The Mordell-Weil lattice of an Inose surface arising from isogenous elliptic curves

Abstract

An elliptic K3 surface having two $II^{*}$ fibers is called the Inose surface. In this paper, we give a method to find a rational section of an Inose surface corresponding to an isogeny of general degree between two elliptic curves. In particular, we show examples of bases of the Mordell-Weil lattices of Inose surfaces arising from isogenies of degrees 5 and 6.