Albanian Journal of Mathematics (ISNN: 1930-1235), Vol 2, No 4 (2008)

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Degree 4 Coverings of Elliptic Curves by Genus 2 Curves

T. Shaska, G. S. Wijesiri, S. Wolf, L. Woodland

Abstract


Genus two curves covering elliptic curves have been the object of study of many articles. For a fixed 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 \cite{Sh1, SV2, Fr, FK}.

When the degree of the cover is even the case in general has been treated in \cite{PRS}. In this paper we compute the the sublocus of $\M_2$ of curves having a degree $4$ elliptic subcover.

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