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We study genus 2 function fields with elliptic subfields of degree 2. Thelocus $\L_2$ of these fields is a 2-dimensional subvariety of the moduli space$\mathcal M_2$ of genus 2 fields. An equation for $\L_2$ is already in the workof Clebsch and Bolza. We use a birational parameterization of $\L_2$ by affine2-space to study the relation between the j-invariants of the degree 2 ellipticsubfields. This extends work of Geyer, Gaudry, Stichtenoth and others. We finda 1-dimensional family of genus 2 curves having exactly two isomorphic ellipticsubfields of degree 2; this family is parameterized by the j-invariant of thesesubfields.

Elliptic Subfields and Automorphisms of Genus 2 Function Fields