curve #3332

y² + xy = x³ − 681440x + 216441600

a-invariants: [1, 0, 0, -681440, 216441600]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/8ℤ
conductor (N): 13530
discriminant (Δ): 3254912100000000
Faltings height: 2.0146
naive height: 51.9095
primes of bad reduction: 2, 3, 5, 11, 41
regulator: 1.277495059582924392776563565717004525563
submitted by: David Renshaw
submitted at: 2026-09-26 20:59:12 UTC
last updated: 2026-09-26 20:59:12 UTC

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

(472, -344)

Commentary

Cremona 13530w1 = LMFDB 13530.v4: https://www.lmfdb.org/EllipticCurve/Q/13530/v/4 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 13530, minimal discriminant 3254912100000000, torsion ℤ/8ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:59:12 UTC · history