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curve #4487

y² + xy = x³ − 35110x + 48596991

a-invariants: [1, 0, 0, -35110, 48596991]
c-invariants: [1685281, -41990328145]
rank (lower bound): ≥ 9
torsion subgroup: trivial
conductor (N): 1017593269521952603
discriminant (Δ): -1017593269521952603
Faltings height: 2.1346
naive height: 48.9214
primes of bad reduction: 1017593269521952603
regulator: 240825.03262450629317563444041567784791185610402675302683
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:31:07 UTC
last updated: 2026-10-17 10:31:07 UTC

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

(-374, 3261)
(317, 8169)
(67, -6856)
(709, 19145)
(-307, -5366)
(-301, 5800)
(143, -6891)
(-111, 7206)
(595, 15144)

Commentary

BASE records/rank_9.md#18 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:31:07 UTC · history

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