curve #4411

y² + y = x³ − 129671269x + 1124584406100

a-invariants: [0, 0, 1, -129671269, 1124584406100]
c-invariants: [6224220912, -971640926870616]
rank (lower bound): ≥ 12
torsion subgroup: trivial
conductor (N): 406802088686884491992318651
discriminant (Δ): -406802088686884491992318651
Faltings height: 3.7966
naive height: 69.0200
primes of bad reduction: 821, 11969, 24407, 12541829, 135240533
regulator: 186400155.70146554621216302483966001027065884975307496547974954
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:22:45 UTC
last updated: 2026-10-17 10:22:45 UTC

(-10223, 1175504)
(-2438, 1194249)
(-2309, 1188143)
(3186, 862433)
(4656, 788523)
(7040, 748740)
(13007, 1280039)
(15865, 1749440)
(25708, 3844664)
(36728, 6775404)
(70955, 18685680)
(75088/9, 21319145/27)

BASE records/rank_12.md#13 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:22:46 UTC · history