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curve #4486

y² + y = x³ − 248599x + 11512500

a-invariants: [0, 0, 1, -248599, 11512500]
c-invariants: [11932752, -9946800216]
rank (lower bound): ≥ 9
torsion subgroup: trivial
conductor (N): 926025768468711109
discriminant (Δ): 926025768468711109
Faltings height: 2.1383
naive height: 48.8844
primes of bad reduction: 543242131, 1704628039
regulator: 173121.38475432066267434039449155949654063987684156644244
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:31:05 UTC
last updated: 2026-10-17 10:31:05 UTC

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

(-28, 4295)
(-513, 2009)
(-390, 7010)
(526, -5127)
(-189, 7193)
(-125, -6375)
(15, 2790)
(-427, -6310)
(503, 3705)

Commentary

BASE records/rank_9.md#17 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:31:05 UTC · history

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