On the Iwasawa invariants of elliptic curves

  title={On the Iwasawa invariants of elliptic curves},
  author={Ralph Greenberg and Vinayak Vatsal},
  journal={Inventiones mathematicae},
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. 
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