Local minimal discriminant of an elliptic curve (reviewed)

Let $E$ be an elliptic curve defined over a number field $K$, and $\mathfrak{p}$ a prime of $K$. The local minimal discriminant of $E$ is the ideal $\mathfrak{p}^e$ where $e$ is is the valuation of the discriminant of a local minimal model for $E$ at $\mathfrak{p}$.