  Let $K$ be a number field, ${\mathcal O}_K$ its ring of integers, and $f(x,
y) \in {\mathcal O}_K[x, y]$ a binary form with integer coefficents. For any
given prime $p \in {\mathcal O}_K$ we determine explicitly a binary form $g$
(resp. $\bar f$), $\mbox{GL}_2 (K)$-equivalent to $f$ which is semistable over
the local field $K_p$ (resp. the global field $K$). Moreover, if $\xi(f) $ is
the corresponding moduli point in the weighted projective space
${\mathbb{WP}}_{\mathbf w}^n (K)$ for a strictly semistable binary form $f$, we
determine the weighted moduli height $\mathfrak{h} (\xi(f))$ for $d=4, 6, 8,
10$.
