Shafarevich–Tate finiteness conjecture for elliptic curves

Let $E$ be an elliptic curve over a number field $K$, and let $\Sha(E/K)$ denote its Shafarevich–Tate group. Shafarevich–Tate finiteness conjecture. The group $\Sha(E/K)$ is finite. This conjecture is one of the standard finiteness hypotheses used in the paper to derive the reflecting-congruent conjecture. It remains open for elliptic curves over general number fields.