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curve #4437

y² + y = x³ + x² − 18710x + 976170

a-invariants: [0, 1, 1, -18710, 976170]
c-invariants: [898096, -848799640]
rank (lower bound): ≥ 7
torsion subgroup: trivial
conductor (N): 2269810368437
discriminant (Δ): 2269810368437
Faltings height: 1.2382
naive height: 41.1241
primes of bad reduction: 6361, 356832317
regulator: 12607.95641698898916006299311316580675538688016192009
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:23:54 UTC
last updated: 2026-10-17 10:23:54 UTC

Witness: 7 independent points log in to add more points →

(-135, 1029)
(-134, 1046)
(-87, 1397)
(1, 978)
(170, 1654)
(405, 7745)
(502, 10878)

Commentary

BASE records/rank_7.md#36 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:23:54 UTC · history

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