  We present an algorithm to determine if the $L$-series associated to an
automorphic representation and the one associated to an elliptic curve over an
imaginary quadratic field agree. By the work of Harris-Soudry-Taylor, Taylor
and Berger-Harcos (cf. \cite{harris-taylor}, \cite{taylorII} and
\cite{berger-harcos}) we can associate to an automorphic representation a
family of compatible $p$-adic representations. Our algorithm is based on
Faltings-Serre's method to prove that $p$-adic Galois representations are
isomorphic.
