curve #996

y² + y = x³ − x² − x

a-invariants: [0, -1, 1, -1, 0]
rank (lower bound): ≥ 1
torsion subgroup: trivial
conductor (N): 141
discriminant (Δ): 141
Faltings height: -0.8965
naive height: 12.4766
primes of bad reduction: 3, 47
regulator: 0.1984952364630847608336826286203908894590
submitted by: David Renshaw
submitted at: 2026-09-23 15:12:13 UTC
last updated: 2026-09-23 15:12:13 UTC

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

(0, 0)

Commentary

Cremona 141d1 = LMFDB 141.d1: https://www.lmfdb.org/EllipticCurve/Q/141/d/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 141, minimal discriminant 141, trivial torsion. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-23 15:12:13 UTC · history