Computing Elliptic Curves of a Given Conductor

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dc.contributor.advisorBauer, Mark
dc.contributor.authorMorrill, Ryan
dc.contributor.committeememberScheidler, Renate
dc.contributor.committeememberNguyen, Dang Khoa
dc.contributor.committeememberScandolo, Carlo Maria
dc.contributor.committeememberBennett, Michael
dc.date.accessioned2024-06-11T16:46:07Z
dc.date.available2024-06-11T16:46:07Z
dc.date.issued2024-06-10
dc.description.abstractThere 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.
dc.identifier.citationMorrill, R. (2024). Computing elliptic curves of a given conductor (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.
dc.identifier.urihttps://hdl.handle.net/1880/118938
dc.language.isoen
dc.publisher.facultyGraduate Studies
dc.publisher.institutionUniversity of Calgary
dc.rightsUniversity 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.
dc.subjectnumber theory
dc.subjectelliptic curve
dc.subjectconductor
dc.subjectgood reduction
dc.subjectalgebraic number theory
dc.subjectcomputational number theory
dc.subject.classificationMathematics
dc.titleComputing Elliptic Curves of a Given Conductor
dc.typedoctoral thesis
thesis.degree.disciplineMathematics & Statistics
thesis.degree.grantorUniversity of Calgary
thesis.degree.nameDoctor of Philosophy (PhD)
ucalgary.thesis.accesssetbystudentI do not require a thesis withhold – my thesis will have open access and can be viewed and downloaded publicly as soon as possible.
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