Quadratic Points on Modular Curves and Involutions

Lead Research Organisation: University of Warwick
Department Name: Mathematics

Abstract

Modular curves classify elliptic curves, objects of central importance in number theory with applications to public-key cryptography. We would like to study the symmetries of these modular curves, so as to attain a better understanding of elliptic curves. The novelty of our approach is to use the complex parametrization of modular curves as a computational tool for determining the symmetries, as well as the traditional algebraic and geometric tools.

The project lies within the EPSRC research area "Number Theory". However writing down explicit models for modular curves and their symmetries could well have applications to cryptography.

Publications

10 25 50

Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/R513374/1 01/10/2018 30/09/2023
2274692 Studentship EP/R513374/1 30/09/2019 31/03/2023 Philippe Alain Michaud-Rodgers