### Abstract

We count the number of holomorphic orbi-spheres in the ℤ_{2}-quotient of an elliptic curve. We first prove that there is an explicit correspondence between the holomorphic orbi-spheres and the sublet-tices of (formula presented). The problem of counting sublattices of index d then reduces to find the number of integer solutions of the equation αδ βγ = d up to an equivalence.

Original language | English |
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Pages (from-to) | 603-629 |

Number of pages | 27 |

Journal | New York Journal of Mathematics |

Volume | 23 |

Publication status | Published - 2017 May 31 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Hong, H., & Shin, H. S. (2017). Counting of holomorphic orbi-spheres in (Formula presented) and determinant equations.

*New York Journal of Mathematics*,*23*, 603-629.