curve #3321

y² + xy = x³ + 5102x + 521220

a-invariants: [1, 0, 0, 5102, 521220]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/6ℤ
conductor (N): 58466
discriminant (Δ): -125669727797248
Faltings height: 1.3867
naive height: 39.8494
primes of bad reduction: 2, 23, 31, 41
regulator: 7.38843309081860429472522719313854994941988
submitted by: David Renshaw
submitted at: 2026-09-26 20:57:25 UTC
last updated: 2026-09-26 20:57:25 UTC

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

(-42, 504)
(498, 11004)

Commentary

Cremona 58466h1 = LMFDB 58466.f4: https://www.lmfdb.org/EllipticCurve/Q/58466/f/4 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 58466, minimal discriminant -125669727797248, torsion ℤ/6ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:57:25 UTC · history