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arXiv · 1910.07335

Kolyvagin Derivatives of Modular Points on Elliptic Curves

Richard Hatton
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Abstract

Let $E / \mathbb{Q}$ and $A / \mathbb{Q}$ 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 $p^{n}$.

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Richard Hatton. 2021-01-07. Kolyvagin Derivatives of Modular Points on Elliptic Curves. https://doi.org/10.1016/j.jnt.2020.10.014

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