Let $E$ be an elliptic curve defined over ${Q}$. The torsion subgroup of $E$ over the compositum of all quadratic extensions of ${Q}$ was studied by Michael Laska, Martin Lorenz, and Yasutsugu Fujita. Laska and Lorenz described a list of $31$ possible groups and Fujita proved that the list of $20$ different groups is complete. In this talk, we will generalize the results of Laska, Lorenz and Fujita to the elliptic curves defined over a quadratic cyclotomic field i.e. $Q(i)$ and $Q(\sqrt{-3})$.