Values for $A$, $B$, $C$, and $D$ are to be selected from $\{1,2,3,4,5,6\}$ without replacement (i. e., no two letters have the same value). How many ways are there to make such choices so that the two curves $y=Ax^2+B$ and $y=Cx^2+D$ intersect? (The order in which the curves are listed does not matter; for example, the choices $A=3$, $B=2$, $C=4$, $D=1$ is considered the same as the choices $A=4$, $B=1$, $C=3$, $D=2$.)