curve #2827

y² + xy + y = x³ + x² − 229x − 229

a-invariants: [1, 1, 1, -229, -229]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 1254
discriminant (Δ): 761097744
Faltings height: 0.3939
naive height: 27.9150
primes of bad reduction: 2, 3, 11, 19
regulator: 2.249900062403558931989000744229923137178
submitted by: David Renshaw
submitted at: 2026-09-26 20:24:13 UTC
last updated: 2026-09-26 20:24:13 UTC

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

(-3, 22)

Commentary

Cremona 1254h2 = LMFDB 1254.g4: https://www.lmfdb.org/EllipticCurve/Q/1254/g/4 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 1254, minimal discriminant 761097744, torsion ℤ/2ℤ × ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:24:13 UTC · history