On the order of Tate-Shafarevich groups over finite Galois extensions

Let A be an abelian variety defined over a number field K. Let L be a finite Galois extension of K with Galois group G and let X(A/K) and X(A/L) denote, respectively, the Tate-Shafarevich groups of A over K and of A over L. Define A(f) to be an abelian variety defined over K derived from nontrivial group representations of G. Assuming X(A/L) is finite, we compute [X(A/L)]/[X(A/K)], where [X] is the order of a finite abelian group X.