curve #3323

y² + xy + y = x³ + 15019x + 75216

a-invariants: [1, 0, 1, 15019, 75216]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/6ℤ
conductor (N): 108262
discriminant (Δ): -219205964132848
Faltings height: 1.4412
naive height: 40.4649
primes of bad reduction: 2, 7, 11, 19, 37
regulator: 9.51443032395511997659471917560482427411551
submitted by: David Renshaw
submitted at: 2026-09-26 20:57:45 UTC
last updated: 2026-09-26 20:57:45 UTC

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

(23, 646)
(170, 2662)

Commentary

Cremona 108262a1 = LMFDB 108262.b4: https://www.lmfdb.org/EllipticCurve/Q/108262/b/4 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 108262, minimal discriminant -219205964132848, torsion ℤ/6ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:57:45 UTC · history