Size of $E$ over $\mathbb{F}_p$ contains $p+1$ points
For every $y \in \mathbf F_p$, there is a unique $x \in \mathbf F_p$ such that $(x,y)$ is on the curve, namely $x = \phi^{-1}(y^2)$, where $\phi : x \mapsto x^3+1$. Adding the point at infinity, that gives $p+1$ points.