  In this work, we consider a quasi-homogeneous, corank $1$, finitely
determined map germ $f$ from $(\mathbb{C}^2,0)$ to $(\mathbb{C}^3,0)$. We
consider the invariants $m(f(D(f))$ and $J$, where $m(f(D(f))$ denotes the
multiplicity of the image of the double point curve $D(f)$ of $f$ and $J$
denotes the number of tacnodes that appears in a stabilization of the
transversal slice curve of $f(\mathbb{C}^2)$. We present formulas to calculate
$m(f(D(f))$ and $J$ in terms of the weights and degrees of $f$.
