An effective Shafarevich theorem for elliptic curves

Abstract: Let \(K\) be a number field and let \(S\) be a finite set of places of \(K\). We prove that there exist an effectively computable Dedekind domain \(R\subset K\) and an effective constant \(C\), depending only on \(K\) and \(S\), such that for each elliptic curve \(E\) defined over \(K\) with good reduction outside \(S\) there is a globally minimal Weierstrass model of \(E\) over \(\text{Spec}(R)\) with height bounded by \(C\).