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.
Nontorsion Points of Low Height on Elliptic Curves over Quadratic Fields
Park City lectures on elliptic curves over function fields
Rank statistics for a family of elliptic curves over a function field
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