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curve #4485

y² + xy = x³ − x² − 178411x + 53424121

a-invariants: [1, -1, 0, -178411, 53424121]
c-invariants: [8563737, -46119903741]
rank (lower bound): ≥ 9
torsion subgroup: trivial
conductor (N): 433738910900398738
discriminant (Δ): -867477821800797476
Faltings height: 2.1345
naive height: 49.1090
primes of bad reduction: 2, 1291, 21683, 24419, 317267
regulator: 2354712.4528919171169514838743242933284426875351600152900
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:31:02 UTC
last updated: 2026-10-17 10:31:02 UTC

Witness: 9 independent points log in to add more points →

(-528, 731)
(-525, 1739)
(-514, 3279)
(-505, 4066)
(-491, 4986)
(-450, 6739)
(-401, 7970)
(-209, 9135)
(2062, 90891)

Commentary

BASE records/rank_9.md#20 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:31:03 UTC · history

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