curve #3313

y² + xy + y = x³ + 31x + 992

a-invariants: [1, 0, 1, 31, 992]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/6ℤ
conductor (N): 3570
discriminant (Δ): -425079900
Faltings height: 0.3350
naive height: 27.3178
primes of bad reduction: 2, 3, 5, 7, 17
regulator: 1.137459011443637370220978692598656233243
submitted by: David Renshaw
submitted at: 2026-09-26 20:56:07 UTC
last updated: 2026-09-26 20:56:07 UTC

Witness: 1 independent point log in to add more points →

(6, 34)

Commentary

Cremona 3570j1 = LMFDB 3570.j4: https://www.lmfdb.org/EllipticCurve/Q/3570/j/4 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 3570, minimal discriminant -425079900, torsion ℤ/6ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:56:07 UTC · history