curve #3116

y² + xy + y = x³ − x² − 1644x − 24922

a-invariants: [1, -1, 1, -1644, -24922]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 289
discriminant (Δ): 6975757441
Faltings height: 0.6934
naive height: 33.8277
primes of bad reduction: 17
regulator: 6.070512355460664321664107206543494672104
submitted by: David Renshaw
submitted at: 2026-09-26 20:38:02 UTC
last updated: 2026-09-26 20:38:02 UTC

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

(-589/25, 3594/125)

Commentary

Cremona 289a2 = LMFDB 289.a2: https://www.lmfdb.org/EllipticCurve/Q/289/a/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 289, minimal discriminant 6975757441, torsion ℤ/2ℤ × ℤ/2ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:38:02 UTC · history