curve #3258

y² + xy + y = x³ − 8151x + 282542

a-invariants: [1, 0, 1, -8151, 282542]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/3ℤ
conductor (N): 7826
discriminant (Δ): -15652
Faltings height: 0.6171
naive height: 38.6311
primes of bad reduction: 2, 7, 13, 43
regulator: 6.33037617317133995821465976173349115765320
submitted by: David Renshaw
submitted at: 2026-09-26 20:47:11 UTC
last updated: 2026-09-26 20:47:11 UTC

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

(57, 34)
(38, 148)

Commentary

Cremona 7826f1 = LMFDB 7826.b1: https://www.lmfdb.org/EllipticCurve/Q/7826/b/1 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 7826, minimal discriminant -15652, torsion ℤ/3ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:47:11 UTC · history