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curve #1413

y² + xy = x³ − 8x + 7

a-invariants: [1, 0, 0, -8, 7]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ
conductor (N): 1525
discriminant (Δ): 7625
Faltings height: -0.5274
naive height: 17.8597
primes of bad reduction: 5, 61
regulator: 0.814290832163904975784704835254714683988820
submitted by: Michael Rubinstein
submitted at: 2026-09-24 23:24:57 UTC
last updated: 2026-09-24 23:24:57 UTC

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

(-3, 4)
(7, 14)

Commentary

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 23:24:57 UTC · history

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