curve #3275

y² = x³ − x² + 25x

a-invariants: [0, -1, 0, 25, 0]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/4ℤ
conductor (N): 1320
discriminant (Δ): -990000
Faltings height: -0.1602
naive height: 21.2300
primes of bad reduction: 2, 3, 5, 11
regulator: 1.349113723629621392171108121322455375132
submitted by: David Renshaw
submitted at: 2026-09-26 20:49:59 UTC
last updated: 2026-09-26 20:49:59 UTC

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

(1, 5)

Commentary

Cremona 1320i1 = LMFDB 1320.e4: https://www.lmfdb.org/EllipticCurve/Q/1320/e/4 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 1320, minimal discriminant -990000, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:49:59 UTC · history