2 problems

Let $E$ be an elliptic curve over $\mathbb{Q}$, and let $\text{\cyr X}(E)$ be its Tate–Shafarevich group, whose elements classify everywhere locally soluble genus-one curves equipp…

Let $E$ be an elliptic curve of rank one over $\mathbb{Q}$ and prime conductor $N_E$. Let $I_E$ be the index of the subgroup of $E(\mathbb{Q})$ generated by the Heegner points, and…