Mahler Measure Of Polynomial X+y+1/x~2y+k

The Mahler measure of bivariate polynomials is closely related to the value of L-function of the corresponding elliptic curve.Villegas study found that Mahler measures of some polynomials exist a relation to modular forms.In this paper,we study the Mahler measure of polynomial x+y+1/x2y+k,calculate its modular form and obtain some relations with the value of L-function of elliptic curve by comparison.