On the class number divisibility of pairs of quadratic fields obtained from points on elliptic curves

Yoshichika Iizuka; Yutaka Konomi; Shin Nakano

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On the class number divisibility of pairs of quadratic fields obtained from points on elliptic curves

机译：从椭圆曲线上的点获得的一对二次场的类数可除性

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摘要

Let l be the prime 3,5 or 7 and let m be a nonzero integer. We give a method for constructing an infinite family of pairs of quadratic fields Q(D~(1/2)) and Q(mD~(1/2)) with both class numbers divisible by l. Such quadratic fields are parametrized by rational points on a specified elliptic curve.

机译：令l为3,5或7的质数，令m为非零整数。我们给出了一种构造无限类对的二次场对Q（D〜（1/2））和Q（mD〜（1/2））的方法，它们的类数都可被l整除。这样的二次场由指定的椭圆曲线上的有理点参数化。

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来源
《Journal of the Mathematical Society of Japan》 |2016年第2期|899-915|共17页
作者
Yoshichika Iizuka; Yutaka Konomi; Shin Nakano;
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作者单位

Department of Mathematics Gakushuin University Mejiro, Toshima-ku Tokyo 171-8588, Japan;

Department of Mathematics Gakushuin University Mejiro, Toshima-ku Tokyo 171-8588, Japan;

Department of Mathematics Gakushuin University Mejiro, Toshima-ku Tokyo 171-8588, Japan;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类
关键词
class number; quadratic field; elliptic curve;

机译：班级编号;二次场椭圆曲线;

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1. On the class number divisibility of pairs of imaginary quadratic fields [J] . Iizuka Yoshichika Journal of Number Theory . 2018,第期

机译：关于虚拟字段对的类号码
2. An infinite family of pairs of imaginary quadratic fields with both class numbers divisible by five [J] . Miho Aoki, Yasuhiro Kishi Journal of Number Theory . 2017,第期

机译：一个无限的一对一对虚构的二次字段，两个班级都可以被五分层
3. Construction of class fields over imaginary quadratic fields using $y$-coordinates of elliptic curves [J] . Ja Kyung Koo, Dong Hwa Shin Journal of the Korean Mathematical Society . 2013,第4期

机译：使用椭圆曲线的$ y $坐标在虚二次域上构造类场
4. The Elliptic Curve Discrete Logarithm Problem and Equivalent Hard Problems for Elliptic Divisibility Sequences [C] . Kristin E. Lauter, Katherine E. Stange Annual International Workshop on Selected Areas in Cryptography . 2009

机译：椭圆曲线离散对数问题和椭圆分配序列的等效难题
5. The Parity of Analytic Ranks among Quadratic Twists of Elliptic Curves over Number Fields. [D] . Balsam, Nava. 2015

机译：椭圆曲线在数域上的二次扭曲之间的解析秩奇偶性。
6. Colloquium Paper: Parametrizations of elliptic curves by Shimura curves and by classical modular curves [O] . Kenneth A. Ribet, Shuzo Takahashi 1997

机译：座谈会论文：Shimura曲线和by的椭圆曲线参数化经典模曲线
7. A family of infinite pairs of quadratic fields Q (sqrtD) and Q (sqrt-D) whose class numbers are both divisible by 3 [O] . Toru Komatsu 2001

机译：一系列无限成对的二次字段q（ sqrtd）和q（ sqrt-d），其类编号均可被3可分开

On the class number divisibility of pairs of quadratic fields obtained from points on elliptic curves

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