Let \( E_1 : \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1, \ a > b. \) Let \( E_2 \) be another ellipse such that it touches the end points of major axis of \( E_1 \) and the foci of \( E_2 \) are the end points of minor axis of \( E_1 \). If \( E_1 \) and \( E_2 \) have same eccentricities, then its value is:
