  Let p be an odd prime. Suppose that E is a modular elliptic curve/Q with good
ordinary reduction at p. Let Q_{oo} denote the cyclotomic Z_p-extension of Q.
It is conjectured that Sel_E(Q_{oo}) is a cotorsion Lambda-module and that its
characteristic ideal is related to the p-adic L-function associated to E. Under
certain hypotheses we prove that the validity of these conjectures is preserved
by congruences between the Fourier expansions of the associated modular forms.
