I was recently working with some ECC crypto and stumbled across the following phrase on the SafeCurves page:
The rational points of a complete Edwards curve are the pairs (x,y) of elements of F_p satisfying the equation; there is no extra "point at infinity".
Normally, if you have a point $G$ on a curve $E$ with order (of the point) $q$, multiplying $qG=0G=\mathcal O$ results in the point at infinity.
But apparently complete Edwards curves don't have said extra point.
So what happens in this case?