If the points of intersection of two distinct conics \( x^2 + y^2 = 4b \) and \( \dfrac{x^2}{16} + \dfrac{y^2}{b^2} = 1 \) lie on the curve \( y^2 = 3x^2 \), then \( 3\sqrt{3} \) times the area of the rectangle formed by intersection points is __________.
