curve #3127

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: 3.044468409020596608839696398203735034874
submitted by: David Renshaw
submitted at: 2026-09-26 20:38:31 UTC
last updated: 2026-09-26 20:38:31 UTC

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

(95, 924)

Commentary

Cremona 1760j1 = LMFDB 1760.g3: https://www.lmfdb.org/EllipticCurve/Q/1760/g/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 20:38:31 UTC · history