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curve #4515

y² = x³ + x² − 18822025x + 12335602359

a-invariants: [0, 1, 0, -18822025, 12335602359]
c-invariants: [903457216, -10663381181440]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 227742765099584
discriminant (Δ): 360952343348270641221632
Faltings height: 3.2136
naive height: 61.8652
primes of bad reduction: 2, 7, 17, 31, 137, 281, 25057
regulator: 2656.869186448825295084473605218594849332186341725757
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:33:14 UTC
last updated: 2026-10-17 10:33:14 UTC

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

(-3415, 191828)
(-4531, 67952)
(274, 84847)
(-2981, 204848)
(-2750, 208103)
(-19841/25, 20453552/125)
(-2113, 206584)

Commentary

BASE torsion/torsion_Z2.tsv.gz:315504 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:33:14 UTC · history

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