椭圆曲线有理点扭子群的明显分类  

Explicit Classification for Torsion Subgroups of Rational Points of Elliptic Curves

作　　者：邱德荣[1] 张贤科[2] 

机构地区：[1]清华大学高等研究中心,北京100084 [2]清华大学数学科学系,北京100084

出　　处：《数学学报（中文版）》2005年第2期407-412,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(19771052)教育部优秀年轻教师基金资助课题

摘　　要：本文给出了有理数域Q上椭圆曲线E按其偶数阶循环扭子群Etors(Q)的分 类,并给出了Etors(Q)的生成元.这些结果,连同新近Ono在Etors(Q)非循环情形 的结果,完全解决了E含2阶有理点时的分类和参数化问题.We study the classification of elliptic curves E over the rationals Q according to the torsion subgroups Etors(Q). More precisely, we classify those elliptic curves with Etors(Q) being cyclic with even orders. We also give explicit formulas for generators of Etors(Q). These results, together with the recent results of K. Ono for the non-cyclic Eaors (Q), completely solve the problem of the explicit classification and parameterization when E has a rational point of order 2.

关 键 词：椭圆曲线 有理点 扭群 

分 类 号：O156.2[理学—数学] O175.25[理学—基础数学]