Dujella (2005)
y2 + xy + y = x3 + x2 - 99693354254976736309048235x
+ 367381667413491416441937241575243024665
Torsion points:
O, [799623476723, -16975741865015910122],
[799623476723, 16975741065392433398], [12588948901683, 33278580255984806998],
[12588948901683, -33278592844933708682], [-45905215149213/4, 45905215149209/8],
[4782017598099, -2391008799050], [6694286189203, -3347143094602]
Independent points of infinite order:
P1 = [-835742939437, -21215935717377581002]
P2 = [3746954832963, 6814774952116046038]
P3 = [-6096171578085, -27360105846461167706]
P4 = [-2303622473757, -24182904784189102202]
P5 = [2494935489403, 11583755159287549598]
P6 = [1441480579203, 15055590839860301398]
P7 = [7012677573523, 3623709821741193398]
Dujella (2005)
y2 + xy + y = x3 + x2 - 41959740466267167794021810255839x
+ 101420623252214369655938971034713774891685508101
Torsion points:
O, [7800185826861527, 498711103150132601849070],
[7800185826861527, -498711110950318428710598], [722868763952863, -267333060096424984336010],
[722868763952863, 267333059373556220383146], [-29816914475444701/4, 29816914475444697/8],
[3192701323453979, -1596350661726990], [4261527295407195, -2130763647703598]
Independent points of infinite order:
P1 = [-3445007038526955, -452864909445844203135878]
P2 = [2492198029680029, 111030669509523025660920]
P3 = [4451874811734813, 53419669922106933968746]
P4 = [242687787774531, 302079129136924019524594]
P5 = [6876160157322373, 371502935939782200743776]
P6 = [17054531626317779, 2084765600175066109066650]
P7 = [6575035045258779, 331330290650557906808050]
Dujella (2006)
y2 + xy + y = x3 + x2 - 1165389362066982859390020804572126935x
+ 479169098415397603082209745065693417368573098611430765
Torsion points:
O,[1121722398993900383, 763770549022673134993708818],
[1121722398993900383, -763770550144395533987609202],
[227498775902112823, -475203958333468654848954522],
[227498775902112823, 475203958105969878946841698],
[2281899376216052387/4, -2281899376216052391/8],
[-1245085431502019701, 622542715751009850]
Independent points of infinite order:
P1 = [-219613035643780957, -851182637388769392857068902]
P2 = [-68223999018942087, -747234281532450366676883702]
P3 = [497293734150587235, 150364681171547564975694874]
P4 = [10796967815787170653/16, 404988480627920631161493627/64]
P5 = [1044774651633868835, 634056668621030138238484890]
P6 = [4919976421604836927/9, 1994819697953126282867607346/27]
P7 = [-328470482217806715463/289, -2845674500282729683306185667926/4913]
Dujella (2006)
y2 = x3 - x2 - 23915436403668100957879238210372478564x
+ 44961725066137056690704922539092621426845072010929824004
Torsion points:
O, [2903013524470034482, 0], [-5646124833195250962, 0], [2743111308725216481, 0],
[4072212466523820944, 3886146862871075405578563406],
[4072212466523820944, -3886146862871075405578563406],
[1733814582416248020, -2951073576030980502660949482],
[1733814582416248020, 2951073576030980502660949482]
Independent points of infinite order:
P1 = [1131018313110890882, 4399969306249670626854871960]
P2 = [2728347748849569104, 146952908391872112013369586]
P3 = [261187619128923630, 6223594389290707973165058528]
P4 = [29320876476743932860, 156688551675810110453020536558]
P5 = [-4606042810657217150, 7576090497154110956612194152]
P6 = [-5268512043362633412, 4972046499534700899993247890]
P7 = [12466639899760292984, 41040781435946053834115762026]
Dujella (2006)
y2 = x3 - x2 - 66316100370037243788808101431860x
+ 207787397329581777063539110158423853553882263492
Torsion points:
O, [4628372593789489, 0], [4774517796226298, 0], [-9402890390015786, 0],
[6213948304937164, 188792790675737045056350],
[6213948304937164, -188792790675737045056350],
[3335087287515432, -153990087256491803556554],
[3335087287515432, 153990087256491803556554]
Independent points of infinite order:
P1 = [2296719982411009, 259986354975552263423820]
P2 = [-754552913305211, 507342881379999424501350]
P3 = [4623547820142394, 3196373093851098851280]
P4 = [4774647845487904, 519325665120008067090]
P5 = [2882111728866944, 201488073470229552730830]
P6 = [4572248586935254, 12595554476372830774560]
P7 = [-14146681940011859/4, 5047542184921547691312855/8]
Dujella (2006)
y2 + xy = x3 - 4352472636817242527981668893860x
+ 3202806006191278796231716596650711645198790975
Torsion points:
O, [907667106246270, -453833553123135],
[1478672062650370, -739336031325185],
[-9545356675586561/4, 9545356675586561/8],
[2964249583270165, 127856115668915058245395],
[2964249583270165, -127856118633164641515560],
[-6905457969425, -56858257917087837736865],
[-6905457969425, 56858257923993295706290]
Independent points of infinite order:
P1 = [-586964814172115, -74534076914908408877600]
P2 = [-2328305178439673, -26738296509185052458918]
P3 = [-419400465474005, -70387952431540002422810]
P4 = [-630447314322050, -75473377079125527624335]
P5 = [-846673128162305, -79252667902607341645985]
P6 = [-268297363924910, -65964004932893602468685]
P7 = [1377377634990063790, 1616512407040009129064037565]
Dujella (2006)
y2 = x3 + x2 - 1974182441851753491140042260957041544x
+ 1067650302694924098203516167151188617468357911014102916
Torsion points:
O, [-1622418946354203118, 0], [811326669343979123, 0], [811092277010223994, 0],
[787442546696709656, -36894683045645829307668798],
[787442546696709656, 36894683045645829307668798],
[835210791991248590, -37626009005611049158919916],
[835210791991248590, 37626009005611049158919916]
Independent points of infinite order:
P1 = [807173041427965811, 6288993601307198150714928]
P2 = [789278583199907432, 34057398752431372965082590]
P3 = [596369565518553920, 320016850497427999752392094]
P4 = [814421506614155896, 5010768410557123065521538]
P5 = [-981176602679102770, 1435299907571197805711062764]
P6 = [41561092163942585600/49, 19934917122155057779445712078/343]
P7 = [39756857357017556954/49, 54250001709421994662548384/343]
Dujella (2006)
y2 + xy = x3 - 7059202548408453936348405003649460x
- 205544995440715384038467753747276578744945665206400
Torsion points:
O, [-242093366040292161/4, 242093366040292161/8],
[-35403361017968480, 17701680508984240],
[95926702528041520, -47963351264020760],
[239267534900752570, -108642684797447273394364010],
[239267534900752570, 108642684558179738493611440],
[-47414129844669530, -4750711426855673634362960],
[-47414129844669530, 4750711474269803479032490]
Independent points of infinite order:
P1 = [-40080467944208480, -3606122876978274455995760]
P2 = [408080083130635270, 254697953786456983119660490]
P3 = [95933492675735920, 373533990830032696210840]
P4 = [-962353464408583355/16, -77146422425694624547527515/64]
P5 = [-36340930482348830, -1731722552202363314731760]
P6 = [16892458715992053910/169, 20552422351563850326861544690/2197]
P7 = [95927004352140082, 78749450426831409587536]
Dujella (2006)
y2 + xy = x3 - 3236364326867793561860795581563976590x
+ 2240038946953594158835601178135288379947620927515076100
Torsion points:
O, [4085603896699595295/4, -4085603896699595295/8],
[-2077199566031870404, 1038599783015935202],
[1055798591856971580, -527899295928485790],
[727518722182179300, 520179734430437450073364890],
[727518722182179300, -520179735157956172255544190],
[1384078461531763860, 641949208250981314550343210],
[1384078461531763860, -641949209635059776082107070]
Independent points of infinite order:
P1 = [1005739555669779996, 49163099954291059347164322]
P2 = [518381451900100280, 837655552211056707012286310]
P3 = [-2405859056872500, -1499274881218127124560219310]
P4 = [843602380471211580, 331958679042130626373098210]
P5 = [940105128640111310, 168460532843765869032724460]
P6 = [848175468782248980, 324365423296277587356836010]
P7 = [120130530737617207683/4, 1314369752929665855682758389883/8]
Dujella (2006)
y2 + xy = x3 - 552333041381848469546578260185903690x
+ 105246264670604440637332918974955977886070209631543475
Torsion points:
O, [825953971768859295/4, -825953971768859295/8],
[618112058064791230, -309056029032395615],
[-824600551007006054, 412300275503503027],
[-152507502803882195, 431200760645876446118157385],
[-152507502803882195, -431200760493368943314275190],
[1388731618933464655, -1420027357952646693708591740],
[1388731618933464655, 1420027356563915074775127085]
Independent points of infinite order:
P1 = [703736453716866055, 255090819294844960769724685]
P2 = [39615732830330262145, 249301833834654463541876995270]
P3 = [-2042038215442845405/4, -4033210585603340196533135145/8]
P4 = [669011498243733907, 187517617205695776364821997]
P5 = [-180114161620463585, -445966550007175173221222675]
P6 = [1164418516389907131295/4, 39733995653091626373596729630705/8]
P7 = [-294620693466003965, -492342902235415687643737520]
Eroshkin (2008)
y2 + xy + y = x3 + x2 - 223647057021425547430678972007035x
+ 1273106313114343201368902765863085728849052445440
Torsion points:
O, [-68988428135422813/4, 68988428135422809/8],
[7881912604174649, -3940956302087325],
[9365194429681053, -4682597214840527],
[3082397035545098, 782958279826254162287598],
[3082397035545098, -782958282908651197832697],
[15647991823817008, -1266902042378890394018832],
[15647991823817008, 1266902026730898570201823]
Independent points of infinite order:
P1 = [-8726288912333155, -1600070202750911236143711]
P2 = [6456748016181118, 313453072716873679262383]
P3 = [18713273063365648, 1908160131603999620825503]
P4 = [-6424268512310840, -1563565672503751617925976]
P5 = [7312072950399488, 169508147861449136621823]
P6 = [9461772364824908, 63837523115230204267143]
P7 = [4432663254435236882/169, 8057681617359104719760519331/2197]
Eroshkin (2008)
y2 = x3 + x2 - 4123297792196061474931925360x
+ 83669201239698270468036960902365235322900
Torsion points:
O, [105340804361380, -904572509820269840550],
[105340804361380, 904572509820269840550],
[-6876184911470, -334210472735844058200],
[-6876184911470, 334210472735844058200],
[23398765230714, 0],
[-72631074955670, 0],
[49232309724955, 0]
Independent points of infinite order:
P1 = [7863233370580, 227448753821255216250]
P2 = [-53445032541830, 389075979691181365440]
P3 = [-19322069176277, 395127953404498572804]
P4 = [11983227764095, 189682759293189672510]
P5 = [21829310745364, 63737975851715924730]
P6 = [20867194460260, 81938705576738152230]
P7 = [-10451426017445, 354431812482973625400]
Eroshkin (2008)
y2 = x3 + x2 - 609255875083793261019303912808600x
+ 5769420440641556969899813369432728161558284302500
Torsion points:
O, [14909494948028675, 0],
[-28491289380416726, 0],
[13581794432388050, 0],
[7318497402772550, -1304823582135807142909500],
[7318497402772550, 1304823582135807142909500],
[22500492493284800, -1858019425995733566315750],
[22500492493284800, 1858019425995733566315750]
Independent points of infinite order:
P1 = [-4832356503434830, 2932698150079894286497680]
P2 = [13129331116915280, 183094773963169535400570]
P3 = [-5283378139483450, 2973359875332604804546500]
P4 = [-5015545724269450, 2949406988156065867657500]
P5 = [1786720755936880, 2164845074961685794361530]
P6 = [13326362147583050, 130039828235976803430000]
P7 = [15081385235732810, 105978840319725141328560]
Eroshkin (2008)
y2 + xy + y = x3 + x2 - 8007418165950294717261920x
- 870716437481702091977368984017213055
Torsion points:
O, [-108900008427, 54450004213],
[2882616151573, -1441308075787],
[-11094864572589/4, 11094864572585/8],
[-1230899311627, -2668455376347768587],
[-1230899311627, 2668456607247080213],
[6996131614773, 16897925184033057013],
[6996131614773, -16897932180164671787]
Independent points of infinite order:
P1 = [-383181597927, -1463323767915288287]
P2 = [3563438686053, 3980478568219330213]
P3 = [-137187778427, -474575037055755787]
P4 = [-109031458027, -32371068443947787]
P5 = [-691731404427, -2082612916549255787]
P6 = [-1049448028427, -2525242524171255787]
P7 = [-183188678427, -768117380830765787]
Dujella - Eroshkin (2008)
y2 = x3 + x2 - 2386801266816420981220x
+ 44845424005663002738546614573600
Torsion points:
O, [18270423230, 2708574311641770],
[18270423230, -2708574311641770],
[39452756090, -3476857524473970],
[-56407666421, 0],
[27546076760, 0],
[28861589660, 0],
[39452756090, 3476857524473970]
Independent points of infinite order:
P1 = [22032102854, 1718678096630670]
P2 = [22764199660, 1519345810983000]
P3 = [4756640090, 5796541328047470]
P4 = [-26758658452, 9463251767513544]
P5 = [-12340124452, 8509977139977456]
P6 = [24822560510, 945284011785750]
P7 = [14209561490, 3714714049911930]
Dujella - Eroshkin (2008)
y2 = x3 + x2 - 5334348061487201120280x
+ 149721135899592401852463095048100
Torsion points:
O, [43529258115, 0],
[-84320610606, 0],
[40791352490, 0],
[24819878790, 5710776107645700],
[62238637440, -7668712654006950],
[24819878790, -5710776107645700],
[62238637440, 7668712654006950]
Independent points of infinite order:
P1 = [5359329240, 11013016898588250]
P2 = [33560492490, 2914994668950000]
P3 = [49198220490, 2522552201778000]
P4 = [40461341130, 355436590214160]
P5 = [16644351690, 8096013181198800]
P6 = [44116137240, 500611414899750]
P7 = [43529729040, 12840247642950]
Dujella (2001)
y2 = x3 - x2 - 84385099279492765124x
+ 262973362131816463305769975044
Torsion points:
O, [-450024320, 548504848910018], [-450024320, -548504848910018],
[13914569924, 1335239311059654], [13914569924, -1335239311059654],
[-10464902242, 0], [3732629441, 0], [6732272802, 0]
Independent points of infinite order:
P1 = [12885805880, 1146827806213782]
P2 = [7979506940, 312565640755122]
P3 = [604008660, 460678184564598]
P4 = [1473384440, 376616759777622]
P5 = [15209138914, 1580409705748016]
P6 = [20163601480277, 90542423098869511770]
Ansaldi - Ford - George - Mugo - Phifer (2005)
y2 = x3 + x2 - 75345731906887386383040x
+ 7956141361808560862806122648470388
Torsion points:
O, [107886244746, 32910620718406200], [107886244746, -32910620718406200],
[161469150507, 0], [-316936855054, 0], [155467704546, 0],
[215052056268, -41212648971204018], [215052056268, 41212648971204018]
Independent points of infinite order:
P1 = [153985039026, 2285947010756640]
P2 = [162803544546, 2167055919336000]
P3 = [30235962867834/169, 31283143086365619240/2197]
P4 = [32189665272114/169, 49863355519584351360/2197]
P5 = [154625377443516/121, 1881611310019500873450/1331]
P6 = [217002711282, 42715445379794880]
Ansaldi - Ford - George - Mugo - Phifer (2005)
y2 = x3 - x2 - 1621105850715834564900x
+ 4979606331160862237085144928452
Torsion points:
O, [-41718901791, 0], [38628969058, 0], [3089932734, 0],
[92065715784, 25220808536003850], [92065715784, -25220808536003850],
[-14807777668, 5073231297419714], [-14807777668, -5073231297419714]
Independent points of infinite order:
P1 = [1291128254, 1699618513398080]
P2 = [-9589966542, 4432154369225880]
P3 = [-166732650939/4, 2867877947917125/8]
P4 = [-987086238936/25, 340817455790473662/125]
P5 = [6033839983202, 14821119830299337984]
P6 = [-14560799125208/3721, 761767378800794319954/226981]
Dujella (2005)
y2 + xy = x3 - 1412825737585924163044x
+ 15284155642547476371073178165264
Torsion points:
O, [66149709524, -14535609729112288],
[66149709524, 14535543579402764], [-5994218500, -4851549910630708],
[-5994218500, 4851555904849208], [-168549044801/4, 168549044801/8],
[12059515688, -6029757844], [30077745512, -15038872756]
Independent points of infinite order:
P1 = [-4710088480, -4672705304733532]
P2 = [10971680384, 1050627482515964]
P3 = [5142674960, 2855599110883388]
P4 = [190936944656, 81893102282965052]
P5 = [188694106912, 80419019486556004]
P6 = [47485021091/4, 3441975241405087/8]
Dujella (2005)
y2 + xy + y = x3 - 20174541800058615341705x
+ 856471220529843128844656290913975
Torsion points:
O, [-639179005053/4, 639179005049/8],
[111893780143, -55946890072], [47900971119, -23950485560],
[-19962627757, -35373042637815172], [-19962627757, 35373062600442928],
[243750188043, 102083834331329428], [243750188043, -102084078081517472]
Independent points of infinite order:
P1 = [-85832332857, -44223889042397072]
P2 = [114334829243, 6667410918555328]
P3 = [-51502844857, -41939263761590072]
P4 = [4095391655, 27819366371819600]
P5 = [113157736403, 4744791614680828]
P6 = [40334772162089/256, 163280485878941726915/4096]
Dujella (2005)
y2 = x3 - x2 - 168258761005814873925308660x
+ 630726626828906815917748614617850058692
Torsion points:
O, [4183796725814, 0], [-14547043674127, 0], [10363246948314, 0],
[22770176501164, 92765011772747132350], [22770176501164, -92765011772747132350],
[-2043682604536, 31081480114842787350], [-2043682604536, -31081480114842787350]
Independent points of infinite order:
P1 = [-1181620857528, 28773162432111226794]
P2 = [-4080437386136, 35346241790698760950]
P3 = [235082596420931926/9, 113980528024566253238850200/27]
P4 = [12397530832897061/4, 1380381075594638902858965/8]
P5 = [21473097297618184/841, 2778642295098362364452690/24389]
P6 = [17594838020822091901/1387684, 37835298438599399762075368625/1634691752]
Dujella (2005)
y2 + xy + y = x3 + x2 - 26114391257594216192350319x
+ 39441729062095446183464976447530972981
Torsion points:
O, [-22972042324701/4, 22972042324697/8],
[4045286938075, -2022643469038], [1697723643099, -848861821550],
[8838891842163, 22342036507934785450], [8838891842163, -22342045346826627614],
[-748317966013, -7652747778169852550], [-748317966013, 7652748526487818562]
Independent points of infinite order:
P1 = [1682911881033, 509744180039882596]
P2 = [-4350450222813, -8409079383332570750]
P3 = [-2732001972537, -9507631680841759250]
P4 = [838116572907, 4259524325765646130]
P5 = [-8602000453, -6298123877540569838]
P6 = [-5174972297007, -5999620042052044670]
Dujella (2005)
y2 + xy = x3 - 890502303468937724149130x
+ 251976732409553090006157393210660900
Torsion points:
O, [742337937460, -371168968730],
[-4247871397281/4, 4247871397281/8], [319629911860, -159814955930],
[-130985906660, 605287285332941470], [-130985906660, -605287154347034810],
[1615661781580, 1740886872995215750], [1615661781580, -1740888488656997330]
Independent points of infinite order:
P1 = [34804303282, 470133559355108026]
P2 = [287152225570, 141225042040120570]
P3 = [-268025483360, -686585417289749030]
P4 = [-952849293368, -485157848702086574]
P5 = [10019541317440/9, 21606662227037110690/27]
P6 = [-501429434660, -756587916758553530]
Dujella (2005)
y2 + xy = x3 - 1009893481532852485509490x
+ 307126098316462880729754569042548100
Torsion points:
O, [-134384068060, 663636142416168350],
[-134384068060, -663636008032100290], [1708894587620, 1889931644827630910],
[1708894587620, -1889933353722218530], [-4527652164641/4, 4527652164641/8],
[787255259780, -393627629890], [344657781380, -172328890690]
Independent points of infinite order:
P1 = [326435595860, 110661301285782830]
P2 = [186678812540, 353703099209895710]
P3 = [-24614318068, -576167519527474978]
P4 = [-644001146800, -830907162445976110]
P5 = [201411568100, 334503195371036990]
P6 = [10088870660, 544920576783541310]
Dujella (2005)
y2 + xy = x3 - 8417650709198283033894x
+ 273611860820485052415499040073444
Torsion points:
O, [-419974072161/4, 419974072161/8],
[40252511948, -20126255974], [64741006092, -32370503046],
[129212262480, -36650458788184122], [129212262480, 36650329575921642],
[269749704, 16472438107887342], [269749704, -16472438377637046]
Independent points of infinite order:
P1 = [31511617284, 6296693126428362]
P2 = [-5242929084, -17821357800987918]
P3 = [11122388942, 13467117330606884]
P4 = [65983525524, 2337990892009122]
P5 = [39733247316, 1370881423554762]
P6 = [14769183135206724, 1794877079819738239098354]
Dujella (2005)
y2 = x3 + x3 - 5881112817909257676180x
+ 172368599382146998973856168201600
Torsion points:
O, [47280943140, 0], [-88482565381, 0], [41201622240, 0],
[76009847310, -12825473417517270], [76009847310, 12825473417517270],
[18552038970, 8345488101247470], [18552038970, -8345488101247470]
Independent points of infinite order:
P1 = [-10176865200, 15204140496080760]
P2 = [40557350480, 747648180255240]
P3 = [151220795688651/625, 1775600563187320377024/15625]
P4 = [12647675942690, 44978827414035407850]
P5 = [576449081936/25, 875190476902116984/125]
P6 = [317899098338454/105625, 426961707725012406012858/34328125]
Dujella (2005)
y2 + xy = x3 - 9779547590023543199800x
+ 348929743858830658241338918280000
Torsion points:
O, [68394784400, -34197392200],
[-113388065200, 56694032600], [179973123199/4, -179973123199/8],
[3172150220, 17830855647907100], [3172150220, -17830858820057320],
[133617418580, -37785854192696680], [133617418580, 37785720575278100]
Independent points of infinite order:
P1 = [41083488392, 4061346698069456]
P2 = [35783467310, 6693471246647390]
P3 = [-28150319350, -24534037344300700]
P4 = [-20650075240, -23282438354786560]
P5 = [111698481602, 25498589338688996]
P6 = [1555253472775/36, 574272931872414175/216]
Dujella (2005)
y2 = x3 - x2 - 2791493234428682804020x
- 8540150483506656022970369599100
Torsion points:
O, [-23510055660, 6640291333025350], [-23510055660, -6640291333025350],
[132115085440, -43916403255002850], [132115085440, 43916403255002850],
[54302514890, 0], [-51232804154, 0], [-3069710735, 0]
Independent points of infinite order:
P1 = [-21686024880, 6465110808903890]
P2 = [-49422123688, 2950516494110262]
P3 = [-39769398760, 6290975605864950]
P4 = [59384756340, 5925451375693850]
P5 = [54646601765, 1450070406881250]
P6 = [104111660675932, 1062304460321303000802]
Dujella (2005)
y2 = x3 - x2 - 119517739302760276059242340x
+ 493654844362203070424193925118382524100
Torsion points:
O, [-12597763694370, 0], [1761006233960, 16989540678288837610],
[1761006233960, -16989540678288837610], [12236759929500, -29384630538664589790],
[12236759929500, 29384630538664589790], [5598880612641, 0], [6998883081730, 0]
Independent points of infinite order:
P1 = [-3476870613810, 29447783619818152680]
P2 = [8139165312860, 7750319300680322590]
P3 = [-5386320853760, 31323239917146322830]
P4 = [5596804484412, 230135778885179202]
P5 = [15921874465260, 51254272875976138290]
P6 = [402587320153869/25, 6549092839649221847622/125]
Dujella (2005)
y2 + xy = x3 - 7615466123341469335310x
+ 188640502062497898331796594948100
Torsion points:
O, [-14471391260, -17199303109311230],
[-14471391260, 17199317580702490], [27502255420, -13751127710],
[-390818401761/4, 390818401761/8], [70202345020, -35101172510],
[154876081300, 52193194636764610], [154876081300, -52193349512845910]
Independent points of infinite order:
P1 = [25856946970, 3002532673595590]
P2 = [12376378780, 9812453110093090]
P3 = [26592901660, 2220165269728450]
P4 = [-96426304790, -5137739966639600]
P5 = [72646817992, 4335753498466582]
P6 = [7650691149283/4, 21139962430624193831/8]
Dujella (2005)
y2 = x3 - x2 - 2752408299758620522098980x
- 1611469491300450666662632159356431100
Torsion points:
O, [-1175270339890, 0], [1897773720210, 0], [-722503380319, 0],
[4735418338480, 9567791352271834990], [4735418338480, -9567791352271834990],
[-939870898060, 381047432275150410], [-939870898060, -381047432275150410]
Independent points of infinite order:
P1 = [-776632537390, 240225199081098000]
P2 = [-734467503248, 117821749403203538]
P3 = [-1032087420738, 360378113098626168]
P4 = [2829381083540, 3640225029168985110]
P5 = [-334684659337090/289, 743201851722475372920/4913]
P6 = [10794181649645/4, 26061142903976023305/8]
Dujella (2005)
y2 + xy + y = x3 + x2 - 457072288368656979319090x
+ 117898635812323031230705122524518847
Torsion points:
O, [-779899861159, 389949930579],
[1440505578803/4, -1440505578807/8], [419773466457, -209886733229],
[687274870297, 358324073089235091], [687274870297, -358324760364105389],
[152272062617, 227661942377971731], [152272062617, -227662094650034349]
Independent points of infinite order:
P1 = [-151762196263, -428683465936312749]
P2 = [59852557787, 301257504077200551]
P3 = [-115229341223, -411140772541082669]
P4 = [323869348697, 61951644391518291]
P5 = [-2822956775117/4, -2386177249846311447/8]
P6 = [1170517069537, 1089322648822519411]
Dujella (2005)
y2 = x3 - x2 - 601167709096816182426749700x
+ 5660909342729347649383846361635078811652
Torsion points:
O, [21520698541184, -51869708377111066750],
[21520698541184, 51869708377111066750], [7867902807684, 37656793045848495750],
[7867902807684, -37656793045848495750], [-28304866216191, 0],
[14694300674434, 0], [13610565541758, 0]
Independent points of infinite order:
P1 = [-11396797435566, 105033329058893235000]
P2 = [13515239353472, 2168037912942469246]
P3 = [17644481570684, 23384464315261708750]
P4 = [9815545575964, 26566866494642436270]
P5 = [3088064301384, 61918599936671473050]
P6 = [15361168746549, 7139794323331981710]
Dujella (2005)
y2 + xy = x3 - 4970973276415392436529590x
+ 4261112314439353076826126873509416100
Torsion points:
O, [1251883897580, -625941948790],
[-10296649990241/4, 10296649990241/8], [1322278599980, -661139299990],
[798552706520, -894849197222925190], [798552706520, 894848398670218670],
[1846004493440, -1172759629054433050], [1846004493440, 1172757783049939610]
Independent points of infinite order:
P1 = [341512408190, 1613472512467305860]
P2 = [274826813060, 1707545814831601730]
P3 = [1063369297196, 421355992217645162]
P4 = [780021064496, 926411449154533082]
P5 = [-179141249180, -2268450868639669190]
P6 = [679519563830, 1094076774315711710]
Dujella (2005)
y2 = x3 - x2 - 41967143645254581562603277540x
+ 2499923757202652047177517799000949313532612
Torsion points:
O, [-229874550646882, 0], [66611176071329, 0], [163263374575554, 0],
[358193220387164, -5781403049573347524510], [358193220387164, 5781403049573347524510],
[-31666471236056, -1948620297182521408810], [-31666471236056, 1948620297182521408810]
Independent points of infinite order:
P1 = [11244440114992, 1424587112757798224066]
P2 = [-12064380792848, 1733342261915366587394]
P3 = [163310459909122, 42310965041794002736]
P4 = [180811017357314, 907187094398719658160]
P5 = [-222648525455948, 898127072944350900794]
P6 = [2819459834400617/16, 48594797208579968891181/64]
Dujella (2005)
y2 + xy + y = x3 + x2 - 24755262175855280781923864788015x
+ 37265034103619296083235936013507719601892332405
Torsion points:
O, [-22416053814052573/4, 22416053814052569/8],
[1705860255937979, -852930127968990], [3898153197575163, -1949076598787582],
[8462310609348023, 658612408264797695479518], [8462310609348023, -658612416727108304827542],
[-666004214197697, 231207113399564700704218], [-666004214197697, -231207112733560486506522]
Independent points of infinite order:
P1 = [288671426882035, 173617258740765416051530]
P2 = [-5570742796939277, -47878956410889819020982]
P3 = [-3215474603382537, -289169963223480703893782]
P4 = [20300351053034403, 2810798012718765226249378]
P5 = [3526052528580254773/121, 6528981776892682037881128408/1331]
P6 = [232261432516477661299/625, 3539377448410546468282674082482/15625]
Dujella (2005)
y2 + xy + y = x3 + x2 - 277997148495295110798222064776730x
+ 1363430168994747642708704333200845201234817963175
Torsion points:
O, [13225086556644393, -6612543278322197],
[-74917888169353549/4, 74917888169353545/8], [5504385485693993, -2752192742846997],
[-2481969017106967, 1427627798260566831998763], [-2481969017106967, -1427627795778597814891797],
[28932142130395753, -4187907851021071588297557], [28932142130395753, 4187907822088929457901803]
Independent points of infinite order:
P1 = [5265008707145513, 213823453339216495759083]
P2 = [-270655797380265, -1199438152550610180794711]
P3 = [88072750892721193, 25691302043561677586804203]
P4 = [-4863993025676647, -1612616483560612937075157]
P5 = [-16767861397425427, -1144716636452792623074777]
P6 = [1644474400624935744755/361, 66686476272493576318143019435221/6859]
Dujella (2005)
y2 = x3 - x2 - 2599204480065528608632618826260x
+ 1318051470724882702726660094314375188894780100
Torsion points:
O, [1239173390745770, 0], [583551476582545, 0], [-1822724867328314, 0],
[2656017629514300, -114678716687042268370610], [2656017629514300, 114678716687042268370610],
[-177670848022760, 42121797345530930308710], [-177670848022760, -42121797345530930308710]
Independent points of infinite order:
P1 = [-830334184200470, 53886750371913854675280]
P2 = [-129872323419770, 40662337149274345851120]
P3 = [220805643944552, 27475404640607938652022]
P4 = [-1071708693390075, 53597763775288563330610]
P5 = [2186813100689125, 78049655307987615333510]
P6 = [-1721542237587030, 26278200538452947375200]
Dujella (2005)
y2 = x3 - x2 - 18185256818907344021519822340x
+ 867781677190111136236716183849682108124100
Torsion points:
O, [-154302193738770, 0], [59029795192641, 0], [95272398546130, 0],
[165968924940, 929926606909301658930], [165968924940, -929926606909301658930],
[190378828167320, 2075042828501670614470], [190378828167320, -2075042828501670614470]
Independent points of infinite order:
P1 = [33470400122640, 544618823369729207970]
P2 = [57112414857680, 124372888676596974050]
P3 = [41350883653560, 431869113743324817690]
P4 = [18552766500702, 732653268165772489032]
P5 = [58462055900370, 66682017950903589120]
P6 = [1760037576895780/9, 59094775417250330911790/27]
Dujella (2005)
y2 + xy + y = x3 + x2 - 2714685581949176342441469535x
+ 54440460625181460179771190482209079698565
Torsion points:
O, [26173285440683, 36304122435932239698],
[26173285440683, -36304148609217680382], [34166397950923, 39665202267150628978],
[34166397950923, -39665236433548579902], [-60162865244101, 30081432622050],
[119972094193187/4, -119972094193191/8], [30169841695803, -15084920847902]
Independent points of infinite order:
P1 = [14161896260893, 137243080592772202858]
P2 = [25575890162203, 41711126192619972898]
P3 = [29360545844283, 6769298049175234018]
P4 = [29945571659813, 979238465267455488]
P5 = [29973001219003, 596008430486665698]
P6 = [28675816049723, 13222290792458270178]
Dujella (2005)
y2 = x3 + x2 - 265134190444488812450005666073620x
+ 1374889946621052563466183441951718633784728817600
Torsion points:
O, [12431169885925460, 0], [-18431709610586821, 0], [6000539724661360, 0],
[26519028621508070, 3604654089224950144108110], [26519028621508070, -3604654089224950144108110],
[-1656688849657150, 1345209212594071042391910], [-1656688849657150, -1345209212594071042391910]
Independent points of infinite order:
P1 = [5387240518134155, 320778317527535807647620]
P2 = [13364159011545550, 467379114205798593393210]
P3 = [16508668537961858, 1223554750360444533377754]
P4 = [6147240338643679402/49, 15117667927972155266195579742/343]
P5 = [-1159827509634813982/121, 2318998591535360087597781726/1331]
P6 = [356156947207798925410/96721, 20145066549572426850639551594250/30080231]
Dujella (2005)
y2 + xy + y = x3 + x2 - 1666737234575129261770056486330225x
+ 20858552697655280228623937828451081716750394990735
Torsion points:
O, [-46041064285956161, 23020532142978080],
[57004492588290307/4, -57004492588290311/8], [31789941138883583, -15894970569441792],
[-5156829197181237, -5414471066226009163347492], [-5156829197181237, 5414471071382838360528728],
[68736711474948403, -15200503231987582349424412], [68736711474948403, 15200503163250870874476008]
Independent points of infinite order:
P1 = [3528584361681783, 3875727521493507661133408]
P2 = [32005321616677603, 546298601836283385271508]
P3 = [75161132508580543, 17893704208546244151802208]
P4 = [14160630547166143, 309904973897683118914208]
P5 = [-17082891368920997, -6659281184658577384901512]
P6 = [113047539153133738247/2809, 648310594134977553865017686016/148877]
Dujella (2006)
y2 = x3 - x2 - 343633641057979504x
+ 36692720733182921224013824
Torsion points:
O, [-167543430, 9463783668262], [-167543430, -9463783668262],
[1213426024, 37501606492824], [1213426024, -37501606492824],
[110729488, 0], [522941297, 0], [-633670784, 0]
Independent points of infinite order:
P1 = [-7755736, 6273546526104]
P2 = [69795322, 3612298454310]
P3 = [-607838712, 4581447129560]
P4 = [106344040, 1162747450008]
P5 = [3003675688, 161566995145320]
P6 = [582225800, 5829859131432]
Dujella (2006)
y2 = x3 - x2 - 4664630695650596406400x
+ 122611657721145018740841654400000
Torsion points:
O, [31069796800, -2770416472639200], [31069796800, 2770416472639200],
[48428296002, 3207868011028802], [48428296002, -3207868011028802],
[39113956000, 0], [-78863002400, 0], [39749046401, 0]
Independent points of infinite order:
P1 = [28260480960, 3654766624544480]
P2 = [-12857421920, 13433587750450560]
P3 = [13143969210, 7973123554358270]
P4 = [34512505410, 1652834075535170]
P5 = [91860783045, 21662718643569190]
P6 = [38608886722, 260090980468158]
Dujella (2006)
y2 = x3 + x2 - 11275024414184475994040x
+ 460709013467704417216360284483300
Torsion points:
O, [-122607564470, 0], [62054292259, 0], [60553272210, 0],
[78703050448, 7799377153768074], [78703050448, -7799377153768074],
[45405534070, 6509331476735220], [45405534070, -6509331476735220]
Independent points of infinite order:
P1 = [60507537238, 113814359125236]
P2 = [-23016513302, 26608786846591824]
P3 = [1090357234, 21175847216507760]
P4 = [-7923414617, 23442445921728834]
P5 = [-23132282480, 26629831414568970]
P6 = [45526382259, 6462063575261700]
Dujella (2006)
y2 = x3 - x2 - 331999964186328512900x
+ 2327612294831641365690701258052
Torsion points:
O, [10362752654, 0], [10676113458, 0], [-21038866111, 0],
[13828609532, 617224053832386], [13828609532, -617224053832386],
[7523617384, -505613082828490], [7523617384, 505613082828490]
Independent points of infinite order:
P1 = [11413318654, 158535977399800]
P2 = [2131189889, 1276611581208600]
P3 = [4902393233, 904344727306020]
P4 = [1363681784, 1370184634353990]
P5 = [10210152404, 47137942544550]
P6 = [10832642558, 48416892483960]
Eroshkin (2008)
y2 = x3 + x2 - 2013664127615449300x
- 649446586170797281317775552
Torsion points:
O, [1558929716, 0], [-1216463408, 0], [-342466309, 0],
[3856128326, -221190362561070], [-738268894, -20851671782970],
[-738268894, 20851671782970], [3856128326, 221190362561070],
Independent points of infinite order:
P1 = [-378679454, 7667119485690]
P2 = [-362626354, 5751217317510]
P3 = [-348685504, 3208608800040]
P4 = [-471766609, 13983374893950]
P5 = [-391521934, 8884307265750]
P6 = [-984546058, 19461437192190]
Eroshkin (2008)
y2 + xy = x3 - 645065532532048725x
+ 182854916195163425393625000
Torsion points:
O, [1399380399/4, -1399380399/8], [-918745000, 459372500],
[568899900, -284449950], [1139755185, 30466262110500],
[-1955385, 13568945674500], [-1955385, -13568943719115],
[1139755185, -30467401865685]
Independent points of infinite order:
P1 = [205490700, 7679551321350]
P2 = [39533832, 12546485410752]
P3 = [343406775, 1353486075300]
P4 = [264680127, 5537123858196]
P5 = [166770315, 8939458354185]
P6 = [348330705, 650394675300]
Eroshkin (2008)
y2 + xy = x3 - 13050070927054823465x
+ 16542549296816918233072779225
Torsion points:
O, [6226715695/4, -6226715695/8], [5183456770, 296928964099795],
[-37111310, -130486775461925], [-37111310, 130486812573235],
[5183456770, -296934147556565], [2573172730, -1286586365],
[-4129851654, 2064925827]
Independent points of infinite order:
P1 = [1096220890, 59615874435235]
P2 = [899520022, 74374166104447]
P3 = [392536090, 107146475356675]
P4 = [435448162, 104606127424147]
P5 = [686748970, 88905865222435]
P6 = [896843530, 74565188888035]
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