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curve #1428

y² + xy + y = x³ + x² + 625x + 8060

a-invariants: [1, 1, 1, 625, 8060]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/4ℤ
conductor (N): 5115
discriminant (Δ): -41904765375
Faltings height: 0.7235
naive height: 31.4468
primes of bad reduction: 3, 5, 11, 31
regulator: 2.41387029471406442048046099839829321682500
submitted by: Michael Rubinstein
submitted at: 2026-09-24 23:38:19 UTC
last updated: 2026-09-24 23:38:19 UTC

Witness: 2 independent points log in to add more points →

(-13/4, 629/8)
(268, 4283)

Commentary

Torsion Z/4. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 23:38:19 UTC · history

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