  Let $C$ be a hyperelliptic curve of genus $g\geq 1$ over a number field $K$
with good reduction outside a finite set of places $S$ of $K$. We prove that
$C$ has a Weierstrass model over the ring of integers of $K$ with height
effectively bounded only in terms of $g$, $S$ and $K$. In particular, we obtain
that for any given number field $K$, finite set of places $S$ of $K$ and
integer $g\geq 1$ one can in principle determine the set of $K$-isomorphism
classes of hyperelliptic curves over $K$ of genus $g$ with good reduction
outside $S$.
