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

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.

arXiv comment19 pages