Let A be an abelian variety defi umber field K. Let L be a biquadratic extension of K with Galois group G and let □(A/K) and □(A/L) denote, respectively, the Tate-Shafarevich groups of A over K and over L. Assuming □(A/L) is finite, we compute [□(A/K)]/[□(A/L)] where [X] is the order of a finite abelian group X.
