Bauer, MarkMorrill, Ryan2024-06-112024-06-112024-06-10Morrill, R. (2024). Computing elliptic curves of a given conductor (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.https://hdl.handle.net/1880/118938https://doi.org/10.11575/PRISM/46534There 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.enUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.number theoryelliptic curveconductorgood reductionalgebraic number theorycomputational number theoryMathematicsdoctoral thesis