An exceptional isomorphism between modular curves of level 13

被引：18

作者：

Baran, Burcu ^{[1
]}

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

来源：

JOURNAL OF NUMBER THEORY | 2014年 / 145卷

关键词：

Elliptic curve; Galois representations; Modular curve; Non-split Cartan group;

D O I：

10.1016/j.jnt.2014.05.017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this note we use representation theory to compute an explicit equation over Q for the modular curve X-ns(13) associated to the normalizer of a non-split Cartan subgroup of level 13. We also prove that the same equation defines the modular curve X-s(13) associated to the normalizer of a split Cartan subgroup of level 13. Hence, these two modular curves are isomorphic over Q. This isomorphism does not seem to have a "modular" explanation. For instance, X-s(13)(Q) contains a cusp but X-ns(13)(Q) does not. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：273 / 300

页数：28

共 10 条

[1]

Baran B., 2012, PREPRINT

[2] Normalizers of non-split Cartan subgroups, modular curves, and the class number one problem [J].