curve #2933

y² + xy + y = x³ − x² − 88x + 242

a-invariants: [1, -1, 1, -88, 242]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ
conductor (N): 341185
discriminant (Δ): 22177025
Faltings height: 0.1151
naive height: 25.0349
primes of bad reduction: 5, 13, 29, 181
regulator: 6.3942574871555130875014712967949363204309602
submitted by: David Renshaw
submitted at: 2026-09-26 20:28:58 UTC
last updated: 2026-09-26 20:28:58 UTC

Witness: 3 independent points log in to add more points →

(8, -2)
(2, 7)
(23, 88)

Commentary

Cremona 341185c1 = LMFDB 341185.c1: https://www.lmfdb.org/EllipticCurve/Q/341185/c/1 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 341185, minimal discriminant 22177025, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:28:58 UTC · history