Computing Elliptic Curves of a Given Conductor

Abstract

There are many algorithms for computing all elliptic curves of a given conductor. However, for large conductors, this task becomes increasingly more difficult. In this thesis, we will be investigating each of these algorithms for the purposes of finding the most efficient way to find all elliptic curves with respect to computation time. We propose a technique which fuses two of these methods. We will also provide some examples which would be beyond the reasonable scope of any single method, but which our fusion handles with ease.