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Mathematics of Computation

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Computing elliptic curves over $ \mathbb{Q}$


Authors: Michael A. Bennett, Adela Gherga and Andrew Rechnitzer
Journal: Math. Comp.
MSC (2010): Primary 11D45, 11D61; Secondary 11J82, 11J86
DOI: https://doi.org/10.1090/mcom/3370
Published electronically: August 1, 2018
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Abstract: We discuss an algorithm for finding all elliptic curves over $ \mathbb{Q}$ with a given conductor. Though based on classical ideas derived from reducing the problem to one of solving associated Thue-Mahler equations, our approach, in many cases at least, appears to be reasonably efficient computationally. We provide details of the output derived from running the algorithm, concentrating on the cases of conductor $ p$ or $ p^2$, for $ p$ prime, with comparisons to existing data.


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Additional Information

Michael A. Bennett
Affiliation: Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada
Email: bennett@math.ubc.ca

Adela Gherga
Affiliation: Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada
Email: ghergaa@math.ubc.ca

Andrew Rechnitzer
Affiliation: Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada
Email: andrewr@math.ubc.ca

DOI: https://doi.org/10.1090/mcom/3370
Received by editor(s): October 6, 2017
Received by editor(s) in revised form: November 1, 2017, February 21, 2018, and March 16, 2018
Published electronically: August 1, 2018
Additional Notes: The authors were supported in part by NSERC
Article copyright: © Copyright 2018 American Mathematical Society

American Mathematical Society