curve #3260

y² + xy = x³ − x² − 1032x + 13022

a-invariants: [1, -1, 0, -1032, 13022]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/3ℤ
conductor (N): 9882
discriminant (Δ): 88938
Faltings height: 0.2606
naive height: 32.4319
primes of bad reduction: 2, 3, 61
regulator: 4.47191036913596181260610114389138798886908
submitted by: David Renshaw
submitted at: 2026-09-26 20:47:31 UTC
last updated: 2026-09-26 20:47:31 UTC

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

(31, 85)
(1, 109)

Commentary

Cremona 9882e1 = LMFDB 9882.d2: https://www.lmfdb.org/EllipticCurve/Q/9882/d/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 9882, minimal discriminant 88938, torsion ℤ/3ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:47:31 UTC · history