curve #3245

y² = x³ + 9

a-invariants: [0, 0, 0, 0, 9]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/3ℤ
conductor (N): 972
discriminant (Δ): -34992
Faltings height: -0.4492
naive height: 17.9176
primes of bad reduction: 2, 3
regulator: 0.8146954405668259814410303905649091225929
submitted by: David Renshaw
submitted at: 2026-09-26 20:45:03 UTC
last updated: 2026-09-26 20:45:03 UTC

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

(3, 6)

Commentary

Cremona 972c1 = LMFDB 972.b2: https://www.lmfdb.org/EllipticCurve/Q/972/b/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 972, minimal discriminant -34992, torsion ℤ/3ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:45:03 UTC · history