An effective class in a closed symplectic four-manifold is a twodimensional homology class which is realized by a J-holomorphic cycle for every tamed almost complex structure J. We first prove that effective classes are orthogonal to Lagrangian tori with respect to the
intersection form. We then deduce an invariant under birational transformations of closed symplectic four-manifolds. We finally prove using
the same techniques of symplectic field theory that the unit cotangent bundle of a compact orientable hyperbolic Lagrangian surface does not
embed as a hypersurface of contact type in a rational or ruled symplectic four-manifold.