curve #3279

y² = x³ − 1451x + 21274

a-invariants: [0, 0, 0, -1451, 21274]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/4ℤ
conductor (N): 272
discriminant (Δ): 69632
Faltings height: 0.3165
naive height: 33.4536
primes of bad reduction: 2, 17
regulator: 2.036297434690738342122104749035702383459
submitted by: David Renshaw
submitted at: 2026-09-26 20:50:38 UTC
last updated: 2026-09-26 20:50:38 UTC

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

(31, 78)

Commentary

Cremona 272b3 = LMFDB 272.b1: https://www.lmfdb.org/EllipticCurve/Q/272/b/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 272, minimal discriminant 69632, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:50:38 UTC · history