curve #3324

y² = x³ + x² − 19105x + 1013600

a-invariants: [0, 1, 0, -19105, 1013600]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/6ℤ
conductor (N): 60180
discriminant (Δ): -3107544750000
Faltings height: 1.2537
naive height: 41.1937
primes of bad reduction: 2, 3, 5, 17, 59
regulator: 2.24432871149074829289161971855829266039145
submitted by: David Renshaw
submitted at: 2026-09-26 20:57:54 UTC
last updated: 2026-09-26 20:57:54 UTC

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

(80, 60)
(83, 81)

Commentary

Cremona 60180k1 = LMFDB 60180.k3: https://www.lmfdb.org/EllipticCurve/Q/60180/k/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 60180, minimal discriminant -3107544750000, torsion ℤ/6ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:57:54 UTC · history