curve #3109

y² = x³ − 91x + 330

a-invariants: [0, 0, 0, -91, 330]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 272
discriminant (Δ): 1183744
Faltings height: -0.0301
naive height: 25.1462
primes of bad reduction: 2, 17
regulator: 1.018148717345369171061052374517851191729
submitted by: David Renshaw
submitted at: 2026-09-26 20:37:43 UTC
last updated: 2026-09-26 20:37:43 UTC

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

(7, 6)

Commentary

Cremona 272b2 = LMFDB 272.b2: https://www.lmfdb.org/EllipticCurve/Q/272/b/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 272, minimal discriminant 1183744, torsion ℤ/2ℤ × ℤ/2ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:37:43 UTC · history