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curve #4508

y² = x³ + x² − 473405585x + 3135605455759

a-invariants: [0, 1, 0, -473405585, 3135605455759]
c-invariants: [22723468096, -2709299454584320]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 523358779488238016
discriminant (Δ): 2542300700264409586787827712
Faltings height: 3.9725
naive height: 71.5400
primes of bad reduction: 2, 17, 71, 79, 89, 199, 953, 5081
regulator: 60738.9687211520201836293805166283310314065679669294192
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:32:57 UTC
last updated: 2026-10-17 10:32:57 UTC

Witness: 8 independent points log in to add more points →

(-3695, 2198728)
(5109, 922148)
(17747, 569136)
(-5213, 2337056)
(542037, 398747444)
(770347, 675862064)
(360561/16, 126581711/64)
(98331/25, 144398096/125)

Commentary

BASE torsion/torsion_Z2.tsv.gz:635369 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:32:57 UTC · history

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