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arXiv · 1511.05108

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

Angelos Koutsianas
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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.

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Angelos Koutsianas. 2015-11-16. Computing all elliptic curves over an arbitrary number field with prescribed primes of bad reduction. https://arxiv.org/abs/1511.05108

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