  Using the Weil-Brezin-Zak transform of solid state physics, we describe line
bundles over elliptic curves in terms of Weyl operators. We then discuss the
connection with finitely-generated projective modules over the algebra
$A_\theta$ of the noncommutative torus. We show that such $A_\theta$-modules
have a natural interpretation as Moyal deformations of vector bundles over an
elliptic curve $E_\tau$, under the condition that the deformation parameter
$\theta$ and the modular parameter $\tau$ satisfy a non-trivial relation.
