  We consider the Euler type integral associated to the configuration space of
points on an elliptic curve, which is an analogue of the hypergeometric
function associated to the configuration space of points on a projective line.
We calculate the {\it twisted homology group}, with coefficients in the local
system associated to a power function $g^{\alpha}$ of an elliptic function $g$,
and the intersection form. Applying these calculations, we describe the {\it
connection matrices} representing the linear isomorphisms induced from analytic
continuations of the functions defined by the integrations of $g^{\alpha}$ over
twisted cycles.
