curve #3266

y² + xy + y = x³ + x² − 1564x − 23299

a-invariants: [1, 1, 1, -1564, -23299]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 1122
discriminant (Δ): 23284318464
Faltings height: 0.7448
naive height: 33.6786
primes of bad reduction: 2, 3, 11, 17
regulator: 1.893763184624783638839174408974854649556
submitted by: David Renshaw
submitted at: 2026-09-26 20:48:31 UTC
last updated: 2026-09-26 20:48:31 UTC

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

(47, 75)

Commentary

Cremona 1122e2 = LMFDB 1122.e4: https://www.lmfdb.org/EllipticCurve/Q/1122/e/4 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 1122, minimal discriminant 23284318464, torsion ℤ/2ℤ × ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:48:31 UTC · history