| Selmer groups and Mordell-Weil groups of two types of elliptic curves |
| |
| 作者姓名： | QIU Derong ZHANG Xianke |
| |
| 作者单位： | Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China,Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China |
| |
| 摘 要： | Let £: y2 = x(x ± p)(x ± q) be two types of elliptic curves, where p and q are twin prime num-
bers. The Selmer groups, the sum of rank(E) and dimension of Shafarevich-Tate group (2-torsion subgroup) of E are determined, and the Mordell-Weil group and Shafarevich-Tate group of E are exhibited explicitly in many cases. Besides, the Kodaira symbol and the torsion parts of E are also obtained.
|
| 关 键 词： | elliptic curve Mordell-Weil group Selmer group rational point. |
Selmer groups and Mordell-Weil groups of two types of elliptic curves |
| |
| QIU Derong,ZHANG Xianke.Selmer groups and Mordell-Weil groups of two types of elliptic curves[J].Progress in Natural Science,2000,10(12):946-949. |
| |
| Authors: | QIU Derong ZHANG Xianke |
| |
| Institution: | Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China,Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China |
| |
| Abstract: | Let £: y2 = x(x ± p)(x ± q) be two types of elliptic curves, where p and q are twin prime num-
bers. The Selmer groups, the sum of rank(E) and dimension of Shafarevich-Tate group (2-torsion subgroup) of E are determined, and the Mordell-Weil group and Shafarevich-Tate group of E are exhibited explicitly in many cases. Besides, the Kodaira symbol and the torsion parts of E are also obtained. |
| |
| Keywords: | elliptic curve Mordell-Weil group Selmer group rational point |
|
| 点击此处可从《自然科学进展(英文版)》浏览原始摘要信息 |
| 点击此处可从《自然科学进展(英文版)》下载免费的PDF全文 |
