curve #2899

y² = x³ − 2x

a-invariants: [0, 0, 0, -2, 0]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ
conductor (N): 256
discriminant (Δ): 512
Faltings height: -0.7907
naive height: 13.6930
primes of bad reduction: 2
regulator: 0.6087090319769813608971904195940853453581
submitted by: David Renshaw
submitted at: 2026-09-26 20:27:30 UTC
last updated: 2026-09-26 20:27:30 UTC

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

(2, 2)

Commentary

Cremona 256b1 = LMFDB 256.b1: https://www.lmfdb.org/EllipticCurve/Q/256/b/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 256, minimal discriminant 512, torsion ℤ/2ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:27:30 UTC · history