Why does the embedding of an elliptic curve in $\Bbb{CP}^2$ look like a torus?

Question

Consider a general elliptic curve of the form $y^2=x^3+ax+b$, where $a,b\in\Bbb{C}$. These set of notes say that embedding this curve in $\Bbb{CP}^2$ make the zero set look like a torus. I am looking for an explanation of this. Thanks!