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curve #4516

y² = x³ + x² − 22245225x + 32635210279

a-invariants: [0, 1, 0, -22245225, 32635210279]
c-invariants: [1067770816, -28203228305920]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 242745432809344
discriminant (Δ): 244201548084922968645632
Faltings height: 3.2037
naive height: 62.3665
primes of bad reduction: 2, 17, 47, 103, 151, 191
regulator: 3511.283357821740683581197492889430184721188200624578
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:33:17 UTC
last updated: 2026-10-17 10:33:17 UTC

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

(1167, 90916)
(3650, 8977)
(12627, 1328596)
(7661, 558484)
(4223, 118420)
(1549, 43548)
(-5121, 110828)

Commentary

BASE torsion/torsion_Z2.tsv.gz:315512 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

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

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