curve #955

y² + xy + y = x³ − x² − x + 1

a-invariants: [1, -1, 1, -1, 1]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/4ℤ
conductor (N): 62
discriminant (Δ): -496
Faltings height: -0.8012
naive height: 13.7024
primes of bad reduction: 2, 31
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:05:45 UTC
last updated: 2026-09-23 15:05:45 UTC

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Commentary

Cremona 62a1 = LMFDB 62.a4: https://www.lmfdb.org/EllipticCurve/Q/62/a/4 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 62, minimal discriminant -496, torsion ℤ/4ℤ.

last edited by David Renshaw at 2026-09-23 15:05:45 UTC · history