curve #4410

y² + y = x³ − 10424167x + 1013182725216

a-invariants: [0, 0, 1, -10424167, 1013182725216]
c-invariants: [500360016, -875389874586840]
rank (lower bound): ≥ 12
torsion subgroup: trivial
conductor (N): 443392455047858519129412443
discriminant (Δ): -443392455047858519129412443
Faltings height: 3.7920
naive height: 68.8114
primes of bad reduction: 1309807, 338517396110922081749
regulator: 223274679.14924924106274171993917907830250662961804494535058658
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:22:43 UTC
last updated: 2026-10-17 10:22:43 UTC

(-10348, 113915)
(-9995, 344777)
(-8831, 645398)
(-7828, 784284)
(-4426, 986213)
(-4353, 987965)
(-3854, 998054)
(-2152, 1012743)
(-1746, 1012946)
(130, 1005897)
(6672, 1113840)
(10496, 1435295)

BASE records/rank_12.md#12 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:22:43 UTC · history