Ramification index of a prime ideal ($e_{\mathfrak{p}}$)

If $\mathfrak{p}$ is a prime ideal of ${\mathcal{O}}_K$ above a rational prime $p$, its ramification index is the exponent $e_{\mathfrak{p}}$ of $\mathfrak{p}$ in the factorization of $(p)$. Equivalently, for the normalized ideal valuation, $e_{\mathfrak{p}}=v_{\mathfrak{p}}(p)$.