Let $(\mathbb{K},\mathfrak{M}_{\mathbb{K}})$ be a global field. Let $0<m_{1}<\dots<m_{r}$ be integer numbers with $\gcd(m_{1},\dots,m_{r})=1$, and $p_{1},\dots,p_{r}\in\mathbb{K}^{\times}$. Let $\varphi\colon\mathbb{T}\to\mathbb{P}^{r}$ be the map given by $\varphi(t)=(1:p_{1}t^{m_{1}}:\dots:p_{r}t^{m_{r}})$, $Y$ the closure of the image of $\varphi$, and ${\overline{L}}=\varphi^{*}{\overline{{\mathcal{O}}(1)}}$, where ${\overline{{\mathcal{O}}(1)}}$ is equipped with the Fubini-Study metric for the Archimedean places and with the canonical metric for the non-Archimedean places. For $v\in\mathfrak{M}_{K}$, set

$\displaystyle q_{v}=\begin{cases}1+\sum_{j=1}^{r}|p_{j}|_{v}^{2}z^{m_{j}},&\text{ if }v\text{ is Archimedean},\\ 1+\sum_{j=1}^{r}p_{j}z^{m_{j}},&\text{ if }v\text{ is not Archimedean}.\end{cases}$

Let $\{\xi_{v,i}\}\subset{\overline{\mathbb{K}}}^{\times}$ be the set of roots of $q_{v}$ and, for each $i$, let $\ell_{v,i}\in\mathbb{N}$ denote the multiplicity of $\xi_{v,i}$. Then

$$\operatorname{h}_{{\overline{L}}}(Y)=\sum_{v|\infty}n_{v}\bigg(\frac{1}{2}\sum_{i}\ell_{v,i}^{2}+\frac{1}{2}\sum_{i<j}\ell_{v,i}\ell_{v,j}\frac{\xi_{v,i}+\xi_{v,j}}{\xi_{v,i}-\xi_{v,j}}(\log(-\xi_{v,i})-\log(-\xi_{v,j}))\bigg)\\ +\sum_{v\nmid\infty}n_{v}\bigg(\sum_{i<j}\ell_{v,i}\ell_{v,j}\log(\max\{1,|\xi_{v,i}|_{v}/|\xi_{v,j}|_{v}\})\bigg).$$