Polarization degree of a polarized order (awaiting review)

Let $(O,\mu)$ be a polarized quaternion order. The polarization degree $\deg(\mu)$ is the square-free part of the integer $\operatorname{nrd}(\mu)/\operatorname{discrd}(O)$. Here, $\operatorname{nrd} : B \to \Q$ is the reduced norm, and $\operatorname{discrd}(O)$ is the reduced discriminant of $O$.