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curve #4474

y² + xy = x³ − x² − 84320329x + 297391514569

a-invariants: [1, -1, 0, -84320329, 297391514569]
c-invariants: [4047375801, -256928055396525]
rank (lower bound): ≥ 11
torsion subgroup: trivial
conductor (N): 83637942651649673596346
discriminant (Δ): 167275885303299347192692
Faltings height: 3.3331
naive height: 66.3640
primes of bad reduction: 2, 4741832723, 8819157859151
regulator: 7293164.71933113790326383126721947413801792159414460166280289
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:30:35 UTC
last updated: 2026-10-17 10:30:35 UTC

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

(-1588, 654465)
(-1306, 637273)
(4156, 134769)
(4260, 122297)
(4887, 42448)
(5086, 6429)
(22019/4, 6705/8)
(6069, 92683)
(6272, 120285)
(6488, 149715)
(6711, 180304)

Commentary

BASE records/rank_11.md#38 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:30:35 UTC · history

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