10. The graph of the function $y=a x^{2}+b x+c$ is a downward-opening parabola, with $a, b, c$ all being distinct and taking values in the set $A=$ $\{n|| n \mid \leqslant 5, n \in \mathbf{Z}\}$. Then, the number of such parabolas that pass through the point $(0,-1)$ is $\qquad$.
10. 36 According to the problem, $c=-1$, $a$ can only take any one of $-5, -4, -3, -2$, and $b$ takes one from the remaining 9 integers. By the multiplication principle, we get the result.