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curve #4521

y² = x³ + x² − 634505x + 179868679

a-invariants: [0, 1, 0, -634505, 179868679]
c-invariants: [30456256, -155589276160]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 562446302336
discriminant (Δ): 2339524641774313472
Faltings height: 2.2669
naive height: 51.6954
primes of bad reduction: 2, 17, 41, 97, 103, 631
regulator: 873.32841116700414169005993597355468972191610936259
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:33:31 UTC
last updated: 2026-10-17 10:33:31 UTC

Witness: 6 independent points log in to add more points →

(-909, 2524)
(1615, 58052)
(-278, 18299)
(-574, 18849)
(250, 6077)
(2001, 83224)

Commentary

BASE torsion/torsion_Z2.tsv.gz:8317 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:33:31 UTC · history

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