On unramified normal coverings of hyperelliptic curves

It is well known that the number of unramified normal coverings of an irreducible complex algebraic curve C with a group of covering transformations isomorphic to image is (24g−3dot operator22g+2)/6. Assume that C is hyperelliptic, say image. Horiouchi has given the explicit algebraic equations of the subset of those covers which turn out to be hyperelliptic themselves. There are image of this particular type. In this article, we provide algebraic equations for the remaining ones.