Computing all elliptic curves over an arbitrary number field with prescribed primes of bad reduction

Angelos Koutsianas

Computing all elliptic curves over an arbitrary number field with prescribed primes of bad reduction

Number Theory 2015-11-17 v1

Authors: Angelos Koutsianas

Abstract

In this paper we study the problem of how to determine all elliptic curves defined over an arbitrary number field $K$ with good reduction outside a given finite set of primes $S$ of $K$ by solving $S$ -unit equations. We give examples of elliptic curves over $\mathbb Q$ and quadratic fields.

Keywords

elliptic curves number fields bad reduction S-unit equations primes quadratic fields

Cite

@article{arxiv.1511.05108,
  title  = {Computing all elliptic curves over an arbitrary number field with prescribed primes of bad reduction},
  author = {Angelos Koutsianas},
  journal= {arXiv preprint arXiv:1511.05108},
  year   = {2015}
}

Comments

19 pages

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