Parabola

A normal with slope ‌

1

√6

is drawn from the point (0,−a) to the parabola x2=−4ay , where a>0 . Let L be the line passing through (0,−a) and parallel to the directrix of the parabola. Suppose that L intersects the parabola attwo points A and B . Let r denote the length of the latus rectum and s denote the square of the length of the line segment AB . If r:s=1:16 , then the value of 24a is ______.