curve #957

y² + xy + y = x³ − x² − 331x + 2397

a-invariants: [1, -1, 1, -331, 2397]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ
conductor (N): 62
discriminant (Δ): 62
Faltings height: -0.1081
naive height: 29.0171
primes of bad reduction: 2, 31
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:06:48 UTC
last updated: 2026-09-23 15:06:48 UTC

Witness: no points (rank ≥ 0 needs none) log in to add more points →

Commentary

Cremona 62a4 = LMFDB 62.a1: https://www.lmfdb.org/EllipticCurve/Q/62/a/1 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 62, minimal discriminant 62, torsion ℤ/2ℤ.

last edited by David Renshaw at 2026-09-23 15:06:48 UTC · history