curve #3261

y² + xy + y = x³ − 120125x + 16014900

a-invariants: [1, 0, 1, -120125, 16014900]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/3ℤ
conductor (N): 58838
discriminant (Δ): -117676
Faltings height: 1.1949
naive height: 46.7025
primes of bad reduction: 2, 13, 31, 73
regulator: 11.0166504753564008527151412121191615958984
submitted by: David Renshaw
submitted at: 2026-09-26 20:47:43 UTC
last updated: 2026-09-26 20:47:43 UTC

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

(193, 74)
(333, 3434)

Commentary

Cremona 58838h1 = LMFDB 58838.a1: https://www.lmfdb.org/EllipticCurve/Q/58838/a/1 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 58838, minimal discriminant -117676, torsion ℤ/3ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:47:43 UTC · history