  We give an explicit construction of the cusp eigenforms on an elliptic curve
defined over a finite field using the theory of Hall algebras and the Langlands
correspondence for function fields and $\GL_n$. As a consequence we obtain a
description of the Hall algebra of an elliptic curve as an infinite tensor
product of simpler algebras. We prove that all these algebras are
specializations of a universal spherical Hall algebra (as defined and studied
in \cite{BS} and \cite{SV1}).
