This expression I found in some research paper, which connects quotient of Dedekind eta function and ray class field of conductor N, which in turn gives the value of j-invariants.
For $K=\mathbb Q(i)$ and N=3$ (conductor), the discriminant of the order is -36.
Now, $ j_{1,3}(\tau)=\dfrac{\eta(\tau)^{12}}{\eta(3\tau)^{12}}$, where $\tau=i$. I evaluated this expression in Pari/Gp, and I got the answer in decimals which I found wrong, if some one knows their reply will be of great help