  We prove a conjecture of Boyd and Rodriguez Villegas relating the Mahler
measure of the polynomial $(1+x)(1+y)+z$ and the value at $s=3$ of the
$L$-function of an elliptic curve of conductor $15$. The proof makes use of the
computation by Zudilin and the author of the regulator of certain $K_4$ classes
on modular curves.
