curve #3254

y² = x³ + x² + 82x − 391

a-invariants: [0, 1, 0, 82, -391]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/3ℤ
conductor (N): 32828
discriminant (Δ): -110433392
Faltings height: 0.2281
naive height: 25.5953
primes of bad reduction: 2, 29, 283
regulator: 9.37595281834571421851847186027113026390392
submitted by: David Renshaw
submitted at: 2026-09-26 20:46:32 UTC
last updated: 2026-09-26 20:46:32 UTC

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

(5, 13)
(98, 979)

Commentary

Cremona 32828a1 = LMFDB 32828.a2: https://www.lmfdb.org/EllipticCurve/Q/32828/a/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 32828, minimal discriminant -110433392, torsion ℤ/3ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:46:32 UTC · history