 Formal coordinates on a short Weierstrass curve

For $y^2=x^3+ax+b$, put $t=-x/y$ and $w=-1/y$. Then $x=t/w$, $y=-1/w$, and the curve equation becomesThere is a unique solution $w(t)\in t^{3}K[[t]]$, and points in the kernel of reduction correspond to parameters of positive valuation.