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curve #1561

y² + xy = x³ − 700122879986x + 267530643638778372

a-invariants: [1, 0, 0, -700122879986, 267530643638778372]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/7ℤ
conductor (N): 7546766106
discriminant (Δ): -8955833670794216205977473536175960704
Faltings height: 5.8095
naive height: 93.7792
primes of bad reduction: 2, 3, 11, 17, 29, 41, 5657
regulator: 120.09632387573393589575246854693958620199816
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:05:59 UTC
last updated: 2026-09-25 01:05:59 UTC

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

(4282456, 8704585438)
(4663571986/1681, 305636417085026/68921)
(477772, 204921382)

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 01:06:00 UTC · history

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