curve #2758

y² + xy = x³ − x² − 13x

a-invariants: [1, -1, 0, -13, 0]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 377
discriminant (Δ): 142129
Faltings height: -0.3211
naive height: 19.3514
primes of bad reduction: 13, 29
regulator: 2.887788827121691722789402623870142297688
submitted by: David Renshaw
submitted at: 2026-09-26 20:21:07 UTC
last updated: 2026-09-26 20:21:07 UTC

Witness: 1 independent point log in to add more points →

(-9/4, 39/8)

Commentary

Cremona 377a2 = LMFDB 377.a2: https://www.lmfdb.org/EllipticCurve/Q/377/a/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 377, minimal discriminant 142129, torsion ℤ/2ℤ × ℤ/2ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:21:07 UTC · history