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curve #4512

y² = x³ + x² − 117092769x + 487626124351

a-invariants: [0, 1, 0, -117092769, 487626124351]
c-invariants: [5620452928, -421342694156800]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 235864182223808
discriminant (Δ): 10174720414251376246784
Faltings height: 3.2865
naive height: 67.3490
primes of bad reduction: 2, 17, 41, 103, 313, 401, 409
regulator: 12782.96943569039654174679609190674664982875710187568
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:33:07 UTC
last updated: 2026-10-17 10:33:07 UTC

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

(5465, 104704)
(6386, 18437)
(7931, 240608)
(-261, 719840)
(12827, 1047040)
(98674/9, 19504801/27)
(53251/9, 1203040/27)

Commentary

BASE torsion/torsion_Z2.tsv.gz:315507 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:33:08 UTC · history

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