We construct an elliptic curve over $\mathbf{Q}(i)$ with torsion group $\mathbf{Z}/4\mathbf{Z} \times \mathbf{Z}/4\mathbf{Z}$ and rank equal to 7 and a family of elliptic curves with the same torsion group and rank $\ge 2$.

We count orientable small covers over cubes. We also get estimates for $O_{n}/R_{n}$, where $O_{n}$ is the number of orientable small covers and $R_{n}$ is the number of all small covers over an $n$-cube up to the Davis-Januszkiewicz equivalence.