Number of points on elliptic curve $E:y^2 = x^3 +1$ over $\mathbb{F}_q$ with $q = p^n$ and $p\equiv 1 \mod 3$ for $p>3$

Question

I am trying to find a general formula for the number of points on the elliptic curve $E:y^2 = x^3 +1$ over $\mathbb{F}_q$ with $q = p^n$ and $p\equiv 1 \mod 3$ for $p>3$. There should be enough literature on this which uses zeta functions etc. However, I can't seem to find a good reference on this. I also tried something myself: the endomorphism ring of $E$ is $\mathbb{Z}[\zeta_3]$ and if we denote $\pi$ by the Frobenius endomorphism we know that $\pi\bar{\pi} = q$. Once we know how to write $\pi$ in this endomorphism ring we can calculate the number of points using some old results. Any idea how to continue/find references on this?