curve #1868

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y² + xy = x³ − 127695478478876884603229323851621855860x + 577342460952044533767438474950704829369645930161171794576

a-invariants

[1, 0, 0, -127695478478876884603229323851621855860, 577342460952044533767438474950704829369645930161171794576]

rank (lower bound)

≥ 24

torsion subgroup

trivial

conductor (N)

213713316301688217012310994068870602989188819752606517462457321743725053424323782507749208278

discriminant (Δ)

-10734041706184021209293502932408704066336440291059635309113888858461903376055852064638162169785217998778711827120128

Faltings height

20.8356

naive height

274.9192

primes of bad reduction

2, 3, 11, 13, 23, 37, 43, 109, 2852873966747930110974755046299, 21889568274623591221591224695511025986933826296735257

regulator

14933372661104857116006142.349276935517444546629444548651505221240150094823317644024144

submitted by

Ritik Jain

submitted at

2026-09-25 17:21:02 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 17:25:52 UTC

Witness: 24 independent points log in to add more points →

(89222827162755675346583700886127280532483752597424456/13830764999790316796650090727556601, -7636120744313290357473543401333376854448785393601670250085875907994653336019676/1626557061183714516529479944218334058487252138330099)
(9972867538682088976/25, -2868106784491542157365626860516/125)
(143946114766375968509728/5041, 50887051156877075207837441097845708/357911)
(14473333094257361297644/2025, 497254899248217123629713499660588/91125)
(960250130391353231989/16, 29264345503582346310986029181725/64)
(6388992095955200065425/64, -507546370369817448292382449970787/512)
(368713880231482232858632/289, -223881008683270620161065317872216596/4913)
(21336546329126029468961872/303601, 97357313786744841556179204385653121364/167284151)
(4130614285610716201576/361, -169996485645254498212431314741756/6859)
(-68276619545489856004400/19881, 87547523976585662451548028213171004/2803221)
(1752272929735686367464, -73348902489608954125348338607284)
(-2805141057760393700, -30223718345172634504533766424)
(29637826158857389343806/3721, 1837822438833957265006303344828808/226981)
(825999934770592116934/121, -6486634306512226992340044076474/1331)
(243376745730232156744/225, -70833451849119541398735137610508/3375)
(-147469776380837210832723251175440/11288585302801, -152159783727681071094069699954171988080342120796/37927942041030637049)
(4733886112385255099248406101264/581008293121, -3906374618721043597926236782433098532816214436/442867180340257919)
(6479530981400938027528/961, 142494593091790539133415373403444/29791)
(256749908586134140906/361, 151346725243074691915437427271674/6859)
(-7084155218484109256, 33562433079309113816136259276)
(30462067482937974691/4, 54579496197210571099211335643/8)
(-467002384334150136851132/113569, 1230040581224338701314896796708842492/38272753)
(7310923457585389904950348092429041328/806319308251782649, 9298558015975249990310240347033742310142586328563300388/724036715210481589487621107)
(10701186794115604230183443662840421956/3506074773393274681, 96490534967272933582782358738867853798681201859860354828/6564955112301462975474733421)

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