curve #2981

y² + xy + y = x³ + x² − 19x + 17

a-invariants: [1, 1, 1, -19, 17]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/4ℤ
conductor (N): 438
discriminant (Δ): 168192
Faltings height: -0.2839
naive height: 20.4502
primes of bad reduction: 2, 3, 73
regulator: 0.6653445420451020814164748484388166893316
submitted by: David Renshaw
submitted at: 2026-09-26 20:31:44 UTC
last updated: 2026-09-26 20:31:44 UTC

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

(5, 6)

Commentary

Cremona 438f1 = LMFDB 438.e3: https://www.lmfdb.org/EllipticCurve/Q/438/e/3 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 438, minimal discriminant 168192, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:31:44 UTC · history