Degree 4 coverings of elliptic curves by genus 2

Abstract

Genus two curves covering elliptic curves have been the object of study of many articles. For a ?xed degree n the subloci of the moduli space M_2 of curves having a degree n elliptic subcover has been computed for n=3,5 and discussed in detail for n odd; see [17, 22, 3, 4]. When the degree of the cover is even the case in general has been treated in [16]. In this paper we compute the sublocus of M_2 of curves having a degree 4 elliptic subcover.