curve #2960

y² = x³ − x² − 600x

a-invariants: [0, -1, 0, -600, 0]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 1680
discriminant (Δ): 13829760000
Faltings height: 0.6353
naive height: 30.8061
primes of bad reduction: 2, 3, 5, 7
regulator: 1.242447211373483671912572321217854360667
submitted by: David Renshaw
submitted at: 2026-09-26 20:30:16 UTC
last updated: 2026-09-26 20:30:16 UTC

Witness: 1 independent point log in to add more points →

(30, 90)

Commentary

Cremona 1680d4 = LMFDB 1680.h3: https://www.lmfdb.org/EllipticCurve/Q/1680/h/3 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 1680, minimal discriminant 13829760000, torsion ℤ/2ℤ × ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:30:17 UTC · history