Computing Elliptic Curves over \(\mathbb{Q}\): Bad Reduction at One Prime

  • Michael A. BennettEmail author
  • Andrew Rechnitzer
Part of the Fields Institute Communications book series (FIC, volume 79)


We discuss a new algorithm for finding all elliptic curves over \(\mathbb{Q}\) with a given conductor. Though based on (very) classical ideas, this approach appears to be computationally quite efficient. We provide details of the output from the algorithm in case of conductor p or p 2, for p prime, with comparisons to existing data.


Elliptic curves Cubic forms Invariant theory 

MSC codes

Primary 11G05 11D25 11D59 Secondary 11E76 11Y50 11Y65 


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© Springer Science+Business Media LLC 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada

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