curve #3290

y² + xy + y = x³ + x² − 204624x + 35542050

a-invariants: [1, 1, 1, -204624, 35542050]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/4ℤ
conductor (N): 609
discriminant (Δ): 38367
Faltings height: 1.2907
naive height: 48.3004
primes of bad reduction: 3, 7, 29
regulator: 7.026920478164243935451002467228854851369
submitted by: David Renshaw
submitted at: 2026-09-26 20:52:25 UTC
last updated: 2026-09-26 20:52:25 UTC

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

(1317, 44646)

Commentary

Cremona 609b4 = LMFDB 609.a1: https://www.lmfdb.org/EllipticCurve/Q/609/a/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 609, minimal discriminant 38367, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:52:25 UTC · history