curve #3287

y² + xy + y = x³ + x² − 265x + 1550

a-invariants: [1, 1, 1, -265, 1550]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/4ℤ
conductor (N): 1155
discriminant (Δ): 12705
Faltings height: -0.0259
naive height: 28.3530
primes of bad reduction: 3, 5, 7, 11
regulator: 3.400361211524176451702109824738060668811
submitted by: David Renshaw
submitted at: 2026-09-26 20:51:55 UTC
last updated: 2026-09-26 20:51:55 UTC

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

(34, 165)

Commentary

Cremona 1155e1 = LMFDB 1155.e4: https://www.lmfdb.org/EllipticCurve/Q/1155/e/4 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 1155, minimal discriminant 12705, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:51:55 UTC · history