  We define and prove the existence of the Quantum $A_{\infty}$-relations on
the Fukaya category of the elliptic curve, using the notion of the Feynman
transform of a modular operad, as defined by Getzler and Kapranov. Following
Barannikov, these relations may be viewed as defining a solution to the quantum
master equation of Batalin-Vilkovisky geometry.
