In the above setting, one has :

	$\displaystyle\deg_{{\mathcal{O}}_{\mathbb{P}(E)}(1)}(\mathbb{P}(E))$	$\displaystyle=\sum_{{i_{0},\dots,i_{r}\in{\mathbb{N}}}\atop{i_{0}+\dots+i_{r}=n}}a_{0}^{i_{0}}\dots a_{r}^{i_{r}}$
	$\displaystyle\operatorname{h}_{{\overline{{\mathcal{O}}_{\mathbb{P}(E)}(1)}}}(\mathbb{P}(E))$	$\displaystyle=\left(\sum_{{i_{0},\dots,i_{r}\in{\mathbb{N}}}\atop{i_{0}+\dots+i_{r}=n+1}}a_{0}^{i_{0}}\dots a_{r}^{i_{r}}\right)\operatorname{h}_{{\overline{{\mathcal{O}}_{\mathbb{P}^{n}}(1)}}}(\mathbb{P}^{n})$
		$\displaystyle\kern 99.58464pt+\sum_{{i_{0},\dots,i_{r}\in{\mathbb{N}}}\atop{i_{0}+\dots+i_{r}=n}}a_{0}^{i_{0}}\dots a_{r}^{i_{r}}A_{n,r}(i_{0},\dots,i_{r}),$

where $A_{n,r}(i_{0},\dots,i_{r})=\sum_{m=0}^{r}(i_{m}+1)\sum_{j=i_{m}+2}^{n+r+1}\frac{1}{2j}$. In particular, the height of $\mathbb{P}(E)$ is a positive rational number.