  In this work we prove congruences between special values of elliptic curves
with CM that seem to play a central role in the analytic side of the
non-commutative Iwasawa theory. These congruences are the analogue for elliptic
curves with CM of those proved by Kato, Ritter and Weiss for the Tate motive.
The proof is based on the fact that the critical values of elliptic curves with
CM, or what amounts to the same, the critical values of Gr\"{o}ssencharacters,
can be expressed as values of Hilbert-Eisenstein series at CM points. We
believe that our strategy can be generalized to provide congruences for a large
class of $L$-values.
