Torsion of elliptic curves in the compositum of Dihedral fields

被引：1

作者：

Chou, Michael ^{[1
]}

Karker, Mary Leah ^{[1
]}

机构：

[1] Providence Coll, Math & Comp Sci, 1 Cunningham Sq, Providence, RI 02918 USA

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2023年 / 19卷 / 02期

关键词：

Elliptic curve; rational points; dihedral fields; POINTS; EXTENSIONS; SUBGROUPS;

D O I：

10.1142/S1793042123500185

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let E/Q be an elliptic curve. Let Q(G) denote the compositum of all fields with Galois group G over Q. We classify the possible torsion subgroups of E over Q(Dn) for n not divisible by 3 or 4, where D-n is the dihedral group on a regular n-gon. We also obtain upper bounds for the torsion of E over Q(G) for various semi-direct products G = F-q(zeta(p)) (sic) Z/pZ by way of classifications of torsion over Q(Z/pqZ).

引用

页码：389 / 408

页数：20

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