curve #1043

y² + xy = x³ + 12948x + 421776

a-invariants: [1, 0, 0, 12948, 421776]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/9ℤ
conductor (N): 1482 ☆ record for ℤ/9ℤ torsion, rank ≥ 1
discriminant (Δ): -215384711233536
Faltings height: 1.4377
naive height: 40.0197
primes of bad reduction: 2, 3, 13, 19
regulator: 1.735730763047140873500173538542793695979
submitted by: David Renshaw
submitted at: 2026-09-23 15:19:43 UTC
last updated: 2026-09-23 15:19:43 UTC

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

(-30, 96)

Commentary

Cremona 1482l1 = LMFDB 1482.j3: https://www.lmfdb.org/EllipticCurve/Q/1482/j/3 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 1482, minimal discriminant -215384711233536, torsion ℤ/9ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-23 15:19:43 UTC · history