Explicit Classification for Torsion Subgroups of Rational Points of Elliptic Curves

作     者：De Rong QIU Center for Advanced Study, Tsinghua University, Beijing 100084. P. R. China Xian Ke ZHANG Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China 

作者机构：Center for Advanced Study Tsinghua University Beijing P. R. China Department of Mathematical Sciences Tsinghua University Beijing P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2002年第18卷第3期

页      面：539-548页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Project supported by the National Natural Science Foundation of China (Grant No. 19771052) 

主　　题：Elliptic curve Rational point Torsion group Mordell group Parameterization 

摘      要：We study the classification of elliptic curves E over the rationals Q according to the torsion subgroups E_(tors)(Q). More precisely, we classify those elliptic curves with E_(tors)(Q) being cyclic with even orders. We also give explicit formulas for generators of E_(tors)(Q). These results, together with the recent results of K. Ono for the non-cyclic E_(tors)(Q), completely solve the problem of the explicit classification and parameterization when E has a rational point of order 2.