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curve #4415

y² + xy = x³ − x² − 93228004x + 346879627684

a-invariants: [1, -1, 0, -93228004, 346879627684]
c-invariants: [4474944201, -299683861070085]
rank (lower bound): ≥ 11
torsion subgroup: trivial
conductor (N): 57609056314579788665554
discriminant (Δ): -115218112629159577331108
Faltings height: 3.3328
naive height: 66.6675
primes of bad reduction: 2, 787123, 36594697597821299
regulator: 6998722.06089844187855928769881153387266442610095339762289230
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:22:56 UTC
last updated: 2026-10-17 10:22:56 UTC

Witness: 11 independent points log in to add more points →

(96, 581270)
(2605, 347543)
(5264, 41758)
(5488, 19842)
(5552, 17058)
(5683, 21275)
(6114, 70448)
(6352, 101490)
(6482, 118800)
(6495, 120542)
(6739, 153563)

Commentary

BASE records/rank_11.md#34 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:22:56 UTC · history

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