For the hyperbola $$H: x^2 - y^2 = 1$$ and the ellipse $$E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$, $$a > b > 0$$, let the
(1) eccentricity of E be reciprocal of the eccentricity of H, and
(2) the line $$y = \sqrt{\frac{5}{2}}x + K$$ be a common tangent of E and H.
Then $$4(a^2 + b^2)$$ is equal to