Genus 2 fields with degree 3 elliptic subfields

Abstract

In this paper we study genus 2 function fields K with degree 3 elliptic subfields. We show that the number of Aut(K)-classes of such subfields of K is 0,1,2, or 4. Also we compute an equation for the locus of such K in the moduli space of genus 2 curves.

Cited by in corpus (6)

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• From hyperelliptic to superelliptic curves
• On Jacobians of curves with superelliptic components
• Genus-2 curves and Jacobians with a given number of points
• Isogenous components of Jacobian surfaces
• Diagonals of rational functions: from differential algebra to effective algebraic geometry (unabridged version)