curve #3294

y² = x³ − x² − 615x + 6000

a-invariants: [0, -1, 0, -615, 6000]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/4ℤ
conductor (N): 30360
discriminant (Δ): 404091600
Faltings height: 0.4522
naive height: 30.8801
primes of bad reduction: 2, 3, 5, 11, 23
regulator: 4.17980490703293174013411532907279159316306
submitted by: David Renshaw
submitted at: 2026-09-26 20:53:03 UTC
last updated: 2026-09-26 20:53:03 UTC

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

(25, 75)
(17, 13)

Commentary

Cremona 30360x1 = LMFDB 30360.m3: https://www.lmfdb.org/EllipticCurve/Q/30360/m/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 30360, minimal discriminant 404091600, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:53:03 UTC · history