curve #2690

y² + xy + y = x³ + x² − 270x + 1482

a-invariants: [1, 1, 1, -270, 1482]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 1155
discriminant (Δ): 161417025
Faltings height: 0.3207
naive height: 28.4091
primes of bad reduction: 3, 5, 7, 11
regulator: 1.700180605762088225851054912369030334406
submitted by: David Renshaw
submitted at: 2026-09-26 20:17:54 UTC
last updated: 2026-09-26 20:17:54 UTC

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

(12, 6)

Commentary

Cremona 1155e2 = LMFDB 1155.e3: https://www.lmfdb.org/EllipticCurve/Q/1155/e/3 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 1155, minimal discriminant 161417025, torsion ℤ/2ℤ × ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:17:54 UTC · history