  We count the number of holomorphic orbi-spheres in the
$\mathbb{Z}_2$-quotient of an elliptic curve. We first prove that there is an
explicit correspondence between the holomorphic orbi-spheres and the
sublattices of $\mathbb{Z} \oplus \mathbb{Z} \sqrt{-1} (\subset \mathbb{C})$.
The problem of counting sublattices of index $d$ then reduces to find the
number of integer solutions of the equation $\alpha \delta - \beta \gamma = d$
up to an equivalence.
