AMC 12 2003a Problem 9

A set $S$ of points in the $xy$-plane is symmetric about the origin, both coordinate axes, and the line $y=x$. If $(2,3)$ is in $S$, what is the smallest number of points in $S$?

$\mathrm{(A) \ } 1 \mathrm{(B) \ } 2 \mathrm{(C) \ } 4 \mathrm{(D) \ } 8 \mathrm{(E) \ } 16$