Let us assume a cartesian space, where the directions are given by $\hat{i},\hat{j},\hat{k}$. 
The degree of freedom of a rigid body is $6$. The first three correspond to the position coordinates $\left(x,y,z\right)$, and the next three correspond to the velocity coordinates $\left(\dot{x},\dot{y},\dot{z}\right)$. Suppose I know the angular momentum of this body along $\hat{i},\hat{j},\hat{k}$. I also know the total energy of this body. Can I say that having knowledge of these four quantities reduces the degree of freedom to $2$?