curve #3123

y² = x³ − 37x + 84

a-invariants: [0, 0, 0, -37, 84]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 1760
discriminant (Δ): 193600
Faltings height: -0.2140
naive height: 22.4464
primes of bad reduction: 2, 5, 11
regulator: 1.877513852280767269307002649567009849479
submitted by: David Renshaw
submitted at: 2026-09-26 20:38:22 UTC
last updated: 2026-09-26 20:38:22 UTC

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

(-5, 12)

Commentary

Cremona 1760f1 = LMFDB 1760.h3: https://www.lmfdb.org/EllipticCurve/Q/1760/h/3 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 1760, minimal discriminant 193600, torsion ℤ/2ℤ × ℤ/2ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:38:22 UTC · history