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curve #4522

y² = x³ + x² − 612649x + 146832231

a-invariants: [0, 1, 0, -612649, 146832231]
c-invariants: [29407168, -127039490560]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 865016887424
discriminant (Δ): 5377166416550764544
Faltings height: 2.3086
naive height: 51.5902
primes of bad reduction: 2, 23, 41, 103, 1697
regulator: 691.54278449019287598934241740807320082624462895736
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:33:37 UTC
last updated: 2026-10-17 10:33:37 UTC

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

(2159, 94300)
(-670, 16031)
(-383, -18040)
(5011, 350612)
(4045, 252724)
(2642, 130295)

Commentary

BASE torsion/torsion_Z2.tsv.gz:8408 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:33:37 UTC · history

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