If E is an elliptic curve over Q and K is an imaginary quadratic field, there
is an Iwasawa main conjecture predicting the behavior of the Selmer group of E
over the anticyclotomic Z_p-extension of K. The main conjecture takes different
forms depending on the sign of the functional equation of L(E/K,s). In the
present work we combine ideas of Bertolini and Darmon with those of Mazur and
Rubin to shown that the main conjecture, regardless of the sign of the
functional equation, can be reduced to proving the nonvanishing of sufficiently
many p-adic L-functions attached to a family of congruent modular forms