curve #6142

y² + xy + y = x³ − x² − 4432606274531486875669998057086171677355x + 120984628206765677877339585838860821491595465543375156602747

a-invariants

[1, -1, 1, -4432606274531486875669998057086171677355, 120984628206765677877339585838860821491595465543375156602747]

c-invariants

[212765101177511370032159906740136240513025, -104530718770645545685063959209476948603593762649145522222465025]

rank (lower bound)

≥ 26

torsion subgroup

trivial

conductor (N)

380843366482036417820211787734098815015323051389165385079204171027173665841397270163012726084119291350

discriminant (Δ)

-749427254228280804652282508290511826083204939346423780128444872258260268715357086514152149917956301309054224593693120000

Faltings height

21.7493

naive height

285.6092

primes of bad reduction

2, 3, 5, 7, 17, 23, 31, 53, 107, 433, 1191559, 486161320541471, 7012193510786768119221749216064941068923745223887202218853880614587

regulator

9426860312427551555997786973.60809822666631931171557210840570804740243939344880419463224889

submitted by

Ritik Jain

submitted at

2026-10-29 13:47:47 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-10-29 13:55:49 UTC

Witness: 26 independent points log in to add more points →

(2408148257593063907711489091186502137887094719/548645655935612341157041, -118161276801875122376050945318241921040592258539035482348737212956790/406385231998296590283906568824077161)
(-8901888167654294890015916195197/214805367841, -48108020618784113546156378632849352220174309130/99556058638636111)
(-16113646980533136566309/289, 2168385977722069540245812069847850/4913)
(-489786152747047320242309/6889, -158408099244102620232342045686115890/571787)
(6468009435106460080189/16, -513562183967223829471973864766895/64)
(1660249848090017009, -337090448804392339662892246090)
(10409985176531311618747/4, 1061779897614269897953408327835005/8)
(18456146426317992733691/289, 1540851866813846153177974645474490/4913)
(5669673675768979672579/121, 169219260009515966652264010337710/1331)
(-13055667727328450293475/169, 107090253442724838815090276295326/2197)
(45087042947621679001039/121, 9430964513711014214525329782591130/1331)
(3232988989058076714085/144, -312876055441013138548764252840167/1728)
(-19572178616242492457, 447485052323639571266082492410)
(582940206858726017946781/6889, -339145131219787425829717218234407060/571787)
(-3710080814515891408493/49, 51485956887954055390257456372830/343)
(-3065615171791143529229/169, 971218263012848711366539479792770/2197)
(2428571231748964238163991/64009, -1395333330934145223498582166552930270/16194277)
(62919316607403161599, -301952981961979888715188134790)
(787302689780515050251/25, -14045073458628508396006276953214/125)
(582710080081208472743, -13978478904752959274982850272290)
(7738830005489480734850399239/447153316, -2102737648084478991469922171620166866847405/9455504020136)
(11161054791211915091275/49, 1133919372064170554485214659747238/343)
(317398039496962573709/25, -32296240290725379014588305583858/125)
(258474904838781172623003451/19651489, -22202936682399212033456680984777222889990/87115050737)
(61979558953263033295, -290423824563163628909622274822)
(-66518376184640300678189665953604240748910524394983119/1750938186682676378184743155468729, 35483345022732374896923482635798921896593559547580312203408991874378892646846320/73266630958388528825469036967657579325396838473683)

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