curve #3328

y² = x³ + x² − 305980x + 65044100

a-invariants: [0, 1, 0, -305980, 65044100]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/6ℤ
conductor (N): 60180
discriminant (Δ): 51128928000
Faltings height: 1.6003
naive height: 49.5074
primes of bad reduction: 2, 3, 5, 17, 59
regulator: 8.97731484596299317156647887423317064156581
submitted by: David Renshaw
submitted at: 2026-09-26 20:58:33 UTC
last updated: 2026-09-26 20:58:33 UTC

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

(400, 2610)
(680, 13110)

Commentary

Cremona 60180k2 = LMFDB 60180.k2: https://www.lmfdb.org/EllipticCurve/Q/60180/k/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 60180, minimal discriminant 51128928000, torsion ℤ/6ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:58:33 UTC · history