  For a superelliptic curve $\mathcal X$, defined over $\mathbb Q$, let
$\mathfrak p$ denote the corresponding moduli point in the weighted moduli
space. We describe a method how to determine a minimal integral model of
$\mathcal X$ such that: i) the corresponding moduli point $\mathfrak p$ has
minimal weighted height, ii) the equation of the curve has minimal
coefficients. Part i) is accomplished by reduction of the moduli point which is
equivalent with obtaining a representation of the moduli point $\mathfrak p$
with minimal weighted height, as defined in [5], and part ii) by the classical
reduction of the binary forms.
