Class fields generated by coordinates of elliptic curves

被引：1

作者：

Jung, Ho Yun ^{[1
]}

Koo, Ja Kyung ^{[2
]}

Shin, Dong Hwa ^{[3
]}

机构：

[1] Dankook Univ, Dept Math, Cheonan Si 31116, Chungnam, South Korea

[2] Korea Adv Inst Sci & Technol, Dept Math Sci, Daejeon 34141, South Korea

[3] Hankuk Univ Foreign Studies, Dept Math, Yongin 17035, Gyeonggi Do, South Korea

来源：

OPEN MATHEMATICS | 2022年 / 20卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

class field theory; complex multiplication; modular functions;

D O I：

10.1515/math-2022-0502

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let K be an imaginary quadratic field different from Q (root-1 ) and Q (root-3). For a nontrivial integral ideal m of K, let K-m be the ray class field modulo m. By using some inequalities on special values of modular functions, we show that a single x-coordinate of a certain elliptic curve generates K-m over K.

引用

页码：1145 / 1158

页数：14

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