curve #3252

y² + xy + y = x³ + 94x + 264

a-invariants: [1, 0, 1, 94, 264]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/3ℤ
conductor (N): 22274
discriminant (Δ): -82369252
Faltings height: 0.2063
naive height: 25.2587
primes of bad reduction: 2, 7, 37, 43
regulator: 5.08127806104704614414562375772898573299412
submitted by: David Renshaw
submitted at: 2026-09-26 20:46:13 UTC
last updated: 2026-09-26 20:46:13 UTC

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

(-1, 13)
(6, 29)

Commentary

Cremona 22274i1 = LMFDB 22274.b2: https://www.lmfdb.org/EllipticCurve/Q/22274/b/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 22274, minimal discriminant -82369252, torsion ℤ/3ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:46:13 UTC · history