Rational homotopy groups of the connected sum of two complex projective planes (${\pi }_2\otimes \mathbb{Q}={\pi }_3\otimes \mathbb{Q}={\mathbb{Q}}^2$)

The Sullivan model of the connected sum of two complex projective planes has two generators in each of degrees two and three, and none elsewhere. Its rational homotopy groups are therefore exactly the displayed two copies of ${\mathbb{Q}}^2$, with all other positive degrees zero.