On the Group of Automorphisms of Shimura Curves and Applications
نویسنده
چکیده
Let VD be the Shimura curve over Q attached to the indefinite rational quaternion algebra of discriminant D. In this note we investigate the group of automorphisms of VD and prove that, in many cases, it is the Atkin–Lehner group. Moreover, we determine the family of bielliptic Shimura curves ðover Q and over QÞ and we use it to study the set of rational points on VD over quadratic fields. Finally, we obtain explicit equations of elliptic Atkin–Lehner quotients of VD. Mathematics Subject Classifications (2000). 11G18, 14G35.
منابع مشابه
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