583955051308889399]
P2 = [4902790317201, 1316766148617553399]
P3 = [-3076314896879, -22620969178104943881]
P4 = [5172320878501, 259446562402368799]
P5 = [1267674645321, 13609124264904414319]
P6 = [-4883644704239, -23940515530725784841]
P7 = [5132894729761, 416080642067811079]

Dujella - Eroshkin (2008)

y2 + xy + y = x3 - 41061306153084043265108x 
	      + 3185903340945571830683716617085118

	Torsion points: 

O, [110033611989, -55016805995], 
[143847305214, -15995081577800645], 
[143847305214, 15994937730495430], 
[-30120225081, -66297445027539305], 
[-30120225081, 66297475147764385]

	Independent points of infinite order:

P1 = [58085745864, 31572195682253005]
P2 = [67056207819, 27092556752728645]
P3 = [-49402075188, -71371174655444750]
P4 = [102305844864, 7474867295631130]
P5 = [46255763829, 37222952221019245]
P6 = [-114023465736, -79908620275049795]
P7 = [-118478078886, -79922932947100745]

Eroshkin (2008)

y2 + xy = x3 - 1523372635414000905181910527726x 
	    + 723243212874903410571391010646562847229006980

	Torsion points: 

O, [697959663027580, -348979831513790], 
[791511270622844, -3653843709347513251774], 
[791511270622844, 3653842917836242628930], 
[35976792126956, 25855052062111292942354], 
[35976792126956, -25855052098088085069310]

	Independent points of infinite order:

P1 = [561238227098684, 6712060319827202302850]
P2 = [374680735006076, 14320077810680157304130]
P3 = [686296076050616, 1002787707780741619910]
P4 = [-560717155492996, -37431708463155880204990]
P5 = [678321148470884, 1419922026769708037666]
P6 = [361042809522293564/529, 14671607665824712289745358/12167]
P7 = [734470260787580, 760771999563439987010]

Eroshkin (2008)

y2 + xy = x3 - 3726896606489538014807823629390x 
	    - 1065145370395664163469346840915100916019739900

	Torsion points: 

O, [3056664594482380, -126893679880281021886190], 
[3056664594482380, 126893676823616427403810], 
[-1328649861082520, 39257048432445075840310], 
[-1328649861082520, -39257047103795214757790], 
[-292515363927620, 146257681963810]

	Independent points of infinite order:

P1 = [-387790567665620, -17938601857657080778190]
P2 = [-581331287466620, -30082513078255057312190]
P3 = [-508441467177620, -26425835943837652786190]
P4 = [2333741368028380, 54291906891132792703810]
P5 = [-298275933778370, -4467775901762557061690]
P6 = [2603086474436380, 82898059700700975523810]
P7 = [2777911298075080, 100092095418999114324310]

Eroshkin (2008)

y2 + xy = x3 - 54059464705737223501792212385x 
	    + 4787734047854039033545219031800955876871497

	Torsion points: 

O, [173473070950634, 793839676003369155083], 
[173473070950634, -793839849476440105717], 
[472318017697274, -9198979192758376947877], 
[472318017697274, 9198978720440359250603], 
[145248077152234, -72624038576117]

	Independent points of infinite order:

P1 = [-106978355783488, -3057225316048442830627]
P2 = [407968471326934, 7115809301665634542483]
P3 = [34571576919914, 1720503642820954580363]
P4 = [1770192589310474, 73865656604392517397323]
P5 = [-19724131498006, -2417919867928123342837]
P6 = [156968131536874, 411895274952756795403]
P7 = [-777338126866, -2197670598490440689917]

Dujella - Eroshkin (2008)

y2 + xy = x3 - 699112954366367467920156400x 
	    + 5722163130057598068986876309705284428032

	Torsion points: 

O, [9356543694304, -4678271847152], 
[28109600724704, -91000939199534643952], 
[28109600724704, 91000911089933919248], 
[-13918500153136, 112944286895464717328], 
[-13918500153136, -112944272976964564192]

	Independent points of infinite order:

P1 = [-2319224044576, -85621772128587684592]
P2 = [-19980795007696, -108231314617690247152]
P3 = [3084205353854, 59960762043281605148]
P4 = [-8602165270046, -105354216093065334452]
P5 = [-8942053648106, -106106824584020535332]
P6 = [8544143171744, 19302450572437221968]
P7 = [-9703877652256, -107668475781078537712]

Dujella - Eroshkin (2008)

y2 + xy + y = x3 - 5871521435329649314324031629344788x 
	      + 172993600167184429589198294960718574003359733763906

	Torsion points: 

O, [50026756825466850, -2112157387935390374766038], 
[50026756825466850, 2112157337908633549299187], 
[112061677002855645, -30368921158594179389981513], 
[112061677002855645, 30368921046532502387125867], 
[45389724976446825, -22694862488223413]

	Independent points of infinite order:

P1 = [13751724756837405, 9739129381467531623506987]
P2 = [2072162199261765, 12682103647933379722415047]
P3 = [28757641336076406, 5284422155549216622773239]
P4 = [-21766829310093075, -17043620298012166054485413]
P5 = [49531516023267525, 1920268459223220554249587]
P6 = [311262675619341225, 168825123175264112083874587]
P7 = [-86121186531920475, -6317223662181808961737913]

Dujella - Eroshkin (2008)

y2 + xy + y = x3 - x2 - 960030060545458886002887849322805356175498x 
	      + 362055559646249146707021073044994258163432080303497826046420681

	Torsion points: 

O, [570599534796257472721, -202077054325406019870532266953], 
[570599534796257472721, 202077053754806485074274794231], 
[758174730999734226393, 8366946312319657185484591168831], 
[758174730999734226393, -8366946313077831916484325395225], 
[565957128180916193937, -282978564090458096969]

	Independent points of infinite order:

P1 = [302402190465795542337, 9969662239818276823425759660391]
P2 = [-36503726239229752362225/841, -489996817120924115497412908474740637/24389]
P3 = [-10627898494304311983365/81, -16067148979418971637722844583511907/729]
P4 = [19984604975097918012261157/35344, 1573607074949468850736100773958865/6644672]
P5 = [153752006639685347310843025/1159929, 19237122998953125515470914485199788558131/1249243533]
P6 = [87448670109363398545681569421/4243600, 25831364797662483060401244279320098647203439/8741816000]
P7 = [-709692878534678985967437575/822649, -17470222587226670588579630248713748783419/746142643]

Dujella - Eroshkin (2008)

y2 = x3 + x2 - 92415860650236343941767865x 
	+ 339812153247400733310842691312151100400

	Torsion points: 

O, [6909772426305, 5580892492438097835], 
[6909772426305, -5580892492438097835], 
[-1595669488665, -21982140267680708115], 
[-1595669488665, 21982140267680708115], 
[5187612265584, 0]

	Independent points of infinite order:

P1 = [5059548243113, 1322560829889679611]
P2 = [2329919087475, 11710623159368235795]
P3 = [5956798424325, 822948425306202195]
P4 = [5911086067635, 270077175616413165]
P5 = [4213852192935, 5020842023157814035]
P6 = [5997383704203, 1129752105506331021]
P7 = [9900583970025, 19882451547851887995]

Dujella - Eroshkin (2008)

y2 + xy = x3 - 14449832020856516030717699280x 
	    + 667048026760547478386730660166577486342400

	Torsion points: 

O, [81342134662560, -172833966506633526480], 
[81342134662560, 172833885164498863920], 
[194935071880320, -2292976280019735004080], 
[194935071880320, 2292976085084663123760], 
[72082042220960, -36041021110480]

	Independent points of infinite order:

P1 = [72959231988960, 34131852917983817520]
P2 = [72183037296960, 10821322957220681520]
P3 = [-59084864531040, -1146537313307031222480]
P4 = [64271200856480, 61892037296444510000]
P5 = [39821144111520, 393426603764064175920]
P6 = [72397034898960, 19489256450671913520]
P7 = [36083711289930, 438892550626700856300]

Dujella - Eroshkin (2008)

y2 + xy + y = x3 - 2775271711608913149065000293562148x 
	      + 56273815466836272280793492720347500222386983036078

	Torsion points: 

O, [30419896594579709, -15209948297289855], 
[30539861846287934, -37625933430885973733130], 
[30539861846287934, 37625902891024127445195], 
[37410378037431539, 2192495549212538777462685], 
[37410378037431539, -2192495586622916814894225]

	Independent points of infinite order:

P1 = [23527031657479259, 2000655201679940358341295]
P2 = [17732988323174264, 3554750357534057941439610]
P3 = [30436311237146339, 6193452439775111945325]
P4 = [30420923954511659, 978699312440024698095]
P5 = [16081107760461884, 3975296090112913905079170]
P6 = [7514721685079492, 5986884421179295713505257]
P7 = [34118644627116959, 1141141183475891614655145]

Dujella - Eroshkin (2008)

y2 + xy + y = x3 - x2 - 447557589334393730351824217x 
	      + 3643868079922687465968426756008094647609

	Torsion points: 

O, [12330077305767, -6165038652884], 
[13017185672167, 4863377085108668716], 
[13017185672167, -4863390102294340884], 
[24751450966047, 87919023142864239436], 
[24751450966047, -87919047894315205484]

	Independent points of infinite order:

P1 = [12378455027367, 706804200079139116]
P2 = [13274227846399, 6470977876774945332]
P3 = [11978561665023, 1235741779388591308]
P4 = [6202585988457, 33263790847686514576]
P5 = [-9143473891253, -83496560120664187764]
P6 = [-4602833014143, -74875794704841561074]
P7 = [12367420151767, 608557163570093116]

Dujella - Eroshkin (2008)

y2 + xy = x3 - 3418877004771000403942399401264510x 
	    + 76895638096171882779790294730021122439698272834372

	Torsion points: 

O, [33066753943523484, -16533376971761742], 
[37490621371389084, 1189383687224792717607858], 
[37490621371389084, -1189383724715414088996942], 
[1726222621743804, 8426092755843902278048818], 
[1726222621743804, -8426092757570124899792622]

	Independent points of infinite order:

P1 = [28696729638957564, 1554629089706794412541138]
P2 = [35759513207518284, 604549560434576731724658]
P3 = [-11929275082666212, -10769528108369840615640654]
P4 = [19914401209264284, 4087599553495003645403058]
P5 = [21438527488223484, 3667876888745444119458258]
P6 = [-988057659082596, -8959504511869625204066382]
P7 = [34667553044632692, 190692351587248200351570]

Dujella - Eroshkin (2008)

y2 + xy = x3 - 492846919517842269542923229020x 
	    + 51349587205341386622021930561564828983536400

	Torsion points: 

O, [106651142448440, -53325571224220], 
[926456309866040, -19747041447198830289820], 
[926456309866040, 19747040520742520423780], 
[-452900735476600, 13478195174708149200020], 
[-452900735476600, -13478194721807413723420]

	Independent points of infinite order:

P1 = [103098163305272, 1278213246139570460516]
P2 = [37096316376800, 5754809409709130827580]
P3 = [23035839331640, 6325240594018567732580]
P4 = [-44624499484360, -8558841692238034584220]
P5 = [-256901914735240, -12688882382832902109340]
P6 = [86677934390252, 3046613018124846715712]
P7 = [-578597171822080, -11950302374007020949220]

Voznyy (2019)

y2 + xy = x3 + 358804192012993775138370x 
	    + 38355557903006419927041938707320900

	Torsion points: 

O, [1388323126260, -1792318404040559430], 
[-415131437281/4, 415131437281/8], 
[158341173060, -314863466865742830], 
[158341173060, 314863308524569770], 
[1388323126260, 1792317015717433170]

	Independent points of infinite order:

P1 = [-2502620820, -193539636517234350]
P2 = [-41564685048, -152873019876940794]
P3 = [59641572270, 244882301332109910]
P4 = [86853728460, 264904141061822370]
P5 = [38028071964820/9, 236911052815360278950/27]
P6 = [43519964480, 232493268154096850]
P7 = [569694173520780, 13597619921833645132050]

Voznyy (2019)

y2 = x3 + x2 - 3644556202475792269518216279468858086405x 
      + 84686319731701109368750690123396573251362730371973553418100

	Torsion points: 

O, [18964173200804056615, 149634880162561915766528758875], 
[34796269593421942644, 0], 
[35567807949339641365, -7292088587989896288245022375], 
[35567807949339641365, 7292088587989896288245022375], 
[18964173200804056615, -149634880162561915766528758875]

	Independent points of infinite order:

P1 = [33397751500810106800, 14782315447325747671195555710]
P2 = [10662355826536264240, 216884585579242517737407857250]
P3 = [30336154988284996240, 45192083152648098137140419750]
P4 = [30421173736485368365, 44360466201973680330105894375]
P5 = [97389258562231353415, 808362818770172035675816589925]
P6 = [45068824145269032615, 109426704356314995618934294875]
P7 = [8209343546510456740, 235202382470193943414901791500]

Voznyy (2019)

y2 + xy = x3 - 379182143604577428048375150248709410351240x 
	    + 119439444845999205909039638251442235171869686073489510859585600

	Torsion points: 

O, [-2943451660168556992641/4, 2943451660168556992641/8], 
[711776418853572531280, -14496576905961913575742954007240], 
[124365538579084476880, -8614278185466188569356043420040], 
[124365538579084476880, 8614278185341823030776958943160], 
[711776418853572531280, 14496576905250137156889381475960]

	Independent points of infinite order:

P1 = [-159251929816652702670, -13258435675498075975181987558790]
P2 = [234489482690010071730, 6589286668496541140498542626810]
P3 = [263816407837796106730, 6145433879995852010424134191810]
P4 = [38831844354250083016516/121, 7387163240857668695242371001465112/1331]
P5 = [4246163864350408571280, 273984145341898524425204325075960]
P6 = [1091388671299218195963760/49, 1139739173469581084421310134086451400/343]
P7 = [-110881052565373000920118788848/152744881, -6583112395199996168503880338967354335155256/1887773984279]

Voznyy (2019)

y2 = x3 + x2 - 89280997598876690534935351936005x 
      + 298360732693992690511174782786675112436099714100

	Torsion points: 

O, [-10811048042186956, 0], 
[8781358813361685, -437610219765512058526905], 
[8781358813361685, 437610219765512058526905], 
[2528572946672295, 297949839218968516856955], 
[2528572946672295, -297949839218968516856955]

	Independent points of infinite order:

P1 = [-597819986672400, 592892100941631170502690]
P2 = [6929473532734800, 111477060444273579201510]
P3 = [3567283670611785, 158951570698240272514695]
P4 = [4097199969093455, 36585829836172420237515]
P5 = [2320810454503619055, 3535541293375506225002053365]
P6 = [7615014145368873444, 21013855300643216828225891580]
P7 = [1502873358525043741/225, 13589014692689874149682761/3375]

Voznyy (2019)

y2 = x3 + x2 - 683296280266159149478668116716868339845x 
	    + 6874806981839357142636691301220260598519026095365342406100

	Torsion points: 

O, [15071505734358181204, 0], 
[15359069197330993685, 1797780623720453310021057975], 
[15359069197330993685, -1797780623720453310021057975], 
[8654052888622325735, 40120439016949728002033743275], 
[8654052888622325735, -40120439016949728002033743275]

	Independent points of infinite order:

P1 = [15025368730457183285, 425780269085801019594197175]
P2 = [14447839800407097635, 4300575588730943467395525075]
P3 = [5301544734267991760, 58320565823305314299141921550]
P4 = [1906048856275312536136915/1369, 2631025394986677305914952404525550775/50653]
P5 = [33282848856756688262555/2209, 10060793028174427310047831353645/103823]
P6 = [8264337748462978578240365/2809, 23757186275805612020621973612558825675/148877]
P7 = [2149460699744144583831540001/141895744, 596907116632457416064423538567941232465/1690262102528]

Voznyy (2019)

y2 + xy + y = x3 - x2 - 45759282422993769515525690163600632x 
	      + 3486039421495312317742621236734755107295292724214139

	Torsion points: 

O, [94801640615732013, -47400820307866007], 
[196592991262446637, -45696490565155265770143639], 
[196592991262446637, 45696490368562274507697001], 
[-89862666452259843, -82900076375008855234001159], 
[-89862666452259843, 82900076464871521686261001]

	Independent points of infinite order:

P1 = [-5813926566561123, -61252624499187751254769079]
P2 = [-83753958701081811, -82042973049661894045649303]
P3 = [37714409349690477, 42589895598837915192433321]
P4 = [39028221395025357, 41947394221910608890981001]
P5 = [87259210355776317, 12550976586701175927014281]
P6 = [150695593197088413, 3533811225281441036413513]
P7 = [89172119619431707, 10707670528746249029692291]

Torsion group Z/6Z, rank = 6

Dujella (2001)

y2 + xy = x3 - 46211161865740185355x 
	    + 110998663417922709680844055025

	Torsion points: 

O, [2967450110, -1483725055], [6326811710, 268105806209345], 
[6326811710, -268112133021055], [-2924705530, 470251457903345], 
[-2924705530, -470248533197815, 6]

	Independent points of infinite order:

P1 = [-2791455490, -467163905997055]
P2 = [443358350, 300994310491745]
P3 = [1073542940, 250251834090065]
P4 = [5292480590, 121122182401745]
P5 = [-2070296240, -444741481882055]
P6 = [47432888960, 10229215180208345]

Dujella (2005)

y2 + xy + y = x3 - 25187421680278445693x 
	    + 48654137710470248344196743556

	Torsion points: 

O, [2904641535, -1452320768], [4685242485, -183013398562718], 
[4685242485, 183008713320232], [2973947160, -7124753763893], 
[2973947160, 7121779816732]

	Independent points of infinite order:

P1 = [2822283975, 6954343660492]
P2 = [-979245690, -269034436509293]
P3 = [2908598655, 789015540112]
P4 = [619219245, 182468948735122]
P5 = [1650637535, 107591777378232]
P6 = [3630285285, 71132120660482]

Dujella (2005)

y2 + xy + y = x3 - 8681604817982520137993x 
	    + 787867843662491679357445631664056

	Torsion points: 

O, [8355021360, -26756612403914168], [8355021360, 26756604048892807], 
[156085683645, -56881258134422228], [156085683645, 56881102048738582], 
[-122859173865, 61429586932, 2]

	Independent points of infinite order:

P1 = [-32068158783, -32144860624255496]
P2 = [-29810853390, -31940263346584418]
P3 = [-122202453495, -4886480574238688]
P4 = [-64863539190, -32834225137298993]
P5 = [217564817460, 95902795270148932]
P6 = [4708554135, 27333025804220932]

Dujella (2006)

y2 + xy = x3 - x2 - 24641984875424581038634209x 
         - 24571734768259940862407109555298069587

	Torsion points: 

O, [-4359551072022, 2179775536011], [8039911064347, 17233977404728400004], 
[8039911064347, -17233985444639464351], [-1748544931818, -3629030032481723181], 
[-1748544931818, 3629031781026654999]

	Independent points of infinite order:

P1 = [-1112660361497, -1211996535271093884]
P2 = [-2838294220061, -4743880335803740135]
P3 = [-2275924564521, -4441018522047020379]
P4 = [38890306676394, 240493160869696681371]
P5 = [1552226360783953, 61154772385499844149171]
P6 = [902137984435375398/73441, 777542618042183179695244761/19902511]

Dujella (2006)

y2 + xy + y = x3 - x2 - 1885102854395997091056548x 
	    + 973413771881424764788534967357439431

	Torsion points: 

O, [513988260093, 374540094579630325], [1099311362821, 479166013869157597], 
[1099311362821, -479167113180520419], [513988260093, -374540608567890419], 
[-1581348239163, 790674119581]

	Independent points of infinite order:

P1 = [924719112261, 144759594450207901]
P2 = [-583009680075, -1369043837190113843]
P3 = [530245547685, 350614046229935197]
P4 = [987116640237, 272842136804095141]
P5 = [1267219218195, 787103093900430247]
P6 = [1109096203237, 496936432152555741]

Dujella (2006)

y2 + xy = x3 - 83818010737520230021560x 
         + 9334402101835969395681636158145600

	Torsion points: 

O, [8870692320, 92690752089959640], [163751652720, -81875826360], 
[185537412720, -13038096734226360], [185537412720, 13037911196813640], 
[8870692320, -92690760960651960]

	Independent points of infinite order:

P1 = [65058758970, 64472262197329890]
P2 = [92503745280, 48707976211031880]
P3 = [110833991250, 37496896782862410]
P4 = [172895207040, 3314040055803720]
P5 = [180319408320, 9137174862722040]
P6 = [94101612552, 47752152781196016]

Dujella (2006)

y2 + xy + y = x3 - x2 - 724963083845838467147663x 
	    + 237586593680168135061122941755311831

	Torsion points: 

O, [491495434995, -245747717498], [493839544051, 2739455152573062], 
[493839544051, -2739948992117114], [380666127315, 129532726725666982], 
[380666127315, -129533107391794298]

	Independent points of infinite order:

P1 = [262390922995, 255789260108384902]
P2 = [275645287155, 242275644241791622]
P3 = [501060887283, 11545420509573766]
P4 = [-695790343437, -636521420764992890]
P5 = [216858734995, 300949033958838502]
P6 = [-1006381515605/9, -15207828875734886206/27]

Dujella (2006)

y2 + xy = x3 + 177804364014978081877274x 
         - 5522974673744579179969706095233820 

	Torsion points: 

O, [30896215148, -15448107574], [194163931244, 190578307857850826], 
[194163931244, -190578502021782070], [1137471946508, 1291678171375136426], 
[1137471946508, -1291679308847082934]

	Independent points of infinite order:

P1 = [31146904016, 6730312822548074]
P2 = [63685875854, 77839257311805860]
P3 = [136650441836, 146033458083911114]
P4 = [159692378380, 164144512375241290]
P5 = [160382465228, 164678914082385386]
P6 = [48280943168, 56339420189611286]

Dujella (2006)

y2 + xy + y = x3 - x2 - 7155075168979273725951497x 
	    + 7366639344211346802891522902591893769

	Torsion points: 

O, [1549129854727, 10281986467072636], [1549129854727, -10283535596927364], 
[1851564002727, 682828996106512636], [1851564002727, -682830847670515364], 
[1544505854727, -772252927364]


	Independent points of infinite order:

P1 = [1345876154727, 417959815081072636]
P2 = [1567336854727, 49593159736072636]
P3 = [1549084968067, 10185220698738496]
P4 = [1546809150727, 5277875453952636]
P5 = [1760363607687, 475668162437671036]
P6 = [2295338038509, 1742550910112745682]

Dujella (2006)

y2 + xy + y = x3 - 42784589788168290967245543x 
	    + 105998799994358063694286205461334210806

	Torsion points: 

O, [3380159641235, -1690079820618], [-1681038746335, 13159443095497371432], 
[5061214509260, -4370853615511242243], [5061214509260, 4370848554296732982], 
[-1681038746335, -13159441414458625098]

	Independent points of infinite order:

P1 = [2050191887510, 5186493508637867757]
P2 = [507711015461, 9187353302890575624]
P3 = [4191738243485, 555557137882996632]
P4 = [1904470506536, 5605740765024339309]
P5 = [16350134082035, 61459697532243620382]
P6 = [-4949313954533, -14018421643985139622]