curve #3307

y² + y = x³ + x² + 4300x − 746746

a-invariants: [0, 1, 1, 4300, -746746]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/5ℤ
conductor (N): 58395
discriminant (Δ): -246908695246875
Faltings height: 1.4418
naive height: 40.5739
primes of bad reduction: 3, 5, 17, 229
regulator: 4.52137705277550826515544974677706910681191
submitted by: David Renshaw
submitted at: 2026-09-26 20:55:09 UTC
last updated: 2026-09-26 20:55:09 UTC

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

(166, 2137)
(76, 157)

Commentary

Cremona 58395i1 = LMFDB 58395.b2: https://www.lmfdb.org/EllipticCurve/Q/58395/b/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 58395, minimal discriminant -246908695246875, torsion ℤ/5ℤ. The witnesses are the generators from Cremona's tables.

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