Mahler's measure and elliptic curves with potential complex multiplication

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}$$isrelatedtothespecialvalueofthe$L$-function$L(E,s)$at$s = 2$.