examples of torsion subgroups of elliptic curves

Mazur’s theorem shows that given an elliptic curve defined over the rationals, the only possible torsion subgroups are the following:

\\mathbb{Z}/N\\mathbb{Z}\\quad\\text{ with }1<N<11\\text{ or }N=12

\\mathbb{Z}/2\\mathbb{Z}\\oplus\\mathbb{Z}/2N\\mathbb{Z}\\text{ with }0<N<5

Here we show examples of curves with the torsion subgroups mentioned above:

随便看

数学辞典收录了18232条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。