  Given a pair of translation surfaces it is very difficult to determine
whether they are supported on the same algebraic curve. In fact, there are very
few examples of such pairs. In this note we present infinitely many examples of
finite collections of translation surfaces supported on the same algebraic
curve.
  The underlying curves are hyperelliptic curves with many automorphisms. For
each curve, the automorphism of maximal order acts on the space of holomorphic
1-forms. We present a translation surface corresponding to each of the
eigenforms of this action.
