curve #1044

y² + xy = x³ − 4767x + 127449

a-invariants: [1, 0, 0, -4767, 127449]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/9ℤ
conductor (N): 1554
discriminant (Δ): -127896039936 ☆ record for ℤ/9ℤ torsion, rank ≥ 1
Faltings height: 0.9476 ☆ record for ℤ/9ℤ torsion, rank ≥ 1
naive height: 37.0403 ☆ record for ℤ/9ℤ torsion, rank ≥ 1
primes of bad reduction: 2, 3, 7, 37
regulator: 1.255479514076165392258624855532740753172
submitted by: David Renshaw
submitted at: 2026-09-23 15:20:45 UTC
last updated: 2026-09-23 15:20:45 UTC

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

(48, 75)

Commentary

Cremona 1554n1 = LMFDB 1554.l2: https://www.lmfdb.org/EllipticCurve/Q/1554/l/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 1554, minimal discriminant -127896039936, torsion ℤ/9ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-23 15:20:45 UTC · history