Computing all elliptic curves over an arbitrary number field with prescribed primes of bad reduction (1511.05108v1)

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.