curve #985

y² + y = x³ + x² − x − 1

a-invariants: [0, 1, 1, -1, -1]
rank (lower bound): ≥ 1
torsion subgroup: trivial
conductor (N): 101
discriminant (Δ): 101
Faltings height: -0.9164
naive height: 12.4766
primes of bad reduction: 101
regulator: 0.1647034529491493510642464267692255331119
submitted by: David Renshaw
submitted at: 2026-09-23 15:11:07 UTC
last updated: 2026-09-23 15:11:07 UTC

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

(-1, 0)

Commentary

Cremona 101a1 = LMFDB 101.a1: https://www.lmfdb.org/EllipticCurve/Q/101/a/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 101, minimal discriminant 101, trivial torsion. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-23 15:11:07 UTC · history