From L-series of elliptic curves to Mahler measures

We prove the conjectural relations between Mahler measures and L-values of elliptic curves of conductors 20 and 24. We also present new hypergeometric expressions for L-values of elliptic curves of conductors 27 and 36. Furthermore, we prove a new functional equation for the Mahler measure of the polynomial family (1+X)(1+Y)(X+Y)−αXY, α∈ℝ.