  Given an elliptic curve $E$ defined over $\mathbb{Q}$ which has potential
complex multiplication by the ring of integers $\mathcal{O}_K$ of an imaginary
quadratic field $K$ we construct a polynomial $P_E \in \mathbb{Z}[x,y]$ which
is a planar model of $E$ and such that the Mahler measure $m(P_E) \in
\mathbb{R}$ is related to the special value of the $L$-function $L(E,s)$ at $s
= 2$.
