Kolyvagin Derivatives of Modular Points on Elliptic Curves

Let $E\mathrm{/}\mathbb{Q}$ and $A\mathrm{/}\mathbb{Q}$ be elliptic curves. We can construct modular points derived from $A$ via the modular parametrisation of $E$. With certain assumptions we can show that these points are of infinite order and are not divisible by a prime $p$. In particular, using Kolyvagin’s construction of derivative classes, we can find elements in certain Shafarevich-Tate groups of order $p^n$.