  Let C be a curve of genus at least 2 imbedded in a product of elliptic
curves. We give an explicit upper bound for the points in the intersection of C
with the union of all algebraic subgroups of a certain codimension. As a
corollary we obtain an explicit upper bound for the height of the rational
points for some families of curves and an explicit version of the
Manin-Dem'janenko method in products of elliptic curves
