In the Page 333 of the book “Elliptic curves number theory and cryptogarphy” Lawrence C. Washington.
Given $\tau_i\in H$(up-half plane),and $j(\tau_i)$ is the j-invariant of the lattice $\mathbb Z_\tau+\mathbb Z$. Compute the values of $j(\tau_i)$ and then can form the polynomial $(x-j(\tau_1))(x-j(\tau_2))(x-j(\tau_3))(x-j(\tau_4))$.
My question is why $j(\tau_i)\in\mathbb C$, but the coefficiets are true integers? And, how to compute them?