curve #1014

y² + xy = x³ + 159x + 1737

a-invariants: [1, 0, 0, 159, 1737]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/7ℤ
conductor (N): 258
discriminant (Δ): -1540767744
Faltings height: 0.4460
naive height: 28.4277
primes of bad reduction: 2, 3, 43
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:15:25 UTC
last updated: 2026-09-23 15:15:25 UTC

Witness: no points (rank ≥ 0 needs none) log in to add more points →

Commentary

Cremona 258f1 = LMFDB 258.f2: https://www.lmfdb.org/EllipticCurve/Q/258/f/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 258, minimal discriminant -1540767744, torsion ℤ/7ℤ.

last edited by David Renshaw at 2026-09-23 15:15:25 UTC · history