7. Given that the parabola $C$ has the center of the ellipse $E$ as its focus, the parabola $C$ passes through the two foci of the ellipse $E$, and intersects the ellipse $E$ at exactly three points. Then the eccentricity of the ellipse $E$ is $\qquad$
7. $\frac{2 \sqrt{5}}{5}$.
Assume the equation of the ellipse $E$ is
$$
\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b>0) \text {. }
$$

Since the parabola $C$ passes through the two foci of the ellipse $E$, the equation of the parabola $C$ is
$$
x^{2}=2 c y+c^{2}\left(c=\sqrt{a^{2}-b^{2}}\right) .
$$

Given that the parabola $C$ intersects the ellipse $E$ at exactly three points, we have $c=2 b$.

Therefore, the eccentricity of the ellipse $E$ is $\frac{c}{a}=\frac{2}{\sqrt{5}}=\frac{2 \sqrt{5}}{5}$.