curve #3314

y² + xy = x³ − x² − 927x + 11097

a-invariants: [1, -1, 0, -927, 11097]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/6ℤ
conductor (N): 306
discriminant (Δ): 14326308
Faltings height: 0.3822
naive height: 32.1101
primes of bad reduction: 2, 3, 17
regulator: 1.687887029480387508849047299795412531648
submitted by: David Renshaw
submitted at: 2026-09-26 20:56:17 UTC
last updated: 2026-09-26 20:56:17 UTC

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

(9, 54)

Commentary

Cremona 306b3 = LMFDB 306.a2: https://www.lmfdb.org/EllipticCurve/Q/306/a/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 306, minimal discriminant 14326308, torsion ℤ/6ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:56:17 UTC · history