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curve #4502

y² = x³ − x² − 10880574500x + 389748098558916

a-invariants: [0, -1, 0, -10880574500, 389748098558916]
c-invariants: [522267576016, -336739223549447360]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 399231976906179971112
discriminant (Δ): 16818394683268334654947380402432
Faltings height: 4.7230
naive height: 80.9443
primes of bad reduction: 2, 3, 13, 29, 37, 163, 193, 2617, 2833, 5113
regulator: 318601.55183115490729561330712051139489585228288706489144
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:32:41 UTC
last updated: 2026-10-17 10:32:41 UTC

Witness: 9 independent points log in to add more points →

(-102260, 20809646)
(-79640, 27407146)
(7076, 17694954)
(9680, 16891746)
(5517128, 12956640822)
(2371228, -3647922722)
(-51115, 28501854)
(4936732/9, 10781823754/27)
(77166, -3102216)

Commentary

BASE torsion/torsion_Z2.tsv.gz:644939 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:32:41 UTC · history

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