curve #2958

y² + xy = x³ − 17x + 289

a-invariants: [1, 0, 0, -17, 289]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/3ℤ
conductor (N): 31246
discriminant (Δ): -36120376
Faltings height: 0.1300
naive height: 24.8658
primes of bad reduction: 2, 17, 919
regulator: 4.30582787846624011247330565938773287746005
submitted by: David Renshaw
submitted at: 2026-09-26 20:30:06 UTC
last updated: 2026-09-26 20:30:06 UTC

Witness: 2 independent points log in to add more points →

(4, 15)
(12, 37)

Commentary

Cremona 31246h1 = LMFDB 31246.d1: https://www.lmfdb.org/EllipticCurve/Q/31246/d/1 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 31246, minimal discriminant -36120376, torsion ℤ/3ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:30:06 UTC · history