Large Shafarevich-Tate groups over quadratic number fields

Let $E$ be an elliptic curve over the rational field $\mathbf{Q}$. Let $K$ be a quadratic extension over $\mathbf{Q}$. Let $\mathrm{S}\mathrm{T}(E\mathrm{/}K)$ dente the Shafarevich-Tate group of $E$ over $K$. We show that (under mild conditions on $E$) for every $r>0$, there are infinitely many quadratic twists $E^d\mathrm{/}\mathbf{Q}$ of $E\mathrm{/}\mathbf{Q}$ such that ${\mathrm{d}\mathrm{i}\mathrm{m}}_{{\mathbf{F}}_2}(\mathrm{S}\mathrm{T}(E^d\mathrm{/}K)[2])>r$