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

2022/09/06 by Utsumi, Kazuki
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.02463

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.

Related

• Elliptic K3 surfaces admitting a Shioda-Inose structure
• Elliptic Surfaces
• Mordell-Weil groups and automorphism groups of elliptic K3 surfaces
• Monodromies of rational elliptic surfaces and extremal elliptic K3 surfaces
• On elliptic K3 surfaces