Number fields generated by the 3-torsion points of an elliptic curve

被引：10

作者：

Bandini, Andrea ^{[2
]}

Paladino, Laura ^{[1
]}

机构：

[1] Univ Calabria, Dipartimento Matemat, I-87036 Arcavacata Di Rende, CS, Italy

[2] Univ Parma, Dipartimento Matemat, I-43124 Parma, Italy

来源：

MONATSHEFTE FUR MATHEMATIK | 2012年 / 168卷 / 02期

关键词：

Elliptic curves; Torsion points; DIVISIBILITY;

D O I：

10.1007/s00605-012-0377-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let be an elliptic curve, m a positive number and the m-torsion subgroup of . Let P (1) = (x (1), y (1)), P (2) = (x (2), y (2)) form a basis of . We prove that in general. For the case m = 3 we provide a description of all the possible extensions in terms of generators, degree and Galois groups.

引用

页码：157 / 181

页数：25

共 16 条

[1]

[Anonymous], 1985, ANN MATH STUDIES

[2]

[Anonymous], 2001, LECT NOTES MATH

[3] Three-descent and the Birch and Swinnerton-Dyer conjecture [J].