curve #4618

y² + xy + y = x³ − 30136852894775863243751650199501148x + 1902835048694321322886001459836692634243812302502022

a-invariants: [1, 0, 1, -30136852894775863243751650199501148, 1902835048694321322886001459836692634243812302502022]
c-invariants: [1446568938949241435700079209576055081, -1644049482071893625143358669722764589536772643725829845]
rank (lower bound): ≥ 16
torsion subgroup: ℤ/2ℤ
conductor (N): 259955327597572535406995941385230425410717342343794896566
discriminant (Δ): 187578733514539157613570583920067494396550465502474168753835989966285466769682554128461929429568311153572
Faltings height: 18.7597
naive height: 249.7868
primes of bad reduction: 2, 3, 7, 11, 13, 17, 43, 53, 71, 109, 149, 173, 233, 241, 263, 487, 691, 773, 1019, 1459, 2579, 5659, 8689, 15877
regulator: 18346308071924898.84006386943445385865279778953687481289269310140392847
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:25:54 UTC
last updated: 2026-10-19 03:25:54 UTC

(1625089426639415, 43056524004579765484270713)
(6733466119477856, 41233661769644314655384925)
(48431895859048823, 23597761170796720507221561)
(119532039112754774, 2894545223214499790581662)
(480488072600131079/4, 32012001284529141939760209/8)
(121204935347341967, 5538715614822400588670031)
(130669203037407155, 13999287320850064559488101)
(605812320924589592, 453854459564934874307069301)
(1687258501510525064, 2180461252391123290106295717)
(-20052498893601016889147/124609, 2236526759313023422657988010027157/43986977)
(10647434767464141581/16, 33655989898031829683322742875/64)
(12278300935043029337/64, 28882735048162085688410753025/512)
(157327325492610068917/729, 1453133677165517691838002335363/19683)
(3410974215471509281760/22801, 93806604463812550887055930254603/3442951)
(4450306094530898834474/32041, 114202335251779217738129152183077/5735339)
(24034939890475471264499819/1015123321, 1121584316604206655056570621054390056977/32342844130381)

X400, T=-2246/1211.

last edited by Andrii Prokhorenkov at 2026-10-19 03:25:54 UTC · history