  We compute quantum cohomology ring of elliptic $\mathbb{P}^1$ orbifolds via
orbi-curve counting. The main technique is the classification theorem which
relates holomorphic orbi-curves with certain orbifold coverings. The countings
of orbi-curves are related to the integer solutions of Diophantine equations.
This reproduces the computation of Satake and Takahashi in the case of
$\mathbb{P}^1_{3,3,3}$ via different method.
