On the Mahler measure of $1+X+1/X+Y+1/Y$

Abstract

We prove a conjectured formula relating the Mahler measure of the Laurent polynomial $1+X+X^{-1}+Y+Y^{-1}$, to the $L$-series of a conductor 15 elliptic curve.Comment: 18 pages, Fixed typos in Lemmas 3 and