curve #2732

y² + xy = x³ − 24080217x + 45421448121

a-invariants: [1, 0, 0, -24080217, 45421448121]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/9ℤ
conductor (N): 128226
discriminant (Δ): 2295658741816117891584
Faltings height: 2.9997
naive height: 62.6043
primes of bad reduction: 2, 3, 7, 43, 71
regulator: 2.128858521445439161318073577066318882480
submitted by: David Renshaw
submitted at: 2026-09-26 20:19:50 UTC
last updated: 2026-09-26 20:19:50 UTC

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

(2730, 4179)

Commentary

Cremona 128226ba1 = LMFDB 128226.s3: https://www.lmfdb.org/EllipticCurve/Q/128226/s/3 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 128226, minimal discriminant 2295658741816117891584, torsion ℤ/9ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:19:50 UTC · history