If $K$ is a local field and $L/K$ is a finite extension, then the valuation $v_K$ can be extended uniquely to a valuation $v_L$ of $L$ such that $v_L$ restricted to $K$ is equal to $v_K$. This is one of the fundamental theorems about local fields. If $L/K$ is finite, $v_L$ is given by $$v_L (x)=\frac{1}{n}v_K(N_{L/K}(x)),$$ for every $x\in L$, where $n=[L:K]$ and $N_{L/K}$ is the norm.
This is not discrete valuation in general. For example, $v_L(\sqrt{-3})=\frac{1}{2}ord_3(3)=\frac{1}{2}$ in an extension $L=\Bbb{Q}_3(\sqrt{-3})/K=\Bbb{Q}_3$.
But when $L/K$ is unratified(Uniformizer does not change under field extension), why is $v_L$ discrete valuation(In other word, why $v_L(x)\in \Bbb{Z}$ ?)
Background: Sorry to ask a basic question about extension of valuation, but this question's comments made me realize that I didn't understand the material and this is separated one from the linked page.
Does $2y^2=4+17x^4$ have solutions in $\Bbb{Q}_2(\sqrt{-3})$?,