  We study the joint distribution of central $L$-values and orders of
Tate-Shafarevich groups of quadratic twists of elliptic curves. In particular,
adapting Radziwill and Soundararajan's principles of establishing upper and
lower bounds for the distribution of central values in families of
$L$-functions, we obtain conditional upper and lower bounds for such a joint
distribution for rank zero twists. These lead us to a conjecture on the full
asymptotic for the joint distribution.
