  Let $C$ be an algebraic curve embedded transversally in a power $E^N$ of an
elliptic curve $E$. In this article we produce a good explicit bound for the
height of all the algebraic points on $C$ contained in the union of all proper
algebraic subgroups of $E^N$. The method gives a totally explicit version of
the Manin-Dam'janenko Theorem in the elliptic case and it is a generalisation
of previous results only proved when $E$ does not have Complex Multiplication.
