curve #1071

y² + xy = x³ − 231240x + 187785792

a-invariants: [1, 0, 0, -231240, 187785792]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/9ℤ
conductor (N): 60990
discriminant (Δ): -14445609579000000000
Faltings height: 2.3585
naive height: 51.6250
primes of bad reduction: 2, 3, 5, 19, 107
regulator: 2.495055653243491789202840627612917558484
submitted by: David Renshaw
submitted at: 2026-09-23 15:24:01 UTC
last updated: 2026-09-23 15:24:01 UTC

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

(-696, 3768)

Commentary

Cremona 60990bj1 = LMFDB 60990.bh2: https://www.lmfdb.org/EllipticCurve/Q/60990/bh/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 60990, minimal discriminant -14445609579000000000, torsion ℤ/9ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-23 15:24:01 UTC · history