在本篇論文，我們提供了一個方法來計算超橢圓志村曲線的方程式。
我們把志村曲線上的模形式想成是Borchers形式，由於integer programming問題的可解性,使我們可以構造足夠多的 eta products。藉由Borcherds提升，我們可以在指定Borcherds形式上零點和極點的前提下，得到我們需要的Borcherds形式。

更進一步,藉著Schofer和Kudla-Yang公式和志村互反定律的使用，我們可以用來決定所有超橢圓志村曲線的方程式。另外,我們也可以用此方法來決定這些曲線上CM點的座標。

We introduce a method for presenting explicit models of
hyperelliptic Shimura curves attached to indefinite quaternion algebras over the rational field and Atkin-Lehner quotients of them. It utilizes Borcherds forms,
Schofer's norm formula, Kudla-Yang's formula for Whittaker functions, eta products and the realization of modular forms on Atkin-Lehner quotient of Shimura curves as Borcherds forms. The solvability of integer
programming problems fatefully make us to produce sufficiently many eta products, which makes it possible to manufacture Borcherds forms with desired divisors in practice. Furthermore, combining with Shimura
reciprocity law and explicit covers between Shimura curves, we could determine defining equations of hyperelliptic Shimura curves and coordinates of CM-points on these curves. We work out several examples and provide a list of equations of Shimura curves and coordinates of CM-points on these curves obtained by our method. Some of these equations
are known by the works of many authors in the past decade, and about half of them are new.

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