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curve #4427

y² + y = x³ − 330799x + 77125362

a-invariants: [0, 0, 1, -330799, 77125362]
c-invariants: [15878352, -66636312984]
rank (lower bound): ≥ 9
torsion subgroup: trivial
conductor (N): 252960276015055691
discriminant (Δ): -252960276015055691
Faltings height: 2.0930
naive height: 49.8450
primes of bad reduction: 409, 618484782432899
regulator: 105763.85016541263615203234778498957857001006455550477608
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:23:28 UTC
last updated: 2026-10-17 10:23:28 UTC

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

(-553, 9536)
(-472, 11318)
(233, -3564)
(363, 2208)
(302, 2183)
(319, -2016)
(595, -9537)
(268, 2778)
(208, -4162)

Commentary

BASE records/rank_9.md#28 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:23:28 UTC · history

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