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curve #1563

y² + xy + y = x³ − x² + 68236798429443x + 231824005240409713989

a-invariants: [1, -1, 1, 68236798429443, 231824005240409713989]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/7ℤ
conductor (N): 9224961790
discriminant (Δ): -43551319485566172922414440588800000000000000
Faltings height: 7.0596
naive height: 107.3082
primes of bad reduction: 2, 5, 11, 113, 742153
regulator: 399.57341110639404800547891763940415088640742
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:07:19 UTC
last updated: 2026-09-25 01:07:19 UTC

Witness: 3 independent points log in to add more points →

(267995653/49, 9508490974018/343)
(15949033823/2209, 3444400010946248/103823)
(320214305487/160801, 1249616758206714376/64481201)

Commentary

Torsion Z/7. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 01:07:19 UTC · history

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