Computing elliptic curves having good reduction everywhere over quadratic fields (Q1598366)

Let \(K\) be a quadratic field, i.e. a quadratic extension of \(\mathbb Q\), with ring of integers \(O_K\). This paper gives an algorithm for finding all elliptic curves with given \(j\)-invariant \(j \in O_K\) and good reduction at every finite place of \(K\). A table of all such curves with rational \(j\)-invariant is given. This contains a correction to an earlier table [see \textit{B. Setzer}, Ill. J. Math. 25, 233--245 (1981; Zbl 0471.14019)].