Why the total angular momentum of Helium ground state is 0?

Every reference I have seen says that the total angular momentum of helium ground state of is zero.

My question is since the the Hamiltonian $H$ commutes with the total angular momentum $J$ why can we have energy eigenstate of the form $$psi(E,J)=k(E)phi(J)$$ such that we have
$$HK(E)=e_0k(E)$$ $$Jphi(J)=j_0phi(J)$$
such that $e_0$ is the ground state energy and $j_0neq0$