Computing Elliptic Curves of a Given Conductor
Date
2024-06-10
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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.
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Keywords
number theory, elliptic curve, conductor, good reduction, algebraic number theory, computational number theory
Citation
Morrill, R. (2024). Computing elliptic curves of a given conductor (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.