curve #3320

y² + xy + y = x³ + 11171x + 294756

a-invariants: [1, 0, 1, 11171, 294756]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/6ℤ
conductor (N): 41230
discriminant (Δ): -126526217059900
Faltings height: 1.3937
naive height: 39.5770
primes of bad reduction: 2, 5, 7, 19, 31
regulator: 2.83540656752120477709686561017778208536915
submitted by: David Renshaw
submitted at: 2026-09-26 20:57:15 UTC
last updated: 2026-09-26 20:57:15 UTC

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

(-7, 468)
(13, 658)

Commentary

Cremona 41230k1 = LMFDB 41230.b4: https://www.lmfdb.org/EllipticCurve/Q/41230/b/4 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 41230, minimal discriminant -126526217059900, torsion ℤ/6ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:57:15 UTC · history