Torsion group Z/2Z × Z/8Z, rank = 3


Connell (2000), Dujella (2000)

y2 + xy = x3 - 15745932530829089880x  
           + 24028219957095969426339278400

	Torsion points:   

O, [-4581539664, 2290769832], [-1236230160, 203972501847720],
[2132310660, 12167787556920], [2452514160, 12747996298920],
[9535415580, 860741285907000], [2132310660, -12169919867580],
[-1236230160, -203971265617560], [9535415580, -860750821322580],
[2452514160, -12750448813080], [2346026160, -1173013080],
[1471049760, 63627110794920], [1471049760, -63628581844680],
[3221002560, -82025835631080], [3221002560, 82022614628520],
[8942054015/4, -8942054015/8]     

	Independent points of infinite order: 

P1 = [2188064030, -7124272297330]
P2 = [-2815745040,-214568724545880]
P3 = [3643261410,-122557804465830]

Dujella (2001)

  
y2 + xy = x3 - 2564530435455464744050430x
	   - 774033544664307864229665861908231100

	Torsion points: 

O, [16618584813010, -67426145676274447880],
[2169649474900, -1968552933159520070], [2169649474900, 1968550763510045170]
[-447882003740, -533599927551503630], [-1227486286730, -724161720859881290]
[-313881055364, 156940527682], [-5684941839585/4, 5684941839585/8]
[1735116515260, -867558257630], [-807983468840, 877828928053364470]
[-807983468840, -877828120069895630], [16618584813010, 67426129057689634870]
[4278216499360, -8158380056050342130], [4278216499360, 8158375777833842770]
[-447882003740, 533600375433507370], [-1227486286730, 724162948346168020] 

	Independent points of infinite order:

P1 = [-331856672240, -201186308576020130]
P2 = [681747812843740/361,-7252543732961516356970/6859]
P3 = [6714894088217635/3844,65964362556960760047245/238328] 

Campbell - Goins (2003)

  
y2 + xy = x3 - 18262097056293794050462967800x
	   + 947221615382521776843113311413294620840000

	Torsion points: 

O, [384056732811440, 7112084226340944585800], 
[86673191107100, 124488424515112474700], [69584365444100, -115721935078771750300], 
[-54632409541840, -1334864242442902982200], [-54632409541840, 1334864297075312524040], 
[69584365444100, 115721865494406306200], [86673191107100, -124488511188303581800], 
[384056732811440, -7112084610397677397240], [74619273455600, -37309636727800], 
[-623977550204801/4, 623977550204801/8], [81375114095600, -40687557047800], 
[41329758236000, -512884940394970007800], [41329758236000, 512884899065211771800], 
[121420469955200, 721056636920400552200], [121420469955200, -721056758340870507400]

	Independent points of infinite order:

P1 = [74021617782920,31794425743000034480]
P2 = [81766735559600,25797576413352528200]
P3 = [8775517172730787722056858700518960/117806438860954586521,  
     18243142868646417426484039651543006669780183825640/1278655473449200890038991093181]

Rathbun (2003)

  
y2 + xy = x3 - 1501011456398147086648544266758850x
	   + 22251270940723503314374317274872523646621572635332

	Torsion points: 

O, [-18004996592822356, -6590911844637378629814682], 
[9895942925525792, -2892482299592193885785902], 
[9895942925525792, 2892482289696250960260110], 
[83801916803450591/4, -83801916803450591/8], 
[23756609930945348, -11878304965472674], 
[37617276936364904, -4360962447048323352828502], 
[37617276936364904, 4360962409431046416463598], 
[-44707089131807996, 22353544565903998], 
[123637769719875434, -41552778147840818577570412], 
[25680076681242524, -800204848264852023727882], 
[-18004996592822356, 6590911862642375222637038], 
[19156257937164014, 726038019382107000286178], 
[25680076681242524, 800204822584775342485358], 
[123637769719875434, 41552778024203048857694978], 
[19156257937164014, -726038038538364937450192]

	Independent points of infinite order:

P1 = [585150090442017404, 446653884639086830911813998]
P2 = [60858503151041321123234/271441, 14802686107078222471948784650679698/141420761]
P3 = [288266315903991120130014776246/367947788569, 154585670444642553138450754364572706622327814/223192345224704003]

Campbell - Goins (2003)

  
y2 + xy = x3 - 590353702194591280765010561772238260x 
	   + 174588372339329184400865798305984325852297773091859600

	Torsion points: 

O, [403892642649189720, 45117248361149658382349340], 
[403892642649189720, -45117248765042301031539060], 
[484536348331430520, -47935326971688922180499460], 
[484536348331430520, 47935326487152573849068940], 
[999365849872638120, -763352998019322222734115060], 
[51562583436942120, -379849048667143531212267060], 
[999365849872638120, 763352997019956372861476940], 
[447143159545088340, -4027018202173742400995460], 
[440073800471053500, -4005683155727988678251640], 
[447143159545088340, 4027017755030582855907120], 
[442993356443270120, -221496678221635060], 
[444214495490310120, -222107247745155060], 
[440073800471053500, 4005682715654188207198140], 
[51562583436942120, 379849048615580947775324940], 
[-3548831407734320961/4, 3548831407734320961/8]

	Independent points of infinite order:

P1 = [4043145978848660830/9, 174836140793270820642525880/27]
P2 = [-344320394143837595000245442992956696/814862753036115169, 
     -434298487065859430358209850792879439798635022311026124/735574559415602783298880303]
P3 = [1451737788330638657633482779601154870036516263378345751837531961063344239611753112849556760/
     3155136161424248768625112088369105899244411500618381837275221737203503929, 
     107360513440730689070029083206307720462995748894071425185832190680260396195579613118258628735894896986022984370130847040150217732224660/
     5604374640684366142548869049661504017759384690908932215403119227589334003883898544252546288500646931113819283]

The third independent point found by M. Watkins (March 2005). 

Dujella (2006)

  
y2 + xy = x3 - 30507963373084413759489146596105237240x
	   + 64489450113318178611265574148979256340153096329702465600

	Torsion points: 

O, [11961670643380191359/4, -11961670643380191359/8], 
[-6373837227150843920, 3186918613575421960], 
[3383419566305796080, -1691709783152898040], 
[3654569228870148080, 1343860220552335814092541960], 
[17525500642981370960, 70090370161258775918222295560], 
[3654569228870148080, -1343860224206905042962690040], 
[17525500642981370960, -70090370178784276561203666520], 
[-2550742205939195920, 11212115863563412748297981960], 
[2737225434923430800, 1220931235200740144167921160], 
[2737225434923430800, -1220931237937965579091351960], 
[-2550742205939195920, -11212115861012670542358786040], 
[1425200857402653680, -4889206373126912123661339640], 
[1425200857402653680, 4889206371701711266258685960], 
[5341638275208938480, 7344415662569582990831357960], 
[5341638275208938480, -7344415667911221266040296440]

	Independent points of infinite order:

P1 = [10895065363091269280, 32021463711584565201301180760]
P2 = [590785466637255702306320/134689, 191846322697158506956592726494653080/49430863]     
P3 = [1178101453122586514401520/237169, 688303727761229397008667652599805880/115501303]     

Dujella (2006)

  
y2 + xy = x3 - 21015960530302473341210266357147569830x
	   + 17566852216331096945097199161461136733028723845196826852

	Torsion points: 

O, [-3679234914110992316, 6714503169501496894330721098], 
[9487461106090734544, -25926112660917713498375025722], 
[9487461106090734544, 25926112651430252392284291178], 
[337356540704445754, 3242741868948536349422940238], 
[-1309484890129172408, -6545341463304099143816536082], 
[-1309484890129172408, 6545341464613584033945708490], 
[3467515766704545951/4, -3467515766704545951/8], 
[-4955867049656917556, 2477933524828458778], 
[4088988107980781068, -2044494053990390534], 
[-3679234914110992316, -6714503165822261980219728782], 
[337356540704445754, -3242741869285892890127385992], 
[36297907350124685614, 216976050617525684940372429838], 
[36297907350124685614, -216976050653823592290497115452], 
[4993815447644799124, -6095388090235017959119842782], 
[4993815447644799124, 6095388085241202511475043658]

	Independent points of infinite order:

P1 = [-323768234654667598073236376174/72977240449, -95528205831866792550988270101905028199626094/19714290666614207]
P2 = [14313485330700724862739929253151/16750995468804, 33087135823218327101262727287106584612554256751/68558440752730073592]     
P3 = [-180780928705551339014149547355608/89374315532401, -6081165188483001212676838107943235738339842820990/844926814805897041399]    

Dujella (2006)

  
y2 + xy = x3 - 15343063417941874422081256126489574987160x
	   + 486503741336910955243717595559583892156442731284430865537600

	Torsion points: 

O, [231617775908238208320, 3059138547705534346041804296040], 
[231617775908238208320, -3059138547937152121950042504360], 
[-96756198617687116560, 1032100640555285783204846146920], 
[20367216277135641420, 427149915439181940159082514040], 
[124378527470717550420, -708727152937284690857720109960], 
[20367216277135641420, -427149915459549156436218155460], 
[-96756198617687116560, -1032100640458529584587159030360], 
[878481558502786758000, -25786786260942624213939494169240], 
[878481558502786758000, 25786786260064142655436707411240], 
[124378527470717550420, 708727152812906163387002559540], 
[103066938249872815920, -51533469124936407960], 
[34349987359939375920, -17174993679969687960], 
[-25483899408492576480, -927876521675299652614082871960], 
[-25483899408492576480, 927876521700783552022575448440], 
[-549667702439248767361/4, 549667702439248767361/8]

	Independent points of infinite order:

P1 = [62974185209012301066421176/7392961, 12000885861522378526762014623886832999128/20101460959]
P2 = [-33877133035878336982966500/844561, -790534983278326482737332351141316687160/776151559]     
P3 = [537614203446300716665300020/16900321, 12157075128111066917277688092780713996040/69477219631]   

Rathbun (2006)

  
y2 + xy = x3 - 59654254810332161499933732539083310x
	   + 936036113034275895945648528397370958419427728893572

	Torsion points: 

O, [2172909887011690234, -3182889877373545939206543392], 
[291435641750171284, -91124467662809922713619542], 
[-197931911432951666, 70633774398514491172482508], 
[-11552285349244316, 40294383897701739456074458], 
[2172909887011690234, 3182889875200636052194853158], 
[291435641750171284, 91124467371374280963448258], 
[-197931911432951666, -70633774200582579739530842], 
[-11552285349244316, -40294383886149454106830142], 
[15756596261393884, -7878298130696942], 
[-1006956083242885089/4, 1006956083242885089/8], 
[235982424549327388, -117991212274663694], 
[563715332994916384, -382678252577154660895909442], 
[563715332994916384, 382678252013439327900993058], 
[-91750483896261608, -75079780211573372996434430], 
[-91750483896261608, 75079780303323856892696038]

	Independent points of infinite order:

P1 = [423636398364728130558/32041, 70153524044528407532259723512964/5735339]
P2 = [-212218555436959806104/1369, -4070672727584190624828727982726/50653]
P3 = [8452319722523363921569428256760017402630395565491507482512250164/
      59692072868085173675728631193552258578545561, 
      777075522029540793165779905112440827567904945232388550670644286763642232436234047429573571171782/
      461184805928472795689461276558991227050395203450511219660991605059]

Rathbun (2006)

  
y2 + xy = x3 - 153010567793393992556815434658906721140x
	   + 728501166933268696802867483882463385720151113375539573392

	Torsion points: 

O, [7136668969896945704, 23099419970919959862732428], 
[4061538115253562644, -13192513775101300439821482052], 
[7136668969896945704, -23099427107588929759678132], 
[10738972043545873064, 17994512995789382383525462028], 
[7146682296961855484, 23110218372866739764213768], 
[4061538115253562644, 13192513771039762324567919408], 
[7146682296961855484, -23110225519549036726069252], 
[10738972043545873064, -17994513006528354427071335092], 
[28565149165049492671/4, -28565149165049492671/8], 
[-14283350103904692376, 7141675051952346188], 
[7142062812642319208, -3571031406321159604], 
[7013160268870079192, 593069146560615481135978700], 
[7013160268870079192, -593069153573775750006057892], 
[7270965356414559224, 600248550074690269251440588], 
[7270965356414559224, -600248557345655625665999812]

	Independent points of infinite order:

P1 = [2496091851384905686508344/301401, 896029991220504039247351192716501452/165469149]
P2 = [12615321377550619950231033409256/1776481125409, 
      442088743692246551824728086371328935967298164/2367777538558009423]
P3 = [3662275643349047922027557491418965900328341380384197044972605735916136/
      1079191891412968056127590909185669355748367493207289, 
      558684560664533643585768362793027922417196104247683786808932066647094821421265579707666093396835958760156/
      35452593441841085321192243655271783294098334214638916283068984995773571997837]

Rathbun (2006)

  
y2 + xy = x3 - 4527869148423161203017834259729075232020x
	   + 109150076525339545219757428860519443874479508277436337856400

	Torsion points: 

O, [1346558508812422040, 321022549679742306432091220780], 
[1346558508812422040, -321022549681088864940903642820], 
[92497102838720102840, 694056236208390273621157556780], 
[92497102838720102840, -694056236300887376459877659620], 
[-44931919096104508060, 471045531643856283598463281280], 
[24308650067491938920, 115965191469086042869418252780], 
[-77095097563239177560, 38547548781619588780], 
[336517414957140387560, 6057558211763587718022317449580], 
[54094265426352592940, 150027981727538736316323676280], 
[120693067557891660479/4, -120693067557891660479/8], 
[46921830673766262440, -23460915336883131220], 
[-44931919096104508060, -471045531598924364502358773220], 
[24308650067491938920, -115965191493394692936910191700], 
[336517414957140387560, -6057558212100105132979457837140], 
[54094265426352592940, -150027981781633001742676269220]

	Independent points of infinite order:

P1 = [21314386723997659557280/81, 3017947060024533467886816450022220/729]
P2 = [14543372431855398965476829823848/485241807649, 
      6469872485529287755605117414151791334525649452/338016046515639857]
P3 = [-114618670527383598003666132031471822360/2270018301844156081, 
      -1563732439397792869697558860057776098758211584995180980620/3420141214189747796089893271]

Dujella - Rathbun (2006)

  
y2 + xy = x3 - 3207498288387657621672732005424372705920328770x
	   + 68304282772313573439179636385556451355850337924379829175788684488900

	Torsion points: 

O, [24746904833392728174940, 2020856876072391701726498934223030], 
[7903034194933076287840, 6591579585310336939196188490682130], 
[7903034194933076287840, -6591579585318239973391121566969970], 
[65448903305619408864040, -11778424027315270370904208754098070], 
[65448903305619408864040, 11778424027249821467598589345234030], 
[228787792826772566585950, -106348966554149434905241308089137280], 
[-32724427516721561041670, 11756854433554349839561625705036740], 
[40985343079033901736940, -2385576778341943854696176733178970], 
[-32724427516721561041670, -11756854433521625412044904143995070], 
[24746904833392728174940, -2020856876097138606559891662397970], 
[228787792826772566585950, 106348966553920647112414535522551330], 
[40985343079033901736940, 2385576778300958511617142831442030], 
[28551814894630863335940, -14275907447315431667970], 
[36675968750276242575940, -18337984375138121287970], 
[-260911134579628423647521/4, 260911134579628423647521/8]

	Independent points of infinite order:

P1 = [22846201954487061296170647421060/7006609, 
      109183226786723806127509952477976944983711420690/18546494023]
P2 = [8781852554545044756170870387874126010/233658035659129, 
      3280159061355109729170468052344035819749855878060270490/3571667993147059821133]
P3 = [258286266983032617397787369369373455186295923375620/18695418702921634383283969201, 
      13190845285796317678557186972781192193361551808962073508112846505160757966030/
      2556246873058335351513763793171125613693801]

Dujella - Rathbun (2006)

  
y2 + xy = x3 - 16188503722614063108729139735755154904562292360x
	   + 786863421808206463969913495490892469346874709447053592901366525761600

	Torsion points: 

O, [126942113771663398101920, 27882680574001240245704236363397240], 
[126942113771663398101920, -27882680574128182359475899761499160], 
[30228264599630424878720, -18031474247759343557251945104801160], 
[30228264599630424878720, 18031474247729115292652314679922440], 
[422083239655931288586320, -262963676295121325354530570456161160], 
[85392774125986994678180, -5211521754389769127545451481401720], 
[-61613633858042970798640, 39375066083178460970956312648094840], 
[61906075162778279941820, 4684356135071180542946299694504840], 
[85392774125986994678180, 5211521754304376353419464486723540], 
[422083239655931288586320, 262963676294699242114874639167574840], 
[61906075162778279941820, -4684356135133086618109077974446660], 
[-61613633858042970798640, -39375066083116847337098269677296200], 
[68209869346874809632016, -34104934673437404816008], 
[78585189185646911490320, -39292594592823455745160], 
[-587180234130086884489345/4, 587180234130086884489345/8]

	Independent points of infinite order:

P1 = [66119657073815781066800, -2355339128918565969721076384104840]
P2 = [401169287265672834550867500080/76335169, 
      -17669918374394464360754418260810255353172665480/666940371553]
P3 = [289687648221921501808291121532003587972851140280852543070142236950355376437227490536812623183120/
      17156914675194799164872812895696296908615977178623591714662702334872955881, 
      -1617954908834725344870195603458416032731793227363235820394569809657744633819656062208905822304087388210043858968407239618913517436708870237508440/
      71065495284003135354842363163578373997823698038097319480954479040616074792502966798554498341539450071275232779]

Flores - Jones - Rollick - Weigandt - Rathbun (2007)

y2 + xy = x3 - 250878395393474545316759183209311840250x 
	   + 1479979592022167493224960512910755689574299477808903560932

		Torsion points:

O, [68156184360686840234, -548620665858774781668749384212],
[19241236869397662104, -61452092383940456995970809102],
[11794281695058898124, -12715881122248678201988334082],
[10456933579800800948, -5228466789900400474],
[11794281695058898124, 12715881110454396506929435958],
[19241236869397662104, 61452092364699220126573146998],
[68156184360686840234, 548620665790618597308062543978],
[7766447618213273204, -3883223809106636602],
[6608547727503159644, -10519135261480367776983634762],
[1672630290203939792, -32634832515464687840622144490],
[-9594066305658249586, -54807180967165504404174184822],
[-72893524792056296609/4, 72893524792056296609/8],
[-9594066305658249586, 54807180976759570709832434408],
[1672630290203939792, 32634832513792057550418204698],
[6608547727503159644, 10519135254871820049480475118]

		Independent points of infinite order:

P1 = [621727883860331879066288/80089, -11195733275105659072676635210992274/22665187]
P2 = [-3121826350817955803774630199394084/180524403067969, 
      61692108418757143009501414171937398097766847203574/2425514506583838201953]
P3 = [62782486665149487218097131208426297104/8547022989099698401, 
      -144593985742523950403942776316687052257460712416405160202/24987471290251272975616507601]

Flores - Jones - Rollick - Weigandt - Rathbun (2007)

  
y2 + xy = x3 - 97786754135136291205325201456018300x
	   + 6192618544071258703787593919472934977414964438890000

	Torsion points: 

O, [2412494120994676600, -3716356678419606264093338300], 
[631768530962716600, -443365234904237874461378300],    
[334018109980616800, -103903016996839909899338300],     
[274236048186676600, -137118024093338300],              
[334018109980616800, 103903016662821799918721500],      
[631768530962716600, 443365234272469343498661700],      
[2412494120994676600, 3716356676007112143098661700],    
[265237400106587199/4, -265237400106587199/8],          
[30252528978676600, -57114004555111060893338300],       
[-83296434589363400, -117302903560073060125298300],     
[-249690636103103600, -122645788091838955199258300],    
[-340545398213323400, 170272699106661700],              
[-249690636103103600, 122645788341529591302361900],     
[-83296434589363400, 117302903643369494714661700],      
[30252528978676600, 57114004524858531914661700]        

	Independent points of infinite order:

P1 = [274887906914724556, -9147492786135424992704588]
P2 = [62718943759824249209034178076092600/1241034587031947761, 
      -51354834432149065162729129239810440358544450486369700/1382534023431602612057272759]
P3 = [30248369105401958555069911173485380/89681232159126001, 
      2890206598473212141332130140412636902647519116897480/26856681562855952889842249]

Flores - Jones - Rollick - Weigandt - Rathbun (2007)

  
y2 + xy = x3 - 1621197495376612287530904105233724120x
	   + 792688598791865073857094426358748343551798168746190400

	Torsion points: 

O, [3511162314817559160, -6195718344276089217794183520]   
[1122265697094317040, -621888891456815245393207320]    
[810503350065758640, -105522308003205826390735320]     
[763710149262110640, -381855074631055320]              
[810503350065758640, 105522307192702476324976680]      
[1122265697094317040, 621888890334549548298890280]     
[3511162314817559160, 6195718340764926902976624360]    
[2824604703815991935/4, -2824604703815991935/8]        
[661499287147697640, -98627247357463778323642320]      
[405154601429904240, -449843532173591237050240920]     
[-494102163653747280, -1213712154536757787182077400]   
[-1469861325216108624, 734930662608054312]             
[-494102163653747280, 1213712155030859950835824680]    
[405154601429904240, 449843531768436635620336680]      
[661499287147697640, 98627246695964491175944680]       
  
	Independent points of infinite order:

P1 = [184265049963459555715756173360/183152329369, 
      33252887250675563312176497099144406413258360/78382420333745347]
P2 = [82783276094283429032303138646750640/107935148321592201, 
      747042050857350584081590197310444933406960306538680/35460457871497193838297051]
P3 = [883193138665626092244648865044768278534403013785057249004972327632/ 
      1015272818993790179595312025606995606967976322481, 
      -206355224855206696230997552878641266346125995941713540380329699739899409129414382783494501582099048/
      1022996479223612825011249658698109282807737802426954717854552678271406871]

Dujella (2008)

  
y2 + xy = x3 - 7508232300031068945507236861692000278143017800x
	   + 98536599045907325394109218811543289797912305023169446880249900840000

	Torsion points: 

O, [185352940682152660141200, 71237602613763561900439287907356600], 
[185352940682152660141200, -71237602613948914841121440567497800], 
[3460036467683584106640, -8520520202765373489564002189488200], 
[3460036467683584106640, 8520520202761913453096318605381560], 
[-69924386382988012520400, 16782593821935533274965810748658200], 
[-27072934080976642950000, 16791769980466891774929961350607800], 
[-27072934080976642950000, -16791769980439818840848984707657800], 
[-69924386382988012520400, -16782593821865608888582822736137800], 
[710878746324524962206960, -594981232775976968162883906137836200], 
[710878746324524962206960, 594981232775266089416559381175629240], 
[96997366319390106771600, 16818338245586195529874878358966200], 
[96997366319390106771600, -16818338245683192896194268465737800], 
[-370350832816127451268225/4, 370350832816127451268225/8], 
[13447704903443854221456, -6723852451721927110728], 
[79140003300588008595600, -39570001650294004297800]

	Independent points of infinite order:

P1 = [-2694568576987041495959178450/942841, -10027582070704208948409204659888495021260500/915498611]
P2 = [3970465520942714626939047462365658730422096528/1812535448603270689, 
      250185504316803131532134327979586853605556137590939217382022442783176/2440224389796887379083798863]  
P3 = [-667104712607831226657178167710669443876760614892400/22554833887350579603456918721, 
      58153301912038353051602983895232189994148255513921056042552709247894836911800/3387345138491485663907457308101563095956769]   

Fisher (2009)

  
y2 + xy = x3 - 87306660786172655975387678466748290400x
	   + 217110378089173582243961228486559615973771263335020160000

	Torsion points: 

O, [1669735329772740800, -8717029941391454078378370400], 
[-7254150279199829800, -21649782187993296417273344800], 
[64987362627595365800, 518659939811183754051030629600], 
[1669735329772740800, 8717029939721718748605629600], 
[-7254150279199829800, 21649782195247446696473174600], 
[9252777066556126400, 14193219739781876098850429600], 
[2716314313200741056, -1358157156600370528], 
[-41603973793557927425/4, 41603973793557927425/8], 
[64987362627595365800, -518659939876171116678625995400], 
[9252777066556126400, -14193219749034653165406556000], 
[7684679135188740800, -3842339567594370400], 
[17163931186181100800, 61441745972443707605574269600], 
[17163931186181100800, -61441745989607638791755370400], 
[-1794572915803619200, 19183564301517113491461989600], 
[-1794572915803619200, -19183564299722540575658370400]

	Independent points of infinite order:

P1 = [3888389281477760302164731675/1675592356, 356417057891849547266702905721618838031525/68588697500504]
P2 = [2496696667790212491908498894596171695618200/1012027927012975570430329, 
      4165195691283669818126200299930369868594696169603332876320143200/1018096033886874322960381838946301517]
P3 = [475895390891232373643072236932203983456664030946407307250/7346994645556866599186914246742747289, 
      10277278351192944745357620448527902233008836938952787496189272376269085022422349633050/19914278893564478018170895166925797756827801313841227837]

Fisher (2009)

  
y2 + xy = x3 - 28496542442921974135365803597630606183560x
	   + 930028463295087397876426818791882627215096824737621502785600

	Torsion points: 

O, [-46478876034243941680, 1467688000093609913464456747640], 
[-46478876034243941680, -1467688000047131037430212805960], 
[1318220985222820328720, -47476800119387027399063701588360], 
[1318220985222820328720, 47476800118068806413840881259640], 
[181967197668850693400, 1330376430063649842385809091760], 
[181967197668850693400, -1330376430245617040054659785160], 
[14531285838585704720, 720420336183260170122559723640], 
[14531285838585704720, -720420336197791455961145428360], 
[-135127039181894266360, -1520971552898403767348893122760], 
[-135127039181894266360, 1520971553033530806530787389120], 
[344898107387090615120, 5668234058802281195223213355640], 
[344898107387090615120, -5668234059147179302610303970760], 
[-183227597275753303280, 91613798637876651640], 
[136071926397319866239/4, -136071926397319866239/8], 
[149209615676423336720, -74604807838211668360]

	Independent points of infinite order:

P1 = [1454325638141897038414999312/9728161, 3185388268925722131952833060406220088584/30342134159]
P2 = [12144380016386165873956187029418761765638815/22403640429430752412804, 
      40347016554723133291863623548476431413478755244280572590806919255/3353342326134477042752517776041592]
P3 = [ -41554486788060054850941013197009849645082098385776680594908666706428165839680/456984738121549624533615308869333699622697646624523348601, 
      16257165155727704525354598119671254058036601043363698765103525012871018751600667532594056111158669097852229731896360/
      9769054766720221536148677821713361495748633903749184319614900927829658669292495398349]

Fisher (2009)

  
y2 + xy = x3 - 1020063221452742528711237053898259919109330x
	   + 394868843305477898697900385068741989177100444077780447528592900

	Torsion points: 

O, [509472723693937984060, -2722948228698735171582685818530], 
[3055457350785280330060, -160634080651079471553909367338530], 
[658849064841141888430, -2965758418130310030348595010030], 
[3055457350785280330060, 160634080648024014203124087008470], 
[658849064841141888430, 2965758417471460965507453121600], 
[509472723693937984060, 2722948228189262447888747834470], 
[-441617925558624786710, 27553945205231124474551726403940], 
[-441617925558624786710, -27553945204789506548993101617230], 
[281996897304422100160, 11385921464251141371819260249470], 
[281996897304422100160, -11385921464533138269123682349630], 
[945540303440433853960, 16604665656425297433098783813470], 
[945540303440433853960, -16604665657370837736539217667430], 
[2207643843335110743519/4, -2207643843335110743519/8], 
[613768600372427977060, -306884300186213988530], 
[-1165679561206205662940, 582839780603102831470]

	Independent points of infinite order:

P1 = [579134216025701576839700860/361201, 11652219128690792038256499913392424136470/217081801]
P2 = [143323974816385441734934161845362823946206810003795773811006467438204090/7948964884044315755199660547148122820476145414569, 
      54176447873373332160916231000719058215537311649154649248789744992316899999673360540222886844741121571845990/
      22411239028772254693265853844917900376122276293008869707453469040609696747]
P3 = [430933266422085631969362497494548572081451961867991799978235392833909967813894605444847310/37450355616357571401354257954458754421597835044552961483731714886201, 
      281833328827024533501859613504123436027656029363155377491439480558717225038613105042812668958632937089083722503447075305829963214679530/
      229183801560450093419805152181230046095710149288529478432080974993176067771023568176008608819939411949]

Fisher (2009)

  
y2 + xy = x3 - 2008408366171799322006725680352504756640960x
	   + 1088347028183149020228866231691755600541724741509337773822873600

	Torsion points: 

O, [3053938585582027027455/4, -3053938585582027027455/8], 
[871743521241881819520, -435871760620940909760], 
[-1635228167637388576384, 817614083818694288192], 
[695824370267989395840, 5267438503757198834553720640320], 
[4601511405809971931520, -298795261999516580916761185901760], 
[-671021622901317882480, 46194064023854910751828279752240], 
[1392706028827395553920, 31504905937655278283136973611840], 
[1392706028827395553920, -31504905939047984311964369165760], 
[4601511405809971931520, 298795261994915069510951213970240], 
[944509962132938770800, 5829388970516230931694453967440], 
[944509962132938770800, -5829388971460740893827392738240], 
[350781013656368085120, -20663934019089673131175540071360], 
[350781013656368085120, 20663934018738892117519171986240], 
[695824370267989395840, -5267438504453023204821710036160], 
[-671021622901317882480, -46194064023183889128926961869760]

	Independent points of infinite order:

P1 = [871842613747313354520, 164071869245135467114538235240]
P2 = [-410817964422770871621437343129527235520498279231413424471788480/857847006594646675719999335580571562220121, 
      34998776697295432541092329560771686852923273751984948676408382261636162471451920470188576467840/794538159898072605034784281027980145244450632749428862426631331]
P3 = [-525085435402319949885392341257799180258824002345638474594062320822714730/361767309951804886153929043055737875902870712633241, 
      211601536457830537100089521791516074418316961471243894677538636372819215707958780804053519513386942444185060/
      6880879949866383030199538005700923073636003189492531396047821220370553417539]

Fisher (2009)

  
y2 + xy = x3 - 151659336416513610120941619754231911069120x
	   + 22664749439132439148133088299158455435686131311858534821990400

	Torsion points: 

O, [-159393769516885084800, -6541306067480576947105262239680], 
[199942708737595601640, -578530836240195601516490281320], 
[-159393769516885084800, 6541306067639970716622147324480], 
[199942708737595601640, 578530836040252892778894679680], 
[352039472636288802240, -3592152380668412467637470648320], 
[214723992423504661376, -107361996211752330688], 
[234806882742480800640, -117403441371240400320], 
[-1798123500663941848065/4, 1798123500663941848065/8], 
[117574292848672799040, -2541421579410793642523330512320], 
[117574292848672799040, 2541421579293219349674657713280], 
[352039472636288802240, 3592152380316372995001181846080], 
[1117227315755487584640, 35323454535688730203369213039680], 
[1117227315755487584640, -35323454536805957519124700624320], 
[250381635568957107480, -623460261013343243760813106560], 
[250381635568957107480, 623460260762961608191855999080]

	Independent points of infinite order:

P1 = [9565362468639540463644849360/39980329, 69273511220115334638960130718296831012560/252795620267]
P2 = [7946033077221090047610008376597275280/27748416318516481, 7620022167008954790909819253714149186428389766511226320/4622291204870560422730879]
P3 = [547496038437564954084383615571937485870742069706003569253760/2143125636953964412929416979206307389089, 
      76426580794187972576232170491340624898413911982337258326017725664328085680948232728331840/99213654566255402344682711715957276003296518493756459539313]

Fisher (2009)

  
y2 + xy = x3 - 9978082456644606532120457534482336270x
	   + 12118558737989607267350601135758073759160572299571620612

	Torsion points: 

O, [2606786632889821664, 1954947376794955237818321218], 
[2606786632889821664, -1954947379401741870708142882], 
[1137975723366891992, 1495797075462005600929148678], 
[1137975723366891992, -1495797076599981324296040670], 
[7812838707763063844, 20274629216554632033751810298], 
[1963174079061117134, 309873841744961716541294828], 
[7812838707763063844, -20274629224367470741514874142], 
[1963174079061117134, -309873843708135795602411962], 
[-1035786544098165676, -4619791638612546445032590902], 
[1686920288833271354, -294615287026185664042676992], 
[-1035786544098165676, 4619791639648332989130756578], 
[1686920288833271354, 294615285339265375209405638], 
[-14588174365020454369/4, 14588174365020454369/8], 
[1774662413126756764, -887331206563378382], 
[1872381178128356828, -936190589064178414]

	Independent points of infinite order:

P1 = [64935066190938207177379921809620324336417876/38334673696173434639203369, 
      65856901684133496078852002264730967351861454596251807552291945974/237349136666849357523634570372143855403]
P2 = [12778692524551274601846592078841174742602753512/1745809761812003076444759729, 
      1327613229257136573838681932815478197257627319929587909972495605591642/72944974419623675473252095060997029084567]
P3 = [359051941184400968436675916287612822567566985575036/33554076578440432506346355899225, 
      65354844147837104087026866\12744978642320928319784476158335695253889445283914/194364943774259187095447069125475692174244412125]

Fisher (2009)

  
y2 + xy = x3 - 1365976977965875684692597442214807543360x
	   + 18275400146363694880998794973679939881728339383321437081600

	Torsion points: 

O, [49507414261719233920, 268311937045162364773521826240], 
[49507414261719233920, -268311937094669779035241060160], 
[13817765426026376320, 45154019775964812751357243840], 
[-24228484401136594640, 192739099074419526727266253840], 
[29219548405715258320, 57526467445969554974803177840], 
[179220827616271895680, 2351607043209729079666903929280], 
[179220827616271895680, -2351607043388949907283175824960], 
[25458109597317512320, -12729054798658756160], 
[-42392002557843161984, 21196001278921580992], 
[13817765426026376320, -45154019789782578177383620160], 
[-24228484401136594640, -192739099050191042326129659200], 
[67735571842102598655/4, -67735571842102598655/8], 
[29219548405715258320, -57526467475189103380518436160], 
[1408804932915790720, 127881981297901038291292987840], 
[1408804932915790720, -127881981299309843224208778560]

	Independent points of infinite order:

P1 = [-28925660493007923778753001979117008/745150831097401, 
      2301812386537434799394254097252369862652645709600176/20340718299490580024851]
P2 = [4858713561949175021004650887477280518480/590734188869803267249, 
      1251422333929718305649458089342982178716579297249330432642880/14357808604429252520186572742807]
P3 = [94599801245197236670533717691501242841684676927370643387429857496192/1864388863284238312382345623195552284825142519201, 
      718229405600637042918975805609126607115846335546517632274099729028455832471003132415297652495662447168/
      2545685507172487454419154834888121191096787138928134722184802519165981199]

Fisher (2009)

  
y2 + xy = x3 - 8891010899996290917768386447341722080650x
	   + 321386381817072190725452682772958817656542992462808507422500

	Torsion points: 

O, [47693008455673008830, -76360594613080145517017489080], 
[61375591786575104300, -83035691204262474207356093650], 
[283065133628641885370, -4526090062980968168907888569620], 
[-40850050216775061700, -785122320411823802443499927650], 
[-40850050216775061700, 785122320452673852660274989350], 
[47693008455673008830, 76360594565387137061344480250], 
[57232463480470841300, -28616231740235420650], 
[26644006047412948400, -321572534610368227648797037750], 
[206392542778223829599/4, -206392542778223829599/8], 
[283065133628641885370, 4526090062697903035279246684250], 
[61375591786575104300, 83035691142886882420780989350], 
[-108830599175026798700, 54415299587513399350], 
[87820920913528734200, -466786580771766177646363443550], 
[87820920913528734200, 466786580683945256732834709350], 
[26644006047412948400, 321572534583724221601384089350]

	Independent points of infinite order:

P1 = [89392066756214910630356189257873946534835729701683869800/719855804601419024567869162141064281, 
      649891980421647813178126367716785302478832479581922219643353993764872869770681868850/610756737355000227681876924815936698859521920190897571]
P2 = [-368968435313200649585277199506744864617553759922024264847699139109203544632772/
      4328444403164795848014330325123657974314266346524105155169, 
      193116610303288450722489965773295721915902917509902894328305820872359766087275734756646629572879483893657265252931194/
      284772314739312089482009570306037437294313894114004262504453611673597510272416409118447]
P3 = [28766481459430656391643599852237810701636893603466567009949133003753092441487540/
      266896153729967253930054573164461436524854233618070584417449, 
      10814728207349576632047809364\ 0030793764931844567497537177312592069943394199538114828302672199934012535673141770846634350/
      137883872685203149277045439575375309781049990438645576453334801987530478392777718420294293]

Fisher (2009)

  
y2 + xy = x3 - 226080057256506952334475656854112608140907120x
	   + 1267994298469520992966682807972243164162876870777885816396482310400

	Torsion points: 

O, [64127947741843644038780, -15826854119140567725521657741491420], 
[11149900468413737620640, -365216258475351806832299578358320], 
[-9049507335513485605600, 1603998396136898559402421904174480], 
[6317043640266678795140, 303180790883885995030238054931680], 
[6317043640266678795140, -303180790890203038670504733726820], 
[64127947741843644038780, 15826854119076439777779814097452640], 
[11149900468413737620640, 365216258464201906363885840737680], 
[-9049507335513485605600, -1603998396127849052066908418568880], 
[18136346128752643712240, -1770102531933242873835420002216320], 
[18136346128752643712240, 1770102531915106527706667358504080], 
[-17302176339777887630624, 8651088169888943815312], 
[29614638961227403335935/4, -29614638961227403335935/8], 
[9898516599471036796640, -4949258299735518398320], 
[1660687070189429881040, 947167381605507567444913299009680], 
[1660687070189429881040, -947167381607168254515102728890720]

	Independent points of infinite order:

P1 = [2959245473855045297342061137004403010608715682200560/54970030243379457721914930729, 
      1552531046526601909251244062\ 89582335237748170657141246708140365470301381282560/12888101979441798948948361629424584241409067]
P2 = [512060347260917001788897959490078633706407935806451924989807029600/21723534311246731949065076064137651776489, 
      366422076289658597796685682052465142560027502594185698660484137029482725810616171521324170523168560/
      3201811250688816818399832322863564884695482292523644085386763]
P3 = [2316413969889418181857636132838130408011087929900872718224632414569742240/1252241975537292661717925870338466433350657521321, 
      3525412655267690774723055357378893060889284546269953836508539101560452647105084875371306547704758154636744720/
      1401304078636720722341028521039490272260202406946754212294789859421758869]

Fisher (2009)

  
y2 + xy = x3 - 19561489879503521317374605750139081505164135760x
	   + 1053053816008115892520186610673109502267446427439678234588062250809600

	Torsion points: 

O, [86491205836884310595120, -2859058070681364861322707234542560], 
[86491205836884310595120, 2859058070594873655485822923947440], 
[75140875867650824975120, -2728201165775701836322389089492560], 
[75140875867650824975120, 2728201165700560960454738264517440], 
[81186738501862181258720, -212853508690366586591486546262160], 
[167699509462983989097620, -49888234138275568930656661346455060], 
[16765378630475005239020, 27015003412279923299186979474193940], 
[80313196752216066785120, 212087347811157498775615681107440], 
[80313196752216066785120, -212087347891470695527831747892560], 
[16765378630475005239020, -27015003412296688677817454479432960], 
[167699509462983989097620, 49888234138107869421193677357357440], 
[81186738501862181258720, 212853508609179848089624365003440], 
[80816040852267567785120, -40408020426133783892560], 
[-645996663980770291750145/4, 645996663980770291750145/8], 
[80683125142925005152416, -40341562571462502576208]

	Independent points of infinite order:

P1 = [18389011576013576110535089896131116628936320/334599617050432933761, 
      73442362420341288201734911223121612522399900224898360724596166960/6120517716199288291152078573759]
P2 = [100084535783919486416594465617917942017455517319874621700/1282373198315859466972893183512641, 
      60739235924036877684532635971124904613272353892307419209443834658700548769055146240/
      45922090380097879912184213308295068868582072622689]
P3 = [3988632811003945475457820367627269144522422973510230831416315/277911900908203826154319692901316644, 
      7965545835899844821401221485175360369850548792500085284448877663702570574565541471709803195/
      146507789969456491753262383159020425879060822911698728]

Rathbun (2013)

  
y2 + xy = x3 - 18247941180734920258951141060855042640x
	   + 30003290659312870154250577706243953923873222960556857600

	Torsion points: 

O, [996308377714867360, -3579340715205085404723893840], 
[2466856489630878880, -1233428244815439440], 
[2465748079099038880, -1232874039549519440], 
[-19730418274919671041/4, 19730418274919671041/8], 
[4300761278960164000, 5574270123073723913554659760], 
[4300761278960164000, -5574270127374485192514823760], 
[2471328717750216880, -13593622749641886074607440], 
[2557419399075237280, -249363871234053165261653840], 
[2557419399075237280, 249363868676633766186416560], 
[2471328717750216880, 13593620278313168324390560], 
[2376293580186520480, 243333683104098404951734960], 
[2376293580186520480, -243333685480391985138255440], 
[2461279221875700880, -13575171870191526761349440], 
[2461279221875700880, 13575169408912304885648560], 
[996308377714867360, 3579340714208777027009026480]

	Independent points of infinite order:

P1 = [2465691851312622880, 696043088391848153696560]
P2 = [299526139374311133233496416291788297474720/121494563208085746024241, 
      89760059383324119916982236967929464095424322071022523698480/42348230280965451005863362419157289]
P3 = [255527827197603823692011696953948551106951690366701807000824460296857544191109177529553040490611277793232865334429328712723331209912026266560051735874593651678513697145420096520365957390391994740532194386646007444478507059729407124477574209059308535275984445648944973857230/
      103741345948284136600850705022998442002558109152508256758777623996807608081546842897751883462637271251523924738965290989759687615869601630298197558014492384361761785748086947557477806560219345196436037328416193242420156187936018082106090908492627291349969, 
      8992236068738592977199417717217168961723342142250581399387476637407351248957542689994258388798686468751719255160174869873244536035971856742110190408345123771373528044331860080447724136172230521346777659126418571630040991933558343397019934246107684499084537550620360793967011092035209774250967253346849204690975758718990696148201123874043382645837168758139928716460061585885269278104241162284541200977586790/
      1056641873779396328820827179162484245273675046949791318104395249215045001870176172014452659115627601514048849596922228268202511367527045717849698016863150848882070412107024720247414591543688472144146764400298035859221663365795113018416176468950462518263225824616334743029549356055831440152227797493555339799615879533493978750678783291869212439586700180038166469129665579881151478297]

Some generators listed on this page courtesy of R. Rathbun 2010.
High rank curves with prescribed torsion Andrej Dujella home page