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curve #4513

y² = x³ − x² − 76166345x + 255821746761

a-invariants: [0, -1, 0, -76166345, 255821746761]
c-invariants: [3655984576, -221008053294080]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 286374696840384
discriminant (Δ): 12816152008671027105792
Faltings height: 3.2268
naive height: 66.0589
primes of bad reduction: 2, 3, 31, 41, 73, 97, 103, 1609
regulator: 3147.368503096697553200590271397411414878855585820226
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:33:10 UTC
last updated: 2026-10-17 10:33:10 UTC

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

(-4075, 706056)
(5123, 7008)
(4831, 24236)
(5561, 64824)
(5101, 496)
(451, 470704)
(5269, 27448)

Commentary

BASE torsion/torsion_Z2.tsv.gz:315533 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

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

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