A normal with slope $\frac{1}{\sqrt{6}}$ is drawn from the point (0, – α) to the parabola x² = – 4ay, where a > 0. Let L be the line passing through (0, – α) and parallel to the directrix of the parabola. Suppose that L intersects the parabola at two 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 ____.