when doing a $2$-descent on the jacobian $j$ of a curve of genus $2$, one wishes to determine whether or not certain twists of $j$ have rational points. as $j$ and its twists are unwieldy, we consider the quotient $k$ of a twist by the involution induced by multiplication by $-1$ on $j$. we construct an explicit curve $c$ and corresponding twist for which there is a brauer-manin obstruction to the existence of rational points on $k$. this yields infinitely many twists of $c$ with nontrivial tate-shafarevich group. this is joint work with adam logan at waterloo.