curve #4402

y² + y = x³ − 2147907577x + 47888102069226

a-invariants: [0, 0, 1, -2147907577, 47888102069226]
c-invariants: [103099563696, -41375320187811480]
rank (lower bound): ≥ 13
torsion subgroup: trivial
conductor (N): 356492038662688596396428055563
discriminant (Δ): -356492038662688596396428055563
Faltings height: 4.3831
naive height: 76.5229
primes of bad reduction: 43201, 8251939507481044336853963
regulator: 55274218349.53423692226043194125811218133649956612812940478911171
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:22:10 UTC
last updated: 2026-10-17 10:22:10 UTC

(-219071/4, 8936925/8)
(-45112, 7278558)
(-38508, 8573069)
(-30707, 9213558)
(-9063, 8161505)
(-668, 7023005)
(606, 6825444)
(1724, 6647573)
(19378, 3680016)
(22558, 3303716)
(33568, 3689433)
(58477, 11056694)
(60591, 11840190)

BASE records/rank_13.md#15 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:22:11 UTC · history