curve #2030

y² + xy + y = x³ − 142083384417276333592114x + 4710152829849752443315367097069812

a-invariants: [1, 0, 1, -142083384417276333592114, 4710152829849752443315367097069812]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 106915252368321342649355608110
discriminant (Δ): 173989290231465257061552033379320863079627183002745363004630116512010000
Faltings height: 12.3605
naive height: 171.5457
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 29, 67, 149, 449, 463, 647, 54877, 67057
regulator: 5111781155.3812122041239072961559615872100777492553160683
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:04:09 UTC
last updated: 2026-09-26 05:04:09 UTC

(-49682510234, -107919288145476871)
(947233148830, -848546057874807952)
(31866385141, 14657003768008229)
(409726829641, -123604857448278271)
(373898867041/25, 6359668779695557921/125)
(430496237641, -152729947826415871)
(-324382764348791/1024, -4387798151661811466603/32768)
(359297448265, -6583185939349579)
(130256479178326/361, 140480205141621959411/6859)

2-isogenous partner of curve#1173 (Eroshkin (2008)).

last edited by Steps Unbounded at 2026-09-26 21:44:04 UTC · history