curve #2976

y² = x³ − 2x + 21

a-invariants: [0, 0, 0, -2, 21]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/4ℤ
conductor (N): 760
discriminant (Δ): -190000
Faltings height: -0.3078
naive height: 19.6122
primes of bad reduction: 2, 5, 19
regulator: 1.722468392870600859639291785876983511059
submitted by: David Renshaw
submitted at: 2026-09-26 20:31:24 UTC
last updated: 2026-09-26 20:31:24 UTC

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

(6, 15)

Commentary

Cremona 760e1 = LMFDB 760.c4: https://www.lmfdb.org/EllipticCurve/Q/760/c/4 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 760, minimal discriminant -190000, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:31:24 UTC · history