Torsion group Z/2Z × Z/6Z, rank = 5

Dujella - Lecacheux (2002)

y2 + xy = x3 - 990429690240960203866170x 
           + 343844266388187332499781887080604900     

 	Torsion points: 

O, [-1137029249260, 568514624630], [424281982740, -212140991370], 
[943719301140, 499638233430874230], [943719301140, -499639177150175370], 
[2850989066079/4, -2850989066079/8], [250969723620, 333292433878461750], 
[250969723620, -333292684848185370], [-442779492540, 834013215008711430], 
[-442779492540, -834012772229218890], [3022967672340, 4997467270386528630], 
[3022967672340, -4997470293354200970]

	Independent points of infinite order:

P1 = [39632200740, 551954334123294630]
P2 = [376196308530, 156489276347919690]
P3 = [-387729217260, -818274779331071370]
P4 = [233546798100, 353936579560301430]
P5 = [276487413090, 301892365554581130]

Dujella - Lecacheux (2002)

y2 + xy = x3 - 2353799432200918732090882185x 
	   + 39989567111692230080439457690563434811225

	Torsion points:

O, [34624316332970, -17312158166485], [-21382917634260, 283802358972118214865], 
[-221809019191761/4, 221809019191761/8], [146226404851800, -1680011543007889672035], 
[20827938464970, -10413969232485], [45759685113870, -167627237761782692985], 
[45759685113870, 167627192002097579115], [146226404851800, 1680011396781484820235], 
[12435568124070, -112435818541217438085], [12435568124070, 112435806105649314015], 
[-21382917634260, -283802337589200580605]      

	Independent points of infinite order:

P1 = [-13272789126870, -262474418962008447285]
P2 = [62997061649340, 376455986997155384865]
P3 = [235292735902330015/49284, 1858717131514493882047582075/10941048]
P4 = [26587804667725663180/471969, 95178457006708979892110235295/324242703]
P5 = [642213269652960633874197/709476496,  
     513932348728130104651370222396511867/18897615947456]     

Dujella (2005)

y2 + xy = x3 - 59964332656283235183736182568175070x 
	   + 5262192586204697880378286484023061659919913201000900

	Torsion points:

O, [-100706799382144800, 101388630581288134821084270], [-100706799382144800, -101388630480581335438939470], 
[699032192471396940, -552199676783521388201772270], [699032192471396940, 552199676084489195730375330], 
[-280570274119751460, 140285137059875730], [109878334916952540, -54939167458476270], 
[682767756811195679/4, -682767756811195679/8], [222633621670444140, 54287327183221293445091730], 
[222633621670444140, -54287327405854915115535870], [69575471922080280, 37774899712984645725722130], 
[69575471922080280, -37774899782560117647802410]

	Independent points of infinite order:

P1 = [-80523452065536324, -97819279597823790397110798]
P2 = [206354965015177680, 40930900421205070714160190]
P3 = [719688550990256835/4, 138035757763448396051529615/8]
P4 = [472440225903704060, 287021215160097630172260530]
P5 = [2425719338252784270722090/841, 3777990174973980213385863394320563470/24389]  

Dujella - Lecacheux (2005)

y2 + xy = x3 - 3150412655044310138959718911736x 
	   + 2017307529136250088009457662898185285042999360

	Torsion points:

O, [1593887607912064, -32328622377009159286664], [1593887607912064, 32328620783121551374600], 
[4972732153199968, 330631504589067259261336], [4972732153199968, -330631509561799412461304], 
[-711649981802372, -62441064393262230727784], [-711649981802372, 62441065104912212530156], 
[520580652338596, 22767151633951757574040], [520580652338596, -22767152154532409912636], 
[4910819220603007/4, -4910819220603007/8], [807403499295088, -403701749647544], 
[-2035108304445840, 1017554152222920]
    
	Independent points of infinite order:

P1 = [751615498434496, 8603230476282383128840]
P2 = [-104225584039806191/64, -27231631312774403459151205/512]
P3 = [18351330710909180554744/13225, 2485999215821573343630941982730648/1520875]
P4 = [3164329883365981282447/4, 178001076569511351346622945349293/8]
P5 = [6012159494875581605596/1352569, 433193404879008808392299881834820/1573037747]         

Dujella - Lecacheux (2005)

y2 + xy = x3 - 1574953367944818401647093988620060x 
	   + 22354378546192575469417478920309874871779369315600

	Torsion points:

O, [-16436081600420560, -6618180935008016054759260], [-16436081600420560, 6618180951444097655179820], 
[113889505087841600, 36334885624328686241602340], [11171372531379320, 2480759994323992163309540], 
[113889505087841600, -36334885738218191329443940], [36208265339600120, 3577496063891096259039140], 
[36208265339600120, -3577496100099361598639260], [11171372531379320, -2480760005495364694688860], 
[-181843109471757761/4, 181843109471757761/8], [17736226214465720, -8868113107232860], 
[27724551153473720, -13862275576736860]
   
	Independent points of infinite order:

P1 = [-715874645805280, -4845769377325125124865860]
P2 = [13341553880886920, 1927903179156513170395940]
P3 = [-1286533431046780, -4937456761403462286962860]
P4 = [4465692559968843235743251576/28561, 298423645416988262182359757871185770972548/4826809]
P5 = [3066243125273656053875457039039671824535840/3120685480327594971834289, 
     5364885633228551570655712209620348921025054651409294263574657820/5512835079841624786126134349007271913]        

Dujella - Lecacheux (2008)

y2 + xy = x3 - 14381792753033634870375842403810854602660x 
	   + 662806499738374270959359777990475800630625702118528528547600

	Torsion points:

O, [59208052914026106680, -137287729378657545002575294420], 
[59208052914026106680, 137287729319449492088549187740], [66988426022129214920, -33494213011064607460], 
[79726693539644536520, 151539232681722156018778592540], [285855606678826504639/4, -285855606678826504639/8], 
[-138452327691835841080, 69226163845917920540], [79726693539644536520, -151539232761448849558423129060], 
[-5191333823748374440, -858677634929515911888813327460], [-5191333823748374440, 858677634934707245712561701900], 
[185163361528655877320, -2085243000169909266116860959460], [185163361528655877320, 2085242999984745904588205082140]
   
	Independent points of infinite order:

P1 = [28773623469583250120, 522314569080532537050235328540]
P2 = [81110098194846295892, 172941860066979775872332866976]
P3 = [99266531033757329720, 461879586573455081296428074540]
P4 = [-365244658089452594680/121, -1118508262713108993277475594769260/1331]
P5 = [6643475559305148645228758169122/99218070121, 164960503768175723311599079042881495649743134/31252600689343669]

Dujella - Lecacheux (2008)

y2 + xy = x3 - 131004709010049976906075974805380776438618525256030x 
	   + 532804231132851068847796904272978574164851588764408546154301817681097384900

	Torsion points:

O, [33389045949132825834906060, 182706700209073226375795426180018347170], 
[33389045949132825834906060, -182706700209106615421744559005853253230], 
[3127620701446987822919880, 12396193453631576739116597007002914770], 
[3127620701446987822919880, -12396193453634704359818043994825834650], 
[10558029488395025352538860, 18071446338362979133433696833680970770], 
[5050331710548974320586460, -2525165855274487160293230], 
[32207788920270924494380319/4, -32207788920270924494380319/8], 
[-13102278940616705444181540, 6551139470308352722090770], 
[10558029488395025352538860, -18071446338373537162922091859033509630], 
[-4842578185394737600209360, -32459876617406316825543566607834908430], 
[-4842578185394737600209360, 32459876617411159403728961345435117790]
   
	Independent points of infinite order:

P1 = [4378088878468599339759660, 6570517514971845768410563030167274770]
P2 = [-7979836683805661968982050116/4225, -7637823045463085681864384316252420666014478/274625]
P3 = [-5231043492938682868912140, -32786494932889596996791154709889209230]
P4 = [713612332777702004897920158469380/59151481, 12106759422063621824787844255195559625208869141750/454934040371]
P5 = [-61885908913425738474318485559213679090785215652/4788303286054431104809, 
      -2713566141931187976838998756110252588426581005608756309845220986212678/331338937706851736182789648257877]

Dujella - Lecacheux (2009)

y2 + xy = x3 - 83451301835836505339622094504595112570x 
	   + 293100037604964283613171289154269227976286656300109500900

	Torsion points:

O, [-137997199399934460, 17453178954992624957144122230], 
[5416960199902475540, -2708480099951237770], 
[20520494531516195679/4, -20520494531516195679/8], 
[-10547083832781524460, 5273541916390762230], 
[4592638561230514440, 2589944805914873981042467830], 
[4592638561230514440, -2589944810507512542272982270], 
[5983710046920885540, 2827914715000468862695402230], 
[5983710046920885540, -2827914720984178909616287770], 
[13496488778932076640, -40314466615391592460655073270], 
[13496488778932076640, 40314466601895103681722996630], 
[-137997199399934460, -17453178954854627757744187770]
   
	Independent points of infinite order:

P1 = [2227320680915289990, 10875517008467119620485618730]
P2 = [5130102277196175540, 9799955405563966460062230]
P3 = [915177317355011795860/9, 27577777338096544291625464472210/27]
P4 = [77307991022750019285927135/145924, 679629834938989962662288789445044730015/55742968]
P5 = [1881847753085976389016547277940/243967832761, 1254262607371269085596579330198284678872884930/120503275603473491]

Dujella (2009)

y2 + xy = x3 - x2 - 1013844706869085241884030494287504370x 
	   + 383312079581955140879990492812070932757128820095066500

	Torsion points:

O, [372381816545586408, -239608573897394989830314706], 
[2365196974526377335, -3349127083733781065594610540], 
[505435806420992700, -252717903210496350], 
[-1159495544674905108, 579747772337452554], 
[2616238953015649635/4, -2616238953015649635/8], 
[-302840664555601920, 813984778618660611482816670], 
[811579375505453941, -308305653494139285606496711], 
[811579375505453941, 308305652682559910101042770], 
[-302840664555601920, -813984778315819946927214750], 
[372381816545586408, 239608573525013173284728298], 
[2365196974526377335, 3349127081368584091068233205]
   
	Independent points of infinite order:

P1 = [138816488023051483, 495225922218480420902721944]
P2 = [-20805761910217395, -635922074440891126374828150]
P3 = [29173783901510224748640/27889, 3184252619282355301660145403115890/4657463]
P4 = [210239585179609966845856728/688485121, 5775024067059628021053518856356152671366/18065161089919]
P5 = [4734982045611269991267678213864193365/3852366745601621809, 
                 7538553348381114164657847937875659347956414918234933330/7561212400828731280214296873]

Dujella - Peral (2012)

y2 + xy = x3 - 9327366518423676643700621544483761x 
	   + 346725314827357591512921699486961685298392990114985

	Torsion points:

O, [55686165040391098, -27843082520195549], 
[-111518973825543590, 55759486912771795], 
[223331235140609967/4, -223331235140609967/8], 
[56728903041825214, -396496424071568625479489], 
[56728903041825214, 396496367342665583654275], 
[32171545190604448, -8941327563408817550451149], 
[54795624443899396, 391940364333221642439115], 
[32171545190604448, 8941327531237272359846701], 
[83219539490971798, 12117854675346295286376151], 
[54795624443899396, -391940419128846086338511], 
[83219539490971798, -12117854758565834777347949]
   
	Independent points of infinite order:

P1 = [54774717293086510, 400465728977361126606115]
P2 = [55675847163928048, 16455177652709572813651]
P3 = [80484750953001166, 10834125295358201848752355]
P4 = [-67602933383033156, -25852014585896411209576709]
P5 = [13073367425784981906862/237169, 29830231763553211898593122469753/115501303]

Dujella - Peral (2012)

y2 + xy = x3 - 141033921768261303722896459969632383196x 
	   + 642982736099115694423636613434152191277519936678545325840

	Torsion points:

O, [7140429854737564728, -3570214927368782364], 
[26274212552414019135/4, -26274212552414019135/8], 
[-13708982992841069512, 6854491496420534756], 
[8094887370939953784, 5635986171296721751204699620], 
[8094887370939953784, -5635986179391609122144653404], 
[19632650368084087248, 73765443624285117558990866916], 
[19632650368084087248, -73765443643917767927074954164], 
[-1028898674559648264, -28053575987518304973062301660], 
[-1028898674559648264, 28053575988547203647621949924], 
[5680910419295422368, 5012007929188345287733592676], 
[5680910419295422368, -5012007934869255707029015044]
   
	Independent points of infinite order:

P1 = [1624079315785374648, 20450334645410411496771746916]
P2 = [785210169637118546516648/109561, 20843012447119584444887913630674396/36264691]
P3 = [407002614541703170176282/54289, 33513228082843323119532320867368422/12649337]
P4 = [18873260401553352497272/1089, 2096758764023109763611133734437732/35937]
P5 = [31441397639117126712542905992/273529, 5575101292757919669044833844001015801588972/143055667]

Dujella - Peral (2012)

y2 + xy = x3 - 119375272592212606342695780292063782980x 
	   + 486730768842864202768007431828034011912604553878407184400

	Torsion points:

O, [7186702817601604360, -3593351408800802180], 
[-50293038049986181185/4, 50293038049986181185/8], 
[5386556694894940936, -2693278347447470468], 
[9009928973919570760, 11940830995394642537562717820], 
[9009928973919570760, -11940831004404571511482288580], 
[26696525803682351680, -127775426176178396551892925500], 
[26696525803682351680, 127775426149481870748210573820], 
[3869412613398909640, 9096856524414413314306898620], 
[3869412613398909640, -9096856528283825927705808260], 
[-3536151495322549040, -29404803688314714302694299780], 
[-3536151495322549040, 29404803691850865798016848820]
   
	Independent points of infinite order:

P1 = [2343446129014487560, 14827368095283138154659050620]
P2 = [1091725459764636760, 18913141813665214635383815420]
P3 = [545146403760595948024/9, 12533662930050056318388641080724/27]
P4 = [-1634630167078604856440/361, -209668865591953312468410008199020/6859]
P5 = [95832549059437402660, 932288089154737905966824615020]

Dujella - Peral (2012)

y2 + xy = x3 - 376654149758617929440196007339872300x 
	   + 88973290232367064730638426983006536029213915195290000

	Torsion points:

O, [557289341150487000, 228355169571059129333265300], 
[1420158389689723199/4, -1420158389689723199/8], 
[353624544151632600, -176812272075816300], 
[-708664141574063400, 354332070787031700], 
[362481868682122200, 8402883729749385334487700], 
[362481868682122200, -8402884092231254016609900], 
[557289341150487000, -228355170128348470483752300], 
[183912451736636040, -161004714997174783171070700], 
[183912451736636040, 161004714813262331434434660], 
[346243813159243560, 8275500081305727894561300], 
[346243813159243560, -8275500427549541053804860, 6]
   
	Independent points of infinite order:

P1 = [358347257963395800, 4082637225896721677476500]
P2 = [7025820502981588440, 18554037310801316873241201300]
P3 = [681661166805871800, 385959566883520032256900500]
P4 = [1112209998150190090440/2401, 13868637324189582326781004463700/117649]
P5 = [1299474683278195497790291456200/3632733076729, 
     23636020401140152349402528689524861972586500/6923891160452402317]

Dujella - Peral (2012)

y2 + xy = x3 - 12384379556305685688479674960590x 
	   - 2940026837163614801093525753452171000804443900

	Torsion points:

O, [19364467648309500, -2649260590238047898444190], 
[-2419685932643340, 113398904890013270211210], 
[-2419685932643340, -113398902470327337567870], 
[-3393831784606404, 1696915892303202], 
[14529300522366495/4, -14529300522366495/8], 
[-238493345985220, 119246672992610], 
[-861549338986620, -84203487104504958321990], 
[5361077458893180, -291118354281752440359390], 
[5361077458893180, 291118348920674981466210], 
[-861549338986620, 84203487966054297308610], 
[19364467648309500, 2649260570873580250134690]
   
	Independent points of infinite order:

P1 = [-238517610907860, -544394123414838588750]
P2 = [-3099342798468420, -75308390132878912748190]
P3 = [-244292692685220, -8414717216670269967390]
P4 = [-3064407798519120, -78956628508393608989490]
P5 = [2896703004612913836/25, 4927823471207915850562375194/125]

Dujella - Peral (2012)

y2 + xy = x3 - x2 - 465940285636697633201648611060890324x 
	   + 122417499952052899686605546724393820791691045238548368

	Torsion points:

O, [386768677089269472, 7944946865395561284150444], 
[394098211784164632, -197049105892082316], 
[-788196494652356232, 394098247326178116], 
[1576393131472766403/4, -1576393131472766403/8], 
[394109678033018857, -12429190695194022132541], 
[394109678033018857, 12428796585515989113684], 
[386768677089269472, -7944947252164238373419916], 
[394086816729850032, 12428556267497078425284], 
[394086816729850032, -12428950354313808275316], 
[401473540279937067, 8044379047495419296074359], 
[401473540279937067, -8044379448968959576011426]
   
	Independent points of infinite order:

P1 = [391646593074566904, 2663000925505702929711780]
P2 = [394075536109341567, 24694208712949089407199]
P3 = [394103796080989552, 6033041857857292520964]
P4 = [50872872039051807, 314396947978510314020534559]
P5 = [745247009732968074875473/1646089, 137957837725051088935246101835182033/2111932187]

Dujella - MacLeod - Peral (2013)

y2 + xy = x3 - 881063736059316881644156022557131x  
             + 10065931953809263718033274148403504846943847748145

	Torsion points:

O, [17185313444501358, -8592656722250679], 
[68357167785661455/4, -68357167785661455/8], [-34274605390916722, 17137302695458361], 
[17632006488294354, -112176451833709824317835], [17632006488294354, 112176434201703336023481], 
[28247179230462348, 2777927187230844394544721], [8001570889982826, -1878387525584867155671891], 
[28247179230462348, -2777927215478023625007069], [16647269344437888, 110048299065372250221561], 
[8001570889982826, 1878387517583296265689065], [16647269344437888, -110048315712641594659449]

	Independent points of infinite order:

P1 = [13498024849181028, 795365943647276665302561]
P2 = [4539421538415920, 2481925289338669423782455]
P3 = [11869989276795498, 1131440016786966052603821]
P4 = [4511386748981706337497/262144, 1645147139917406191237288916253/134217728]
P5 = [12072799671624900858/361, 29103076160457501209030460099/6859]

Dujella - Peral (2015)

y2 + xy = x3 - 2782943443885745159100949025619723531275020246x  
             + 55855240810754614011637810490868813280940664269627083967668818447140

	Torsion points:

O, [109044001755668684633888, -32388114159646556159099305470467674], 
[-11859255132686138171464, 9337610431701331808095791331289774], 
[-11859255132686138171464, -9337610431689472552963105193118310], 
[21920741782073992669628, -2320428269964301346440204723992934], 
[21920741782073992669628, 2320428269942380604658130731323306], 
[33091046042849616095948, -16545523021424808047974], 
[27745338877258652001740, -13872669438629326000870], 
[-243345539680433072390753/4, 243345539680433072390753/8], 
[39701829468352179710684, -2818992444225403465094308378033654], 
[39701829468352179710684, 2818992444185701635625956198322970], 
[109044001755668684633888, 32388114159537512157343636785833786]

	Independent points of infinite order:

P1 = [23750284577699813908448, 1776656408644779962971766512279526]
P2 = [691511353654463965517684/25, 25247144434411739376289791577276138/125]
P3 = [43882187782816701847822692716/1585081, 340503355387749636940932181921830291036910/1995616979]
P4 = [258228789379105828496987398005752939756/4798947067471489, 
     2615761019520217898452643310301670673767287754132891480410/332444337096100144140737]
P5 = [248639842573471033744096758586198560139616/7327510688458875121, 
     13931299141484207325603352816906406436354981512505798207492214/19835113544842763845899563831]

Voznyy (2021)

y2 + xy + y = x3 - 348661090280842928414956055328x  
             - 69498818575042908305872415175040554816160994

	Torsion points:

O, [-381593629198075, 2825380307511178717947], 
[-1737357454244041/4, 1737357454244037/8], 
[-237993012458495, 118996506229247], 
[672332376019505, -336166188009753], 
[1006702674801530, 24489716365498934750847], 
[1006702674801530, -24489717372201609552378], 
[-283551980438020, 2562548784890491873122], 
[-283551980438020, -2562548501338511435103], 
[-381593629198075, -2825379925917549519873], 
[3685253634040685, 220670281450625494808967], 
[3685253634040685, -220670285135879128849653]

	Independent points of infinite order:

P1 = [-240171308953870, -621247444955021283753]
P2 = [-417386751107620, -1820451841460823094878]
P3 = [-266630790215083, -2123594247488660870277]
P4 = [-238064752167250, -113220964616005608573]
P5 = [15636454929856645/9, 1825056392925785937002669/27]

Voznyy (2021)

y2 + xy = x3 - 6197797046695940443964155104654510x  
             + 187019492054500460547935663802146486647242944372100

	Torsion points:

O, [47830036075018620, -23915018037509310], 
[-90862854324373380, 45431427162186690], 
[172131272997419039/4, -172131272997419039/8], 
[55118008093963020, -3585733863365528982805710], 
[55118008093963020, 3585733808247520888842690], 
[139122923093151840, 44916746742646614585688290], 
[36348189189015000, 3124689995692526475661890], 
[-10117088000277780, -15769832298757428779876910], 
[139122923093151840, -44916746881769537678840130], 
[36348189189015000, -3124690032040715664676890], 
[-10117088000277780, 15769832308874516780154690]

	Independent points of infinite order:

P1 = [3736079207114460, 12802975458836286078398850]
P2 = [17399073735640880, 9189708745003891677705890]
P3 = [843659680296300, 13482998963612651322007890]
P4 = [52472885165348490, 2506438549187687404954470]
P5 = [1475365588551503368544205/10061584, 1573604402734677496637739759093073995/31915344448]

Voznyy (2021)

y2 + xy = x3 - 4028572659064894023414572918864821346x  
             + 3112168796466128387581738718030132919162515996041103940

	Torsion points:

O, [-9270510544804082465/4, 9270510544804082465/8], 
[1203084669747638884, 82552084269228768088586446], 
[1115092754148174436, -80488890411719426219861810], 
[1203084669747638884, -82552085472313437836225330], 
[1163739668569845348, -581869834284922674], 
[1153887967631175268, -576943983815587634], 
[1115092754148174436, 80488889296626672071687374], 
[2035448615515411588, 1828984337950250199405058126], 
[2035448615515411588, -1828984339985698814920469714], 
[458712639579330628, -1166504465214563949436550834], 
[458712639579330628, 1166504464755851309857220206]

	Independent points of infinite order:

P1 = [1073078466252617316, 157611180937799075795888334]
P2 = [934624517147565988, 404205418992088242868878286]
P3 = [25042035195641956, 1735310013241079826671796430]
P4 = [-7867685447511738176249036/343842849, -11413243846839785027182805270851642603870/6375877949007]
P5 = [-120503554414854594680690304724526492/393664551234371041, 
    -513172580752754859972470104862082491536720220754482386/246995740437144581501163089]

Voznyy (2021)

y2 + xy = x3 - 468312065267662447228789199795656x  
             + 3900741312653255147077993282735174539118428998720

	Torsion points:

O, [12463249639904528, -6231624819952264], 
[50100175611483007/4, -50100175611483007/8], 
[-24988293542775280, 12494146771387640], 
[6080638165306988, -1130456365207197609003064], 
[12825842681503904, 64220667583109492275256], 
[12825842681503904, -64220680408952173779160], 
[6080638165306988, 1130456359126559443696076], 
[20231554711826048, -1645343520344575517260744], 
[20231554711826048, 1645343500113020805434696], 
[12165335167378676, 63098911819690278557384], 
[12165335167378676, -63098923985025445936060]

	Independent points of infinite order:

P1 = [8671174107417104, 701359408561599392702456]
P2 = [9183141518117696, 612029795581277769324680]
P3 = [10115504773499408, 445624943269457163349496]
P4 = [11900128677713636, 113934806054214381019604]
P5 = [8418214931637846683/676, 92515648494787439424077671/17576]

Voznyy (2021)

y2 + xy + y = x3 - 105455825278195299631919905771897634x  
             + 13178722945426306188744160727143699395082191822986996

	Torsion points:

O, [201202702394535534, 10291736345803189985440033], 
[201202702394535534, -10291736547005892379975568], 
[758282614238315927/4, -758282614238315931/8], 
[185398632004329453, -92699316002164727], 
[37470473419704573, 96331994433678898052504953], 
[-374969285563908435, 187484642781954217], 
[392051990101461168, -179150258295211168962917237], 
[392051990101461168, 179150257903159178861456068], 
[37470473419704573, -96331994471149371472209527], 
[174085643662440861, -9807364457912653325761223], 
[174085643662440861, 9807364283827009663320361]

	Independent points of infinite order:

P1 = [94604227941768429, 63630653443573038027060553]
P2 = [127746321874244013, 42330096247818113384313193]
P3 = [3369585581105630810123190/14641, 6185350358909320495935871953869636977/1771561]
P4 = [288334298817559185504213/1792921, 46716519882591907588754259908198587/2400721219]
P5 = [18263518093295102163768909/1575025, 78020390991905769781968397036774778767/1976656375]

Voznyy (2021)

y2 + xy = x3 - 514699340979237751433018301474842276796x  
             + 3177802237122375626573582025203115898158662221080781313040

	Torsion points:

O, [27117945431420751935/4, -27117945431420751935/8], 
[-25303854261104285832, 12651927130552142916], 
[18524367903249097848, -9262183951624548924], 
[25887162763841435784, 84863740100344849697395563396], 
[25887162763841435784, -84863740126232012461236999180], 
[-12941123680953690264, 87585988467352811959371767940], 
[-12941123680953690264, -87585988454411688278418077676], 
[2164945191290844228, 45537385138504360685270689716], 
[2164945191290844228, -45537385140669305876561533944], 
[88437666781187153388, -805822264385110129942418919264], 
[88437666781187153388, 805822264296672463161231765876]

	Independent points of infinite order:

P1 = [-5538456890173823112, -76541184509189528900998280124]
P2 = [-7450806400483643652, -81234841474253379328658746224]
P3 = [87378857036592605783796/4225, 10197959963232511932626310366457524/274625]
P4 = [285452347796037706088, 4807887431728541141027194671236]
P5 = [100806461536217489781506621878356/204030179809, 1011067054733901074786535654870131890545616860408/92159820129185873]

Voznyy (2021)

y2 + xy = x3 - 414104152508615055741297665x  
             + 3074071041390765679087545341686733505225

	Torsion points:

O, [6311795924380, -26679289343758129415], 
[55511488658095/4, -55511488658095/8], 
[9482319979546, -4741159989773], 
[-23360192144070, 11680096072035], 
[17856849858430, 37059902826223922035], 
[17856849858430, -37059920683073780465], 
[55014532766230, 383143867497462306535], 
[55014532766230, -383143922511995072765], 
[-7755779115320, -76283971522859637965], 
[-7755779115320, 76283979278638753285], 
[6311795924380, 26679283031962205035]

	Independent points of infinite order:

P1 = [1958847943180, 47648925981895337035]
P2 = [7221683466580, 21451623563466090385]
P3 = [-14817169105988, -77180527964414791253]
P4 = [23116405228600, 76512361836467296915]
P5 = [98677865228980, 960764862135085379035]

Voznyy (2021)

y2 + xy = x3 - 50693641981429217970733502331x  
             + 4236624121693012204114505394297557612475345

	Torsion points:

O, [109405293423470, -54702646711735], 
[-258948829808562, 129474414904281], 
[598174145540367/4, -598174145540367/8], 
[188891825955954, 1183508630463301337481], 
[188891825955954, -1183508819355127293435], 
[-76602157438224, 2769543934343731474215], 
[-76602157438224, -2769543857741574035991], 
[77040869785308, 887920108591135153281], 
[77040869785308, -887920185632004938589], 
[566236765520778, -12533202556232394308679], 
[566236765520778, 12533201989995628787901]

	Independent points of infinite order:

P1 = [108696293830938, 103185468687769355481]
P2 = [193089718277808, 1283468049814857223911]
P3 = [53537120318946, 1294635771683411706549]
P4 = [151989120480858, 206871951370157723481]
P5 = [353299089897679681338/32137561, 349528215854277001002627687709749/182187833309]

Voznyy (2021)

y2 + xy = x3 - 240169668868104529524321303756x  
             + 29668756031923445007028869559325820330802320

	Torsion points:

O, [-2171862672433345/4, 2171862672433345/8], 
[409543984671768, -204771992335884], 
[133421683436568, -66710841718284], 
[576484441927704, 9099463364587052640756], 
[576484441927704, -9099463941071494568460], 
[32553933514776, -4678118004305654158860], 
[32553933514776, 4678117971751720644084], 
[1985010840325368, 85874349808384139728116], 
[1985010840325368, -85874351793394980053484], 
[-288111448057032, -8657295769399060822284], 
[-288111448057032, 8657296057510508879316]

	Independent points of infinite order:

P1 = [-86377451671656, -7054752418018569558540]
P2 = [-8889727242996, -5639423401321035640560]
P3 = [-370202468947632, -8236744372377746818884]
P4 = [50272235005464, 4209743779052349577716]
P5 = [-195003322326090480/361, -9163909818068780772090540/6859]

Voznyy (2021)

y2 + xy + y = x3 - x2 - 1288486888765840006660359584402x  
             + 551370471381336433474899429016996626668795729

	Torsion points:

O, [577046853188433, -288523426594217], 
[2922668902723323/4, -2922668902723327/8], 
[-1307714078869263, 653857039434631], 
[899407260730837, 10957033832167775874631], 
[899407260730837, -10957034731575036605469], 
[-321133164169113, -30529149856666623424769], 
[-321133164169113, 30529150177799787593881], 
[2586402855898797, 120501093259509121458331], 
[2586402855898797, -120501095845911977357129], 
[432952090462827, -8641364217841357493459], 
[432952090462827, 8641363784889267030631]

	Independent points of infinite order:

P1 = [275840694411987, 14728935480961756884631]
P2 = [568996051166427, 1562911512615410438941]
P3 = [532841297240187, 4011940191599356415431]
P4 = [6247507242483057, 486158572625421684880231]
P5 = [65379001260055649067/6241, 525651766712267023133539893859/493039]

Voznyy (2021)

y2 + xy + y = x3 - 5921210863417782419714992146735948799x  
             + 5524830626653038861178962501969823785813463007317420766

	Torsion points:

O, [-2808614064646311317, 1404307032323155658], 
[4238740266726745846, -7522197749662870757086449148], 
[1333765269366898563, -666882634683449282], 
[5899395181117651015/4, -5899395181117651019/8], 
[1693499219739517564, 595078260135746304674688398], 
[1693499219739517564, -595078261829245524414205963], 
[1132585747119422893, 520938097171964836494799058], 
[1132585747119422893, -520938098304550583614221952], 
[-290828354627616047, -2687431496293880925563754082], 
[-290828354627616047, 2687431496584709280191370128], 
[4238740266726745846, 7522197745424130490359703301]

	Independent points of infinite order:

P1 = [1289429859729585178, 183544217819259648716796128]
P2 = [494126600207490316, 1649135933016295054295384117]
P3 = [11992362905149649766238/7921, 123114258653345251146234002061532/704969]
P4 = [202449507361683268049572/124609, 19336016324470257905535755771762566/43986977]
P5 = [64228647787147045297774292529696426780517/48210376955183151666409, 
     315817278123257251768803411396023613936217204907412178900064/10585485725459076724972707698381173]

Voznyy (2021)

y2 + xy = x3 - 221422828675439390675119069152360x  
             + 1266197666980267981171221363221926401817016961600

	Torsion points:

O, [-642880100038080, 1186709863014372079737240], 
[8867159455114320, -4433579727557160], 
[33248492479277439/4, -33248492479277439/8], 
[-17179282574933680, 8589641287466840], 
[9892095348858720, 209376650868465114412440], 
[9892095348858720, -209376660760560463271160], 
[22972160382553500, 2881407442846185209601960], 
[22972160382553500, -2881407465818345592155460], 
[-642880100038080, -1186709862371491979699160], 
[7347005764060740, 189692307017778846385320], 
[7347005764060740, -189692314364784610446060]

	Independent points of infinite order:

P1 = [4195034918606166, 641207239982690905407462]
P2 = [4886343022503720, 548559748326369962692440]
P3 = [8879386291378980, 13443901219425852700980]
P4 = [-4475639473204980, -1472261293983701489220660]
P5 = [-176889523854753322530960/14753281, -84001713223621359438865979753462760/56667352321]

Voznyy (2021)

y2 + xy = x3 - 82492810198517692342909712087311x  
             + 284377774067939248842180650488520353697909136185

	Torsion points:

O, [-41885627500571185/4, 41885627500571185/8], 
[4730689833866678, -2365344916933339], 
[5740717041276118, -2870358520638059], 
[3680959953458546, 174928799888829425206889], 
[6943226212077914, 215251688022605063169461], 
[6943226212077914, -215251694965831275247375], 
[3680959953458546, -174928803569789378665435], 
[-2209097207367292, 675153148391083733881631], 
[-2209097207367292, -675153146181986526514339], 
[19357815890142488, 2437489559326281306066341], 
[19357815890142488, -2437489578684097196208829]

	Independent points of infinite order:

P1 = [9066373053373394, 530768374588287732040265]
P2 = [5911393033912124, 57458016541011477925655]
P3 = [-5069357389517632, -756497860293603070060309]
P4 = [3469963785968438, 199778187618534203699141]
P5 = [69276725902411852/9, 8768544253715343656342047/27]

Voznyy (2021)

y2 + xy + y = x3 - x2 - 1263666669102290724790728969503798x  
             + 17119892113634056796927854710258041642517396043781

	Torsion points:

O, [88658063689704123/4, -88658063689704127/8], 
[-41002440857473575, 20501220428736787], 
[18837924935047545, -9418962467523773], 
[71613477011165493, 17143317475448721382302775], 
[26413960693309021, 1473227722013945233042147], 
[26413960693309021, -1473227748427905926351169], 
[71613477011165493, -17143317547062198393468269], 
[15066018935092815, 1225245009071844276834187], 
[15066018935092815, -1225245024137863211927003], 
[-7437613866331245, -5109512907153176481830573], 
[-7437613866331245, 5109512914590790348161817]

	Independent points of infinite order:

P1 = [888530277408837, 3999723427475064745929991]
P2 = [22962431763148281, 458812578579656492504611]
P3 = [22496192159832795, 277572899804263119535777]
P4 = [158848242338619939795, 2002043961719062352023371196627]
P5 = [1501641105838839943/81, 185257589111358572675306179/729]

Voznyy (2021)

y2 + xy + y = x3 - x2 - 124856416426804531428973887042476135567x  
             + 536444682937608293255617228437420927441476335282881625559

	Torsion points:

O, [-12901077559752907533, 6450538779876453766], 
[7292123365029486067, 3706131675427217685197157766], 
[7292123365029486067, -3706131682719341050226643834], 
[26472256899649755243/4, -26472256899649755247/8], 
[6283013334840468723, -3141506667420234362], 
[5642638791918604707, 3403395767600331505588207366], 
[5642638791918604707, -3403395773242970297506812074], 
[16320337273620720627, 53345321440329835065121951366], 
[16320337273620720627, -53345321456650172338742671994], 
[-86605970450867133, -23393532107208837308847280634], 
[-86605970450867133, 23393532107295443279298147766]

	Independent points of infinite order:

P1 = [-4719758178400875093, -31946813435927769470385988274]
P2 = [6675785120953725427, 666205508136130117768067206]
P3 = [3640514695967254769283/49, 217303389729783294444972669913738/343]
P4 = [2374785257334295959104667/39601, 3600162767155921919191275404729917834/7880599]
P5 = [1156299286615366263332123217/56595529, 34363078200554743675640007811100966949596/425768164667]

Voznyy (2021)

y2 + xy = x3 - 26310612843461234027093097624115120x  
             + 1563288988383126212137269620122636034204666343430400

	Torsion points:

O, [109987824626497376, -54993912313248688], 
[-745144142883896065/4, 745144142883896065/8], 
[76298211094476640, -38149105547238320], 
[140985866562259040, 25617231644304098589619280], 
[140985866562259040, -25617231785289965151878320], 
[431987255281856240, 266105002294332323464185680], 
[431987255281856240, -266105002726319578746041920], 
[51427156055320160, 18607017175925656511489360], 
[51427156055320160, -18607017227352812566809520], 
[-60456811650399280, -54156934248563492982324400], 
[-60456811650399280, 54156934309020304632723680]

	Independent points of infinite order:

P1 = [20132484687743840, 32276167904809046450918480]
P2 = [10838040276631760, 35768793330061334980166480]
P3 = [59748126675347120, 14302808458382792386695680]
P4 = [-101815472490977260, -56450487334404311762084320]
P5 = [-121907698967347360, -54396926018712397620710320]

Voznyy (2021)

y2 + xy = x3 - 245985416803455144146042999267601216631620x  
             + 46954441904923525514836857385775826023658917005202875412240400

	Torsion points:

O, [284232376236077786376, -142116188118038893188], 
[-2290762678048794880065/4, 2290762678048794880065/8], 
[288458293276120933640, -144229146638060466820], 
[302211928317226143240, 465133944877890864224425907580], 
[302211928317226143240, -465133945180102792541652050820], 
[82821034914051758040, -5210544252749635259479892834820], 
[82821034914051758040, 5210544252666814224565841076780], 
[270761383169222229000, 448413550904277772692617617020], 
[270761383169222229000, -448413551175039155861839846020], 
[553053366868404442680, 8948336206653011049758786815740], 
[553053366868404442680, -8948336207206064416627191258420]

	Independent points of infinite order:

P1 = [1357927810735124162250, 47083960645089232936252175372520]
P2 = [28440622512024839381520, 4795601017485981295914955146936180]
P3 = [900820899076218936840, 23587332242770403643484700281980]
P4 = [6361293037180531818569610/1849, 15885953634228521147977723140582536760/79507]
P5 = [853797154916693678488/9, 133568060301930273117884549896612/27]

Voznyy (2021)

y2 + xy = x3 - 22880617554837472146922585847918490x  
             + 1232498527451728130572600367913964471440301574528100

	Torsion points:

O, [424673080310329695/4, -424673080310329695/8], 
[67027651961434580, -33513825980717290], 
[-173195922039017004, 86597961019508502], 
[139030529917024980, 27180565381896663367148310], 
[139030529917024980, -27180565520927193284173290], 
[438905191165339860, 275208634424478520230775830], 
[438905191165339860, -275208634863383711396115690], 
[-63557394628607100, -49294910207857434639120810], 
[-63557394628607100, 49294910271414829267727910], 
[41743793214342180, 18711364637540474463754710], 
[41743793214342180, -18711364679284267678096890]

	Independent points of infinite order:

P1 = [-17058403431021420, -40222400746773193683973290]
P2 = [-19521041170539948, -40886588269560674260813674]
P3 = [-19446092830582380, -40866656205390961878234090]
P4 = [-53631005635523628, -48014070952562816225439978]
P5 = [36015484472476470, 21334437652400815242190410]

Dujella - Voznyy (2021)

y2 + xy = x3 - 36647212731638199187985833963168330016x  
             + 76371683672189214878691736554410504236279260047618688000

	Torsion points:

O, [1445028671874505216, -5141282551022937723464732960], 
[-2773441008067287752, -12517081420633345263696798944], 
[-2773441008067287752, 12517081423406786271764086696], 
[18850710432396968008, 78000847035345171867586237216], 
[18850710432396968008, -78000847054195882299983205224], 
[-27627404801904218625/4, 27627404801904218625/8], 
[5840766032068061824, 7847227571863048617697275616], 
[5840766032068061824, -7847227577703814649765337440], 
[2521348563454017088, -1260674281727008544], 
[4385502637022037568, -2192751318511018784], 
[1445028671874505216, 5141282549577909051590227744]

	Independent points of infinite order:

P1 = [8881345861317100264, 21247131897672217751577689080]
P2 = [2331128496052222036, 1900012407335714414016257584]
P3 = [15570515284891718776, 57277274340363366629586498664]
P4 = [2341202583328293568, 1845481860843624345627666016]
P5 = [9763013782774992447404212800958817567842691810695118868352/97050033166274289071683881299270945689, 
     962951512490873711223404392547604860965169634472895096254004588916210948317715183548192/956078456391070424814957754415416330401754876266920488637]

Voznyy (2021)

y2 + xy = x3 - 12913072637171051888677804949040443350x  
             + 17860454427774866303901560588040876524723206009752222500

	Torsion points:

O, [2160397549770260300, -215279798667560135785766950], 
[2160397549770260300, 215279796507162586015506650], 
[-4149389133702629300, 2074694566851314650], 
[2074692576989722700, -1037346288494861350], 
[8298786226851626399/4, -8298786226851626399/8], 
[2074985586480673100, 726038039555627976460250], 
[2074985586480673100, -726040114541214457133350], 
[2074403560827895580, -725972224158946223312950], 
[2074403560827895580, 725970149755385395417370], 
[1990155648843863420, -209471418075960560180762470], 
[1990155648843863420, 209471416085804911336899050]

	Independent points of infinite order:

P1 = [18672288726193530700/9, 247624511660099641479550/27]
P2 = [1055849964973119238508/1369, 146455827243922269852127580686898/50653]
P3 = [2466096609556729460, 1006709011686618887522751290]
P4 = [2075341748578598300, 1614671593418156387295050]
P5 = [68371369283414265772601450/32959081, 123985285448950414763387413004236150/189218084021]

Voznyy (2021)

y2 + xy = x3 - 10725241111515187057410059103590984240x  
             - 13339604973888106830803921557232597049875922697496774400

	Torsion points:

O, [-1974956283466572620, 372900161994451686425484460], 
[-1974956283466572620, -372900160019495402958911840], 
[3775976374783130080, -1887988187391565040], 
[5662913499942020080, 10369471037726069145953194960], 
[5662913499942020080, -10369471043388982645895215040], 
[-8264614513097040641/4, 8264614513097040641/8], 
[-1709822746508869920, 854911373254434960], 
[20760512430560392780, 93336790293566509540405641760], 
[20760512430560392780, -93336790314327021970966034540], 
[-1796815647267759920, 361349222976348675958084960], 
[-1796815647267759920, -361349221179533028690325040]

	Independent points of infinite order:

P1 = [-1894293682756177070, -423987625676556479827943540]
P2 = [104036883358475826545380/11881, 30760074288190655318935270499115340/1295029]
P3 = [-57158301244607293057220/32041, -1955593937125474291278492475279060/5735339]
P4 = [9667299693537648452789620/11881, 30057596513811678724363722176719654780/1295029]
P5 = [-491174567706076821675615095/246615616, -1347682590252948323403014878189219715935/3872851633664]

Voznyy (2021)

y2 + xy + y = x3 - 383292262549105310433612901641149477497838102353x  
             + 91333398188716126714408734977750957596497997554010622783252021342962256

	Torsion points:

O, [136860655840710911581405, 203566408534334765731436879146718222], 
[136860655840710911581405, -203566408534471626387277590058299628], 
[-2859518281378886304450905/4, 2859518281378886304450901/8], 
[359071494985721360055055, -179535747492860680027528], 
[343299298641823321165210, -14448842265384173928127033563612658], 
[371766715496275311086080, 14837548964700171607665701651611472], 
[355808075359000216057671, -177904037679500108028836], 
[371766715496275311086080, -14837548965071938323161976962697553], 
[343299298641823321165210, 14448842265040874629485210242447447], 
[635140192006291700511625, 322655506952847596373272520613613672], 
[635140192006291700511625, -322655506953482736565278812314125298]

	Independent points of infinite order:

P1 = [-196223449247220601503455, -398734260588690001235780166804063328]
P2 = [774643794648516315368048530/2209, 703453796820271267985637439664177652586/103823]
P3 = [332660856376680668143982965855/1069156, 51810422238103030828335002541199540327224613/1105507304]
P4 = [166015227066042643330318107490432/362483521, 751450649734764036247563580011817373834285406512/6901323756319]
P5 = [-1454735737572989330917746336706505/2207778169, -24942402987208463017150783202988014605667555788384/103736872826803]

Dujella - Peral (2021)

y2 + xy = x3 - 950036066648113768553286013014724920x  
             + 355183166597122262848437818696235991225146982720142400

	Torsion points:

O, [1676562670591247340, -1864128514147805380616167620], 
[1676562670591247340, 1864128512471242710024920280], 
[674858248946048640, 146275937320557701771015880], 
[674858248946048640, -146275937995415950717064520], 
[2141953963500510335/4, -2141953963500510335/8], 
[456797467394701620, 128554464695052056476145880], 
[-1125051147167231760, 562525573583615880], 
[589562656292104176, -294781328146052088], 
[-108785391147803040, -676199539256700703723777320], 
[-108785391147803040, 676199539365486094871580360], 
[456797467394701620, -128554465151849523870847500]

	Independent points of infinite order:

P1 = [229962678565491630, 385838574973465936945281780]
P2 = [258509610098401992, 356181402572113306682812296]
P3 = [530389007562585072, 22350333078408587366619912]
P4 = [-236422331858741424, -752713730247577301754562968]
P5 = [477790069914244560, 101670477694338601775428680]

Dujella - Peral (2021)

y2 + xy = x3 - 159520416329925967706535990409997531503116x  
             + 24522926859083189886645834180635667334784400113135096253958800

	Torsion points:

O, [315651185590835582616, -2370703690163703975097272560460], 
[315651185590835582616, 2370703689848052789506436977844], 
[228271304841664641048, 60878353373282820693687115956], 
[-461187450215474276712, 230593725107737138356], 
[230458993010431612568, -115229496505215806284], 
[922913828820170656575/4, -922913828820170656575/8], 
[232923942044915472024, 61289175469059737037837505716], 
[232923942044915472024, -61289175701983679082752977740], 
[228271304841664641048, -60878353601554125535351757004], 
[154849335702246192408, -1879979463301026150724840126284], 
[154849335702246192408, 1879979463146176815022593933876]

	Independent points of infinite order:

P1 = [229783850908868794008, 20991961254247479105774621876]
P2 = [5956049490694251042953112/12769, 10364864131843247760031005240381298932/1442897]
P3 = [635848597788368013518857368/863041, 14045998101537491518821434459164669102644/801765089]
P4 = [1454404616095436283293581848/201601, 55382877006377108980374777008965921198644/90518849]
P5 = [275503645813772095607704385788/24413481, 144518205763016207175706145631870701802671476/120627009621]

Dujella - Peral (2021)

y2 + xy = x3 - 164352473471553491334797170752177228211103411950x  
             + 25645444881388228159922635208522423751703002009026207672567652383802500

	Torsion points:

O, [123983185272808795313900, 84701535926726419276994330821218050], 
[123983185272808795313900, -84701535926850402462267139616531950], 
[364600730244112817335400, -119122350521775797734510271462353450], 
[364600730244112817335400, 119122350521411197004266158645018050], 
[228971710554922246792400, 4232831922443350838840692071918050], 
[228971710554922246792400, -4232831922672322549395614318710450], 
[934502836547306339488799/4, -934502836547306339488799/8], 
[234494339343538457563900, -117247169671769228781950], 
[-468120048480365042436100, 234060024240182521218050], 
[239185208690614619813900, 4294849612920732194974207471218050], 
[239185208690614619813900, -4294849613159917403664822091031950]

	Independent points of infinite order:

P1 = [233182612156567182451400, 638445600004178625866933511018050]
P2 = [-311945008822902931186100, -215775594128657727590531879228781950]
P3 = [6397430406917474939218402378700, 16181111678712836250999865447582338735736453250]
P4 = [5670444694121262361027283049959900/3829010641, 412435698917362404654451573570105917714879196923950/236935349454439]
P5 = [13262771391014713948585702381309100/3854795569, 1517239251743038029351040973695255271625782828629150/239332692492503]

Dujella - Peral (2021)

y2 + xy = x3 - 26207261857539148160527038741500591440255813530x  
             + 1632072530067015458124404951372067060642159391312332672006501483084900

	Torsion points:

O, [220074578841973148809620, -80767276377115048669459481511181290], 
[220074578841973148809620, 80767276376894974090617508362371670], 
[6226223750189019592860, -38329383230026920352641196328621130], 
[6226223750189019592860, 38329383230020694128891007309028270], 
[-186918980867639016874540, 93459490433819508437270], 
[381029958500068776997215/4, -381029958500068776997215/8], 
[91661491242621822625236, -45830745621310911312618], 
[103387034527942096407060, 5260507227868912621734135532149270], 
[103387034527942096407060, -5260507227972299656262077628556330], 
[83860300991664120818700, 4906671904262320961214734044814070], 
[83860300991664120818700, -4906671904346181262206398165632770]

	Independent points of infinite order:

P1 = [25305260376926510994260, 31386228276734947482052546492680470]
P2 = [-121579948215785036905200, -54965386541350861127610272788367430]
P3 = [41223965032409844957768634554/466489, 795819358030442345857098705737598956368254/318611987]
P4 = [46719841886202035309906305860/619369, 4478629707756684881851480783948966559771970/487443403]
P5 = [1428473484199531019207888856052500/1218079801, 53500064083844027663599077434350244334981029651070/42512203134701]

Dujella - Peral (2021)

y2 + xy = x3 - 15622933632667427555352743356961351817383702736x  
             + 749082653415201100820417350907437334048641866059790504097975141935360

	Torsion points:

O, [214100914027031071885728, -84961245271985591930310171623883984], 
[302214663665811209564927/4, -302214663665811209564927/8], 
[68720426666640032008608, -34360213333320016004304], 
[-144274092583092834399840, 72137046291546417199920], 
[86395712135794260380064, -6648661454187098177299945887368400], 
[86395712135794260380064, 6648661454100702465164151626988336], 
[214100914027031071885728, 84961245271771491016283140551998256], 
[-13622939808103528417632, 30973936327116638239649765570047536], 
[-13622939808103528417632, -30973936327103015299841662041629904], 
[58709162188455237672096, -5850644142555742768631724151338960], 
[58709162188455237672096, 5850644142497033606443268913666864]

	Independent points of infinite order:

P1 = [-60009418069837723670112, -38347152151520694699810577423656144]
P2 = [-117593936693777304537432, -30985749873484263719543460838414104]
P3 = [2233756480215991057579188018336/47045881, 3450479533038140311776648051974535812424033936/322687697779]
P4 = [-89878497836731772089571202308334904/1239822121729, -53478770501549010988088662423614613646620193928931640/1380508457347954817]
P5 = [310008417523612271826470330391794942106127185363646857714/1539377967296279634632062602961681, 
     4587919737911008363888256617340340561387982590901884721386361538539398212606409336564/60397352169370247286545951662569408665728317891079]

Dujella - Peral (2021)

y2 + xy = x3 - 713603864890201881215581682056x  
             + 173565939028395978646185524923160350368249920

	Torsion points:

O, [938090099580704, 18156891718865997249656], [938090099580704, -18156892656956096830360], 
[-947035750516592, 473517875258296], [2703479485405055/4, -2703479485405055/8], 
[271165879165328, -135582939582664], [101714534923148, -10101206749490936349844], 
[3180620891307776, 173436252866448575899784], [101714534923148, 10101206647776401426696], 
[3180620891307776, -173436256047069467207560], [-468065127488812, -20125431230160703337464], 
[-468065127488812, 20125431698225830826276]

	Independent points of infinite order:

P1 = [783905935534154, 9792063060958885627490]
P2 = [46479406191344, 11853204869518918689560]
P3 = [-151796825230624, -16685052990404966422360]
P4 = [421910501388963328/81, 270592897898471141215286344/729]
P5 = [88151709135339248/121, 8455013912276220192150856/1331]

Dujella - Peral (2021)

y2 + xy + y = x3 - 1704963512980998304463394440323349x  
             + 27063627201552616127672199868307888303240469365516

	Torsion points:

O, [20651051582454321, -813208284720184431319574], [20651051582454321, 813208264069132848865252], 
[27163068765633864, 890716376428834387105012], [27163068765633864, -890716403591903152738877], 
[92613520909030247/4, -92613520909030251/8], [24519074887545903, -12259537443772952], 
[-969806452045662, 5358749825785841183806978], [-969806452045662, -5358749824816034731761317], 
[-47672455114803465, 23836227557401732], [61807961166492933, -12561989091903578830235702], 
[61807961166492933, 12561989030095617663742768]

	Independent points of infinite order:

P1 = [571252196395714176/25, 23617351500371298336456311/125]
P2 = [-13933520750099286, -6936474325283993695310438]
P3 = [11405006781530102073/121, 35309287096808407900148496668/1331]
P4 = [59854907596452146158617/2209, 14643643350928626080478671906603444/103823]
P5 = [-507292698459470302503/12769, -8174207927177590788896922767974/1442897]

Dujella - Peral (2021)

y2 + xy = x3 - 13595883660149605052308511455995x  
             + 18036730221659744241723788396566551765213731025

	Torsion points:

O, [1067455477426890, -68848049405631380314695], [1067455477426890, 68848048338175902887805], 
[2558598640029390, -1279299320014695], [1667913500529390, -833956750264695], 
[-16906048562235121/4, 16906048562235121/8], [-1494263280742560, 187125987433338951231255], 
[10411367867711340, 1002517657012719234814305], [3328186688131890, 98248856603028822535305], 
[3328186688131890, -98248859931215510667195], [10411367867711340, -1002517667424087102525645], 
[-1494263280742560, -187125985939075670488695]

	Independent points of infinite order:

P1 = [117195404063982, 128237922544546185572937]
P2 = [-1056942542075440, -176708964835875437379415]
P3 = [-436816652758110, -154571310694155898077195]
P4 = [359287798699885640, 215348036226614053698285305]
P5 = [-438134746958610, -154626821586630691024695]

Dujella - Peral (2021)

y2 + xy + y = x3 - 211084024962119940270849973565928418x  
             + 37323562301640255964141090570739506548206276867389556

	Torsion points:

O, [1070130164411636119/4, -1070130164411636123/8], [-530507722318704515, 265253861159352257], 
[262975181215795485, -131487590607897743], [281542738692776110, -14534196633246465731588368], 
[281542738692776110, 14534196351703727038812257], [527126073705877360, 269302654950672062658824132], 
[249285327202471285, 13956848555782996677067457], [68216815169979685, -152451735496493299908252943], 
[527126073705877360, -269302655477798136364701493], [249285327202471285, -13956848805068323879538743], 
[68216815169979685, 152451735428276484738273257]

	Independent points of infinite order:

P1 = [13542736756183453765/49, 3356125006164727873507324151/343]
P2 = [-3616979735237624360/49, -78593205258729037554083172724/343]
P3 = [-6376454841780639991331/60025, -3558403050002412007983030916243043/14706125]
P4 = [101324842454223428642965/375769, 773818755882839457305079365118029/230346397]
P5 = [35592898343683827479685/96721, 2928740498970575253130428180931367/30080231]

Dujella - Peral (2021)

y2 + xy + y = x3 - 2189256808324576348475573115752858564x  
             + 1244409080600296936231266379308108547684693121678406386

	Torsion points:

O, [722137491377422053, -200116881632516294077277417], [722137491377422053, 200116880910378802699855363], 
[2344814728948122756, -3000527439311457638781956459], [823593659475670793, -411796829737835397], 
[3538218233370568695/4, -3538218233370568699/8], [-1708148217818312967, 854074108909156483], 
[992791086949820994, 222403294773995496644277667], [992791086949820994, -222403295766786583594098662], 
[-88578959476081827, 1199014662021267941361808903], [-88578959476081827, -1199014661932688981885727077], 
[2344814728948122756, 3000527436966642909833833702]

	Independent points of infinite order:

P1 = [380323631520276153, 683224192543728651871273363]
P2 = [955138900084183293, 157253654554600403335956103]
P3 = [1411810733772322341, 983680564386229479937407511]
P4 = [1438208062633148901, 1034723570897220637081227031]
P5 = [269704339707127687681503555070910817/14079665906741824, 
     139659706832300195881606207080101876420985796193754181/1670661730679680988088832]

Dujella - Peral (2021)

y2 + xy = x3 - 777343687573960224838790540965720626x  
             + 263017165141660690430538026243083770207460137839413380

	Torsion points:

O, [418117925302499268, -105319978504444784390701314], [418117925302499268, 105319978086326859088202046], 
[1482797810763722508, -1539670549324836989147365674], [1482797810763722508, 1539670547842039178383643166], 
[486283705345662980, -243141852672831490], [-4070927766777569313/4, 4070927766777569313/8], 
[531448236348729348, -265724118174364674], [604994278794367044, 119027409351885333499903230], 
[604994278794367044, -119027409956879612294270274], [-85932899683120644, 573743840032348099272735654], 
[-85932899683120644, -573743839946415199589615010]

	Independent points of infinite order:

P1 = [583803924757392768, 90426892200040688703182046]
P2 = [-852259828914012156, -553606132308161401641146370]
P3 = [795398841440983626, 384623691521038213786108644]
P4 = [-1016587577390475420, -51598080033619730599664610]
P5 = [33115067051820499325039473848246052319088825161696483996/62308644497444397689695269612167769025, 
     582336119059831215059405961944149350741639635836341250147577023535334547193253446/491838425066243670328132776121201026445104531670737438625]

Voznyy (2021)

y2 + xy = x3 - 1136338151495929349647447081459159877160x  
             + 14611348635346821519730522288274715550782714201962318337600

	Torsion points:

O, [-6754198782319825680, 148250737746394492287528899640], 
[-6754198782319825680, -148250737739640293505209073960], 
[14440771592105430960, 34830561434320050533959095000], 
[14440771592105430960, -34830561448760822126064525960], 
[66927774355743347280, 488211174190880897607126411480], 
[66927774355743347280, -488211174257808671962869758760], 
[17936002756237620816, -8968001378118810408], 
[-38885604981049756080, 19442802490524878040], 
[24871449055176317520, 41643444201216256385594164440], 
[24871449055176317520, -41643444226087705440770481960], 
[83798408899248541055/4, -83798408899248541055/8]

	Independent points of infinite order:

P1 = [11327544438835968720, 56505768864539837897388801240]
P2 = [-35315141362123589040, -103429624890388062677112585000]
P3 = [213971913630682315730820/8281, 37685545002334751817136669118330040/753571]
P4 = [-6056328360317096182320/169, -211998333802164691262140156347720/2197]
P5 = [-1549981239839040456381385027710/75327742681, -3537752476454209083133928517722777169172585170/20674376928484579]

Voznyy (2021)

y2 + xy = x3 - 2565739986296345342279591139426658269700x  
             + 49748454436423307737039101481715843342116365330659498090000

	Torsion points:

O, [36082174835895053000, -64398767679298017206801383300], 
[36082174835895053000, 64398767643215842370906330300], 
[-7776647547483454960, 263117858671475899597475051060], 
[-7776647547483454960, -263117858663699252049991596100], 
[93187754765713545800, -787331836435957896945882789700], 
[22835417289455068160, -55374931240953633005119552060], 
[93187754765713545800, 787331836342770142180169243900], 
[22835417289455068160, 55374931218118215715664483900], 
[27458325279849547400, -13729162639924773700], 
[123980873891180964799/4, -123980873891180964799/8], 
[-58453543752644788600, 29226771876322394300]

	Independent points of infinite order:

P1 = [5916983237284314200, 186478340873034395104076445500]
P2 = [193043111665092761480, 2597753971937001177103613440700]
P3 = [-4185860103858699181912384/72361, -1319830559575615906660577686796143892/19465109]
P4 = [7415743769031756790891400/1708249, 439174939189803281414740354824886477300/2232681443]
P5 = [118794041458163551029385072587819956795113857182533550/424848664923158002503716731528681, 
     40314078962515687713553943046659203632163516162549028351425870633439582358619400/8756920092259025003701084481546965590745285948171]

Voznyy (2021)

y2 + xy = x3 - 2559144409238521291125723904482226597740x  
             - 35041189055874968080678116856670050092476397761934866444400

	Torsion points:

O, [307463448020124877980, -5314489147749364909706124035040], 
[307463448020124877980, 5314489147441901461685999157060], 
[-20853797921141643960, 96217322529790677946545023460], 
[-20853797921141643960, -96217322508936880025403379500], 
[-33990654400312087980, -112579775035509376778778185340], 
[-33990654400312087980, 112579775069500031179090273320], 
[56395816963107073496, -28197908481553536748], 
[-165521630100887194305/4, 165521630100887194305/8], 
[-15015409437885274920, 7507704718942637460], 
[84206331899557048680, 588680743853729307461677205460], 
[84206331899557048680, -588680743937935639361234254140]

	Independent points of infinite order:

P1 = [43605457269211809200205/16, 9104079898333813719773338962137115/64]
P2 = [-18389571300046580520, -76167327268357034121260562540]
P3 = [-19047371253900479086890/529, -1242198661350197145136779911469930/12167]
P4 = [-6474729869684000939130/169, -180769442457177353218825399712880/2197]
P5 = [-200679154772736715077513957811320/12596898722521, -1835258023511299800659285314310904879272001652740/44709051511857480931]

Voznyy (2021)

y2 + xy + y = x3 - 5523948314048898966461050391284767828464x  
             - 74123692715562482090350059367740115892863764950837222269714

	Torsion points:

O, [-24942698074750593387, -219409838638814063702500619957], 
[-24942698074750593387, 219409838663756761777251213343], 
[-51004266275170485219, 273746133248356630113713928091], 
[-51004266275170485219, -273746133197352363838543442873], 
[321175429296724239927/4, -321175429296724239931/8], 
[-66388511523113617087, 33194255761556808543], 
[-13905345801067442895, 6952672900533721447], 
[119356547680662967194, 983315082438328298128487205967], 
[119356547680662967194, -983315082557684845809150173162], 
[434016607391909980188, -8904172037270636535651575965007], 
[434016607391909980188, 8904172036836619928259665984818]

	Independent points of infinite order:

P1 = [91083116056927249005, 422345380703474704910468617207]
P2 = [-15603398899459107987, -90938321503665132279738837257]
P3 = [-16787037002874366387, -117797994865313579160234244457]
P4 = [1006715512961403578538, 31853523633953801680160100304543]
P5 = [-519225424244447752863363/37249, -93146230354111824369377060284585049/7189057]

Voznyy (2021)

y2 + xy + y = x3 - 20363542572789657236198319220870594745638x  
             + 1029634598131390752217300230960990268500894528109538987937656

	Torsion points:

O, [132236486760410485750, -805718974750689603327996936988], 
[132236486760410485750, 805718974618453116567586451237], 
[-60900067127028830075, -1429653255788379487125684501163], 
[-60900067127028830075, 1429653255849279554252713331237], 
[38500930050676964965, 550172728090012650232110038837], 
[38500930050676964965, -550172728128513580282787003803], 
[419108597357583322360, -8130951300080262943640667303073], 
[419108597357583322360, 8130951299661154346283083980712], 
[62622225632519856981, -31311112816259928491], 
[-163304996066249914475, 81652498033124957237], 
[402731081734920229975/4, -402731081734920229979/8]

	Independent points of infinite order:

P1 = [-24503782362972353963, -1230408662316026432509447426027]
P2 = [47564549108375343670, 410683896899890135986558817637]
P3 = [34724315653151679141093778/744769, 273862783108162794006085473373612191508/642735647]
P4 = [414004741796782436630766925/11978521, 25119063419669289681143571926615947960897/41457661181]
P5 = [1156034343374878987813038089200/5063603281, 1036835988074940538080122357707347247407431848/360320945872679]

Voznyy (2021)

y2 + xy = x3 - 9944816006259625977840425958566800694899876310x  
             + 375738276399934272663968156456694999584647377181948541112073059128100

	Torsion points:

O, [77043682996139089364620, -8177007697820074987542427236017510], 
[77043682996139089364620, 8177007697743031304546288146652890], 
[39720314973873860489740, 6587406858246402304661374580574490], 
[39720314973873860489740, -6587406858286122619635248441064230], 
[216866281392827942664820, -91752262214343159973872175311240110], 
[-25455547378284535060700, 24746599792479738754613995896240610], 
[216866281392827942664820, 91752262214126293692479347368575290], 
[-25455547378284535060700, -24746599792454283207235711361179910], 
[-459800372302021174747745/4, 459800372302021174747745/8], 
[63363431945411390320716, -31681715972705695160358], 
[51586661130093903366220, -25793330565046951683110]

	Independent points of infinite order:

P1 = [505343094113415799718245/16, 617685185951738289714345313651370935/64]
P2 = [63378106446509969182320, 175660941238051290942977192695290]
P3 = [6983903877269231621898220, 18454544932777381162846533677652620890]
P4 = [-6121826715729027757640, -20889932753961655924822839260315750]
P5 = [6388799673388952876951380, 16146422246131651375633576530876796090]

Voznyy (2021)

y2 + xy = x3 - 235334273455987394964523963592499652082662660x  
             + 1389402580778507925321471401829214532306675301334259269130495747600

	Torsion points:

O, [-17713592508539269416184, 8856796254269634708092], 
[35123770131392305413055/4, -35123770131392305413055/8], 
[8932649975691193062920, -4466324987845596531460], 
[8324684053622011773020, -84986747813303999307768983615560], 
[9399561602653911543320, -88495057857603409615862175429460], 
[9399561602653911543320, 88495057848203848013208263886140], 
[2283538303606014961400, 929470479046565883278906488263740], 
[8324684053622011773020, 84986747804979315254146971842540], 
[17590462450733707895540, -1640939251923493885705935348883360], 
[2283538303606014961400, -929470479048849421582512503225140], 
[17590462450733707895540, 1640939251905903423255201640987820]

	Independent points of infinite order:

P1 = [206946589867894971170525/16, 45675550735643670913237818091716665/64]
P2 = [-12518320150898180668870, -1540671021156262192894655110215010]
P3 = [929038251531101978048927435/131044, 13191199944656450945582348350676960241295/47437928]
P4 = [42719681396010799000706710190/5329, 8829603729325063855518595257046393294014680/389017]
P5 = [79866011974008773566048579018055735720/8695588796519881, 
     42418551643942796551821313230492034051066341250572036140/810864881353499212553221]

Voznyy (2021)

y2 + xy = x3 - 42693004392254822691146438859313194074450x  
             + 3359207226047701256669553879937400540351481107950013217802500

	Torsion points:

O, [154483743969444722500, -671283626547956925642541398050], 
[154483743969444722500, 671283626393473181673096675550], 
[-44805494146687354700, 2276431397511848982223183605550], 
[-44805494146687354700, -2276431397467043488076496250850], 
[86741972306189710660, -555511607751253584941881259810], 
[421514753748831811540, -7762472428228756496155840760690], 
[86741972306189710660, 555511607664511612635691549150], 
[421514753748831811540, 7762472427807241742407008949150], 
[109099573046621132356, -54549786523310566178], 
[-953219872473537557025/4, 953219872473537557025/8], 
[129205395071763256900, -64602697535881628450]

	Independent points of infinite order:

P1 = [20968239079751177980, 1572650357424422086612110410950]
P2 = [1117022014076790208810, 36734468775526460924938314569650]
P3 = [66445982937032809268788437509308/502974568849, 56083354176153855306866796690788534407648244458/356713085049692743]
P4 = [2081173737229765653192401527870036/63889727541025, 722760854524922092608404075101791730631457377272126/510677300656804632625]
P5 = [-59660750591113098070041993637518800/303778720704001, 
     -10810288589344831857970518441636969767427519130898050/5294634964051488725249]

Voznyy (2021)

y2 + xy + y = x3 - x2 - 221506764278437274448719554022739328072223x  
             + 35787899343915179404831418999844261161663873286820744117085831

	Torsion points:

O, [111073688478176754435, 3543258749803038861623555022982], 
[111073688478176754435, -3543258749914112550101731777418], 
[-216837605628529963665, 8580414124287050971178093098282], 
[-216837605628529963665, -8580414124070213365549563134618], 
[1472723483952051985143, 53886741837426410483722773840550], 
[1472723483952051985143, -53886741838899133967674825825694], 
[-2147271755200301326485/4, 2147271755200301326481/8], 
[195083395994395577235, -97541697997197788618], 
[341734542805679754387, -170867271402839877194], 
[455653188933899591971, 5427731829088030712555007439222], 
[455653188933899591971, -5427731829543683901488907031194]

	Independent points of infinite order:

P1 = [43336619706622572435, 5125420355709819210002986524982]
P2 = [-3284902576241995065, -6042804981009096147290692445018]
P3 = [26731464063722371128535546980499/151707913009, 88207043771879254458002454216799231253370305398/59089776993266473]
P4 = [26631335035204828592399870056217014784047421235/136576834248559309852228081, 
     158475440344481189709897153545445355553919377452412350474952007469222/1596120085620350820590212477803910952521]
P5 = [3025041115479090771712278489767944649230768790153115/8292743626094904585330850129369, 
     44843722188649622758366818288360916755814738751208649426284716981062910003554/23880716821978143361375123953353717715705845347]

Voznyy (2021)

y2 + xy = x3 - 827032909959112298726631507615191753773214925270x  
             + 288127645881258220697348458198134400304626845787652428488732462738948900

	Torsion points:

O, [-1049551119512600094332724, 524775559756300047166362], 
[1981476010215589949087135/4, -1981476010215589949087135/8], 
[554182116958702607060940, -277091058479351303530470], 
[641421902261232654792540, -146784678300382701125753213712292470], 
[641421902261232654792540, 146784678299741279223491981057499930], 
[415664301164127854277840, -127187821091944462490669109297431370], 
[-126745067536140595034820, 625231089742831979294374667196555930], 
[415664301164127854277840, 127187821091528798189504981443153530], 
[1635346473155710705134600, -1819105373352407561228700783345379170], 
[-126745067536140595034820, -625231089742705234226838526601521110], 
[1635346473155710705134600, 1819105373350772214755545072640244570]

	Independent points of infinite order:

P1 = [193793998226366574369720, 367602748951367108786605174770456750]
P2 = [4372138810048096376051714711925342/5371570681, 154598000758191039736821674449031027112259037879802/393687786781171]
P3 = [113249716382601191550121127842255735740/9997554695881, 
     1201420164895995238686956254722867710968703711539197294030/31611178214913870971]
P4 = [295107012026421880610408477742215561996341362828/445436237909363205649, 
     160313052808274119255135394338985157148189260485956893269111202865440438/9401092339415306655087003339143]
P5 = [123355506290569320578200133619218684618079286332657/445222385042736709718323456, 
     2661342507644913827370836203719247869741534524746359854250054425051950976673/9394322989328717083368077371136349999104]

Voznyy (2021)

y2 + xy = x3 - 3629711399120990987208528045020168923896110x  
             + 2616136739358682501122496342486861256513342071284194381865524100

	Torsion points:

O, [-503292711002229577580, 65692147154293576551854455500490], 
[-503292711002229577580, -65692147153790283840852225922910], 
[748728343261590942820, -17838207664657011966176337763910], 
[4861744969704486170655/4, -4861744969704486170655/8], 
[-2195719208923265620484, 1097859604461632810242], 
[980282966497144077820, -490141483248572038910], 
[1483693292801838837820, 22290811136181928539975577561090], 
[1483693292801838837820, -22290811137665621832777416398910], 
[4205644246146155148220, 248471239719970436956123193665090], 
[4205644246146155148220, -248471239724176081202269348813310], 
[748728343261590942820, 17838207663908283622914746821090]

	Independent points of infinite order:

P1 = [109390165422325370320, 47121024972647047445729041448590]
P2 = [-810597278584100937920, -70892548486719489521107791886370]
P3 = [102654172908530766441965633263779766417351420/1963171052764440173281, 
     1039394551775607353122072641296229568430038198666952522302624134110/86983566882320444553066125317679]
P4 = [121538647148005477840107625552776400136667225820/78363085078014767026799401, 
     18580448815790522576761642601667900894016291487511840850453729002109910/693692961699049935791051270703718665899]
P5 = [708177838072619933089493089694230263803172436128377980/178510521569476569560420590043809, 
     536780326745438189847748288476200533213903485748549239075982388864848521972611870/2385040336538150238003888095373797225473237716623]

Voznyy (2021)

y2 + xy = x3 - 15764345399107376296711918301793546648155x  
             + 754886651310602098736420881924474674635760382616318551403025

	Torsion points:

O, [249891986421429273610, -3524238821182878911440825817255], 
[66760600051280429710, -33380300025640214855], 
[-144832586272724926290, 72416293136362463145], 
[312287944885777986319/4, -312287944885777986319/8], 
[92746411175711869810, -300990443768505971486389075355], 
[92746411175711869810, 300990443675759560310677205545], 
[-25343980791918850100, -1066835994603299830646538780095], 
[53691227897625185920, 251511167030388181950372695785], 
[249891986421429273610, 3524238820932986925019396543645], 
[-25343980791918850100, 1066835994628643811438457630195], 
[53691227897625185920, -251511167084079409847997881705]

	Independent points of infinite order:

P1 = [-11196833322013890590, -964361790259040635581132952055]
P2 = [112235479578674153260, 631962021882242327337314377345]
P3 = [-814314956127744298697600/6889, -562185634894659783048139109948422915/571787]
P4 = [7142091897702697133509156977819390580861087720163890/385455242983604589507646331094889, 
     5183429480808371831215643861382491745118405883569433864739320842097005491581735/7567648223683025257561451436537728431066924565963]
P5 = [45958780359030185766656453243053124462216884947941804964104199767527/524692895111366277044062786905203785136674720996, 
     81596030171846789141517713680638406279159778584825579505230883531681427635967551758507467279464210777/380064910455926937381159478021733022444808471200165852554121185413700456]

Voznyy (2021)

y2 + xy = x3 - 4469237839814477484470531557126804846x  
             + 3603941229386954504659111217580938134526475769277393540

	Torsion points:

O, [1559825472001811084, -654104086494405511189178254], 
[1559825472001811084, 654104084934580039187367170], 
[905597696839247468, 547080355719555690762583826], 
[905597696839247468, -547080356625153387601831294], 
[4197533839940791448, -7668228714467872422090092314], 
[4197533839940791448, 7668228710270338582149300866], 
[-423655120774605664, -2328372296899197504220146910], 
[-423655120774605664, 2328372297322852624994752574], 
[-9754648707902280673/4, 9754648707902280673/8], 
[1313845266027756028, -656922633013878014], 
[1124816910947814140, -562408455473907070]

	Independent points of infinite order:

P1 = [-159375943235587456, -2076579390774325173572405794]
P2 = [1014543504225598424, 337599080554729311234355586]
P3 = [1086351542298105776, 175630550960973606802950254]
P4 = [972708493235108348, 420731809112546113070340866]
P5 = [1121664227963166944, 46445144802707091876068606]

Voznyy (2021)

y2 + xy = x3 - x2 - 3942275499678093720068242698374256264x  
             + 3012787958456231147248818900541865512948858000195896048

	Torsion points:

O, [1149144785331054337, -5204243178679302348477481], 
[1149144785331054337, 5204242029534517017423144], 
[955410370004215587, -344099150875907700117594981], 
[955410370004215587, 344099149920497330113379394], 
[1348489594467274812, 385741573811681605981246644], 
[1348489594467274812, -385741575160171200448521456], 
[1143534391521672612, -5195759921005494807992256], 
[1143534391521672612, 5195758777471103286319644], 
[4585033408665170307/4, -4585033408665170307/8], 
[1146418538359478712, -573209269179739356], 
[-2292676890525771288, 1146338445262885644]

	Independent points of infinite order:

P1 = [-394576649758055688, -2122942742766054082635733356]
P2 = [-8684098608631789497/4, -9256419909924715640296671333/8]
P3 = [2265924500183861212, 2390414906913126870134928144]
P4 = [417192403543748453941404/22801, 267941773357415523888737964637611660/3442951]
P5 = [272845421181114188778168/146689, 81709052721011528373680225888583228/56181887]

Voznyy (2021)

y2 + xy = x3 - x2 - 1221007349912216022153983564423166975072264x  
             + 502997137095049939950574730260859043947204033822706106851138048

	Torsion points:

O, [-5085843875307794033277/4, 5085843875307794033277/8], 
[2715230445833359896072, -131170321026526566974397020653656], 
[543277234203197020608, -271638617101598510304], 
[728183734623751487712, -364091867311875743856], 
[388781783516238108627, -9330411794989209985423516944606], 
[-361224570169524150888, 29948643675392509906731097764744], 
[914262553060024617937, -12283565460985117190252168187481], 
[914262553060024617937, 12283565460070854637192143569544], 
[388781783516238108627, 9330411794600428201907278835979], 
[-361224570169524150888, -29948643675031285336561573613856], 
[2715230445833359896072, 131170321023811336528563660757584]

	Independent points of infinite order:

P1 = [-85268153784702078483, -24627022231459606335968318347281]
P2 = [-672258963704442307563, -31937671455348624584854947978081]
P3 = [496439554037474056497, 4380573978634119278432874559719]
P4 = [5781233843861559972182453170047/173159281, 13892990906630303691714723895209383394527264901/2278602978679]
P5 = [46959495112758237050433074313109371927/3142426290721, 
     321799323819444015158889778737577248780989994816711335811/5570544518871918769]

Voznyy (2021)

y2 + xy + y = x3 - 11990207986263964897842354318696226836518748x  
             + 15980321123175843014595712317106892393603802898535350716844124506

	Torsion points:

O, [2045686121044005797570, -3601554772261431474431467488798], 
[2045686121044005797570, 3601554770215745353387461691227], 
[1953033873691208366180, 3546344756078653273080483250542], 
[1953033873691208366180, -3546344758031687146771691616723], 
[1032703067350619014745, 68551799444188359611488814307927], 
[1032703067350619014745, -68551799445221062678839433322673], 
[3151321422090190011785, -97419447630372497371468312697673], 
[3151321422090190011785, 97419447627221175949378122685887], 
[-15993459666821400996745/4, 15993459666821400996741/8], 
[1995122789791318087841, -997561394895659043921], 
[2003242126914032161345, -1001621063457016080673]

	Independent points of infinite order:

P1 = [516935138913326843270, 99600691271220843527765186901327]
P2 = [2127290342466814583570, 10021528379625938359470475486827]
P3 = [2382100686482048129720, 30584953012020040135732900808577]
P4 = [4249986631970079733061188162067945/1941087046441, 40475284358205997003934163339608301504365314391403/2704378764625947989]
P5 = [14731891982258001604418553468495200705/7430073999307129, 
     789292624344105955380025365709957012544598627055621491/640456604693173990765133]

Voznyy (2021)

y2 + xy + y = x3 - 161044051689742900487239966952214099286568734x  
             + 786201722367030537844604137909292722605646200662984563807439399696

	Torsion points:

O, [8093395220668630018534, -113800725580874013935092301316868], 
[8093395220668630018534, 113800725572780618714423671298333], 
[527970115863722236213, -837449967877146254275426272937987], 
[527970115863722236213, 837449967876618284159562550701773], 
[6584280957513353381653, -106250475284997888815424907877107], 
[6584280957513353381653, 106250475278413607857911554495453], 
[17167934588628814437736, -1755406022795206335097962464620873], 
[17167934588628814437736, 1755406022778038400509333650183136], 
[7188322696518255213573, -3594161348259127606787], 
[-14652645163764004069307, 7326322581882002034653], 
[29857289868982995422935/4, -29857289868982995422939/8]

	Independent points of infinite order:

P1 = [4902690257362180530613, 338371843964935947022946592799613]
P2 = [10936733441591615598115830683158/3495056161, 115580968244482951491363273064847722093920646052/206624225182159]
P3 = [408888095393703404536269505124650813/50469956016841, 
     41262391462667841477512959521812684064360926681207233/358549721403918185861]
P4 = [8385585843128007825804615939788437/1001854859329, 157415424890521354759566528348415234370318919980819/1002783578783597983]
P5 = [-20561865645128725129767160944757568577525405068/6944941398751395952584169, 
     -20356204197506292572409101671787786479515151534038899162802443029482641/18302182360311093611186036147249016053]

Voznyy (2021)

y2 + xy = x3 - x2 - 31222422610742019752623139266636835611865499x  
             + 67017069206373043390537819365900798960266856589683718416487864593

	Torsion points:

O, [-6450700544903920780518, 3225350272451960390259], 
[3108006884379967198482, -1554003442189983599241], 
[13370774642095814328147/4, -13370774642095814328147/8], 
[3756223062859851905707, 52307090303330520300763276751259], 
[2720739699649709895972, 47000582302967808080481118054659], 
[3756223062859851905707, -52307090307086743363623128656966], 
[2720739699649709895972, -47000582305688547780130827950631], 
[-352724743674917893608, -279259925624120532514900366995441], 
[-352724743674917893608, 279259925624473257258575284889049], 
[8900654232604763714757, 703023156062396076329868295419234], 
[8900654232604763714757, -703023156071296730562473059133991]

	Independent points of infinite order:

P1 = [3805594215710130057732, 57549080650654426121393230412259]
P2 = [4875146410227490701442383/1444, 515120148801052477295799870327035973/54872]
P3 = [10328331386729450110857, 919951301644073521150104497495634]
P4 = [119292474827391984025840117065108473068801992/2283597522778568588881, 
     1295758363683021417030699904219274304888178356337999357327776209511/109126278495327871307573206509529]
P5 = [393423546382210942720861330207639060572192/117679810444516218721, 
     1336345006955780804800087364093274636242251015938094150820409/1276594415474419824578005774481]

Dujella - Kazalicki - Peral (2021)

y2 + xy = x3 - 659170610017003993889422708126510548832096868165970130x  
             + 187579700001340084852208249705366490286218317964972057784371942610770083685680900

	Torsion points:

O, [2442397308006932340434393060, -114661532773087122024861216514357961371330], 
[578929406178782607039296836, -289464703089391303519648418], 
[349128412292473429687694660, -174564206146236714843847330], 
[208917727555174410019230020, -7680223050204757147852184533264801213090], 
[-3712231273885024146907965985/4, 3712231273885024146907965985/8], 
[-357006354786287129929342300, 19426941959275205385136799872604237160830], 
[764769560258606540174760260, -11434979318224329788473041888293227744930], 
[764769560258606540174760260, 11434979318223565018912783281753052984670], 
[2442397308006932340434393060, 114661532773084679627553209582017526978270], 
[-357006354786287129929342300, -19426941959274848378782013585474307818530], 
[208917727555174410019230020, 7680223050204548230124629358854781983070]

	Independent points of infinite order:

P1 = [138727651962305806569924932, 9940038874770021205270501801021138892126]
P2 = [804443299098980614961111492, 13337650646960485374850436183748004655966]
P3 = [3146106111602046876326065243074949360310/1828907321641, 
     159219665030051917644777375441041982720342016069456311968870/2473361223474960811]
P4 = [153087168445505300640827249832806393942660/572711953822801, 
     75668935458582550831353956305466634280274244415407953567466670/13705799424426933674201]
P5 = [-56222378804119003358043175619279408925628/306474356075281, 
     -93289318015581937566453214397495493555344637119731634351262866/5365265425465503975929]

Dujella - Kazalicki - Peral (2021)

y2 + xy + y = x3 - 103471331626105226343652117500237344836489274834409534x  
             + 12810800276634399094397736261466905912471874573304568599312566592865955814482096

	Torsion points:

O, [741591583011804446291039447/4, -741591583011804446291039451/8], 
[186033983105654057529531973, -93016991552827028764765987], 
[-371431878858605169102291835, 185715939429302584551145917], 
[189569678947175563995012134, -90966261710895410377554129597366599268], 
[189569678947175563995012134, 90966261710705840698606954033371587133], 
[100495981931255404910409128, 1851297000080027372814563675657868013143], 
[100495981931255404910409128, -1851297000080127868796494931062778422272], 
[286324562457784861548308213, -2580272596227721020257096978196530883027], 
[286324562457784861548308213, 2580272596227434695694639193334982574813], 
[181888492452486425526319061, 89720759249614448426159850720125168061], 
[181888492452486425526319061, -89720759249796336918612337145651487123]

	Independent points of infinite order:

P1 = [-154892054053555117871606347, -5012143967891710258257143865280106641107]
P2 = [185161780859938283365015109, 10706300240857808900707137553708160733]
P3 = [-1371036273203550732809072965/4, -22638596286609059519629862328536187006489/8]
P4 = [87676741641055419774313271910866389/473106001, 56624649442302885481481892849339740788680934050347/10290528627751]
P5 = [990800577653611154409811928381091179444/5484893740225, 
     1528502882664357247657064641677609994391483843705791386552/12845538866200846625]

Fisher - Voznyy (2021)

y2 + xy + y = x3 - 737894644327026219218841358570509913846652580014x  
             + 190908291625785611127850212005200136993025927512858679851032108028536736

	Torsion points:

O, [123121337629362845437773, 319255533346175398256712239176372453], 
[2697602411445279985947095/4, -2697602411445279985947099/8], 
[292706449185843816856533, -146353224592921908428267], 
[-967107052047163813343307, 483553526023581906671653], 
[929737247379508789629894, 555459795600627480533795589823130413], 
[929737247379508789629894, -555459795601557217781175098612760308], 
[3128235132857569912762056, -5338076048751105550148719747698439673], 
[3128235132857569912762056, 5338076048747977315015862177785677616], 
[-462144728348406389310147, 658193421686178321454623988574296813], 
[-462144728348406389310147, -658193421685716176726275582184986667], 
[123121337629362845437773, -319255533346298519594341602021810227]

	Independent points of infinite order:

P1 = [-11770388000247148570827, -446757168044703123403874819446287227]
P2 = [-81834810594693810894027, -500745162308676208711090313029106747]
P3 = [848475159454149564192509, 419104818982980770090598605433148437]
P4 = [272027986699563246582461, 101538945612934640714606857958859501]
P5 = [-68875020373746272797526140878398236498931516469726529879839854796627388935993996848472042334397687627959471774163637507189518132798206838809415510442597307433339217890193238247486168196/
      164545873218778442401307168403345336722612846663938134018355350552969099611244109826598124664736457750495736710819925127654914952873128518527802763322143223505849, 
      43587064776070360317729896035128769999279485478150860416582196262611823406441993653879794541133219555246788462013711592871367082444580836433453550942486965816276076626914767570173741330115772530568396810961976902213582868811104620613161599393890323052659349197892017323771893272/
      66746806559562777985743241528296366902717491451739710640368213307083202299375765279347797208412820571731146284303768096587987209758960825189855069158946129883729436692058120461469183969632637592734334725038006184666972092257590693872268243757]

Fisher - Voznyy (2021)

y2 + xy = x3 - 14578233419504842866768626074144915305633167440x  
             + 677262813789165866285590491715440177836227774714086370178932369721600

	Torsion points:

O, [70758299942212843304480, -35379149971106421652240], 
[-557654666616527941059841/4, 557654666616527941059841/8], 
[155414455085033567750540, -46534088652306971144451728707673740], 
[68655366711919141960480, -34327683355959570980240], 
[63612030127066887748880, -2705043081319790242055738474178640], 
[8910983221132061368820, 23410766808437032977159386168440460], 
[75979156144410838956080, -2869818325046407319753479281142240], 
[75979156144410838956080, 2869818324970428163609068442186160], 
[155414455085033567750540, 46534088652151556689366695139923200], 
[63612030127066887748880, 2705043081256178211928671586429760], 
[8910983221132061368820, -23410766808445943960380518229809280]

	Independent points of infinite order:

P1 = [42539581561272601822460, 11579774247444742179793233760034180]
P2 = [64676567475997891673780, 2222290249393354839936527519680460]
P3 = [261214749164537080276239891011690300714534080/3930006245950275895881, 342601353576263684507732951818141284253188856905225372126545938960/246371155788765578938536597670971]
P4 = [700393915051554413654555183512765609116769751270/10292440995168160717706689, 19270407931967799053872464231714295419647261573192276170227925120677470/33020038774683169374914720879045183137]
P5 = [8652155375218086006579972938857618262247801501505888939272707069948056134340093291762663859154982381217171294475997436064889873087464490600954575635109910389333490988154801591975166003131950352605821357360791538520/
      126049130514331225154679387299895667396557355738709861773118231539591136718902852815085816766679258510817115720808149927839126987535011106587974986019883895925060693537799631077908183400082289, 
      3543281644870837967575167900571976137426000862271729122142162226414476385238182633234876127160016401765003064929181560880038662609336338977838589903772142315511054661737446661343553551629565796966242409610666368870785922910653941736602455074725446357924320117351816032804073913857871059584841624438610111237589629856880/
      44751725113948075901016142532847720042577863133606322064030422248325579691376450814206872972424266505627639297468464264057174572362702381810950160836798385134851224027147925326488676158214191248498105919689038373661915511274374506613375490005241141836811871272582274071267672796291595913]

AttarBashi - Voznyy (2021)

y2 + xy = x3 - 18344990390026697364172972562894635575223977734230x  
             + 30242963345408228178130902590094453683264001065271744604221214839616196900

	Torsion points:

O, [9890696309661689691878815/4, -9890696309661689691878815/8], 
[2473029830474284317606860, -1236514915237142158803430], 
[-4945703907889706740576564, 2472851953944853370288282], 
[2466684649360211624675960, -16783934509371926069051480117648530], 
[2913302236855456852227680, -1234754654755031371155279835972219930], 
[2479024385622534895863260, -16811875479238879453158891125133430], 
[2479024385622534895863260, 16811875476759855067536356229270170], 
[2057086270651936210686140, -1100231709960747541573420836861943510], 
[2913302236855456852227680, 1234754654752118068918424379119992250], 
[2057086270651936210686140, 1100231709958690455302768900651257370], 
[2466684649360211624675960, 16783934506905241419691268492972570]

	Independent points of infinite order:

P1 = [716599819818404596428170, 4179106544473309959718329214806662360]
P2 = [105598844053265782120792880123578340/42709595569, 7709706514112916577247690683895116710785957187790/8826493149076247]
P3 = [1084126052584727608884979658280824239036650678035026991183359275044203276820/444360173309773411522544107475855904119159767011649,
       842729398345876938651752961704038137494422708871692393197684490111337555191356622743463317766729774847867551750/9367046824744760635123856233738425099858910689796850081991190225496397402143]
P4 = [993308932890019896367568988452110057684147317537846580211480747020739936060/399757831306333168835262310612414337565130508631361, 
      259778765072766013859731394489454387437765204239959245805895024828450407009991231847597686029227817763312705130/7992736038907403140417620963165056807152504509638984137717960159998878896609]
P5 = [1094326446134999657420067486252545709725394283496251065599188530561537311876510/442613997947926487563019872223938155916349961767954041,
       318191480492662449834082755685772549086804166131322317912744441761262426817590341002904157522614675116583895019270/294467735771041495118223243293755585691983260590844361212227303703757743358707661]

Voznyy (2022)

y2 + xy = x3 - 75532826995689993241153458590x  
             - 5840213618603934546445210719307440984003900

	Torsion points:

O, [1229817602398495/4, -1229817602398495/8], 
[-85634097421220, 42817048710610], 
[-221820303178404, 110910151589202], 
[459286762310380, -7506830265766332620990], 
[459286762310380, 7506829806479570310610], 
[1677727483388620, -67748450640145529440430], 
[1677727483388620, 67748448962418046051810], 
[-183874475113160, -1353359400267116729390], 
[-183874475113160, 1353359584141591842550], 
[-115992721344320, 1166380074025490404210], 
[-115992721344320, -1166379958032769059890]

	Independent points of infinite order:

P1 = [-207427058050208, -950044687422111532814]
P2 = [329688080136540, 2256702237605723222610]
P3 = [1770804080101511260/9, 2356434359469010158129722470/27]
P4 = [-105637632121324145/1156, -21492782850147037633254635/39304]
P5 = [-53362557561389300600/388129, -337288001548961885585058687730/241804367]

Voznyy (2022)

y2 + xy = x3 - x2 - 725725749888808798467228522840x  
             + 237914533611148516496229543972918686770176000

	Torsion points:

O, [1944729058745475/4, -1944729058745475/8], 
[497480170109952, -248740085054976], 
[-983662434796320, 491831217398160], 
[528602365050481, -1412976562581641882185], 
[528602365050481, 1412976033979276831704], 
[94712978674035, -13039498254394207720485], 
[94712978674035, 13039498159681229046450], 
[1035161047086888, 24411206232419628126144], 
[455933069390520, 1345077913595166231120], 
[1035161047086888, -24411207267580675213032], 
[455933069390520, -1345078369528235621640]

	Independent points of infinite order:

P1 = [802075139061645, 13108110167152346053620]
P2 = [1186620595911207/4, 55846173364895457747747/8]
P3 = [531208742642688, 1516773542115084783744]
P4 = [180507989444005605/361, 1567045258450190238510165/6859]
P5 = [12440798197833519/25, 6341623292913960894462/125]

Voznyy (2022)

y2 + xy + y = x3 - 101908137750838357809618088772229x  
             + 395965852016171735867395371862166620722082268956

	Torsion points:

O, [5978955159438824, -19919487335035692545997], 
[5978955159438824, 19919481356080533107172], 
[9385277830006466, -515962427942374687478094], 
[9385277830006466, 515962418557096857471627], 
[5678960844786113, 19580636577703037421828], 
[5678960844786113, -19580642256663882207942], 
[2872626803523893, -356267704993209618612432], 
[2872626803523893, 356267702120582815088538], 
[23368672914921575/4, -23368672914921579/8], 
[-11656640223809417, 5828320111904708], 
[5814471995079023, -2907235997539512]

	Independent points of infinite order:

P1 = [5812667641073021, 964301290726496976216]
P2 = [84397758199896533/16, 4607635379719499981643117/64]
P3 = [5474976184554838, 46212874837421602578203]
P4 = [4996725165879023, 107300714100246682246488]
P5 = [12318973676481148469/49, 43203289579009891953851178048/343]

Voznyy (2023)

y2 + xy = x3 - 130071903672063900200456928082630x  
             + 570976360674310160301312895749995336563403180900

	Torsion points:

O, [26413098066362015/4, -26413098066362015/8], 
[6565960114721836, -3282980057360918], 
[6776147247422060, -26920773971657472383830], 
[6776147247422060, 26920767195510224961770], 
[10871150362293740, -664619034525516755659030], 
[10871150362293740, 664619023654366393365290], 
[3062382239856260, 448738296476315289971570], 
[3062382239856260, -448738299538697529827830], 
[6394909140116180, 26406200972364903384650], 
[6394909140116180, -26406207367274043500830], 
[-13169234631312340, 6584617315656170]

	Independent points of infinite order:

P1 = [6562748692706600, 1602503907270038717930]
P2 = [4960683827737772, 218643964765884942536042]
P3 = [2713732755716732, 487832798489412168982826]
P4 = [6350380082000660, 32621917197530982987170]
P5 = [-1600362989048929460/169, -2145350257436536810358090510/2197]