Kolyvagin Derivatives of Modular Points on Elliptic Curves
Number Theory
2021-01-08 v3
Abstract
Let and be elliptic curves. We can construct modular points derived from via the modular parametrisation of . With certain assumptions we can show that these points are of infinite order and are not divisible by a prime . In particular, using Kolyvagin's construction of derivative classes, we can find elements in certain Shafarevich-Tate groups of order .
Keywords
Cite
@article{arxiv.1910.07335,
title = {Kolyvagin Derivatives of Modular Points on Elliptic Curves},
author = {Richard Hatton},
journal= {arXiv preprint arXiv:1910.07335},
year = {2021}
}
Comments
Final Version. To appear in Journal of Number Theory. 23 pages