curve #4408

y² + xy = x³ − x² − 490124959x + 4213132611529

a-invariants: [1, -1, 0, -490124959, 4213132611529]
c-invariants: [23525998041, -3640040709369885]
rank (lower bound): ≥ 12
torsion subgroup: trivial
conductor (N): 66233056438848840448971334
discriminant (Δ): -132466112877697680897942668
Faltings height: 3.8307
naive height: 71.6615
primes of bad reduction: 2, 523, 9154523381, 6916834335109
regulator: 2107711206.8221344245039427962955840790092365837546138533975422
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:22:37 UTC
last updated: 2026-10-17 10:22:37 UTC

(-3172, 2396557)
(-972, 2165807)
(3801, 1548929)
(4164, 1496063)
(13180, 200013)
(13570, 239883)
(13626, 247079)
(13831, 275739)
(13847, 278110)
(14188, 332205)
(15096, 496685)
(337676/25, 29021259/125)

BASE records/rank_12.md#35 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:22:37 UTC · history