Elliptic curves with isomorphic groups of points over finite field extensions

被引：4

作者：

Heuberger, Clemens ^{[1
]}

Mazzoli, Michela ^{[1
]}

机构：

[1] Alpen Adria Univ Klagenfurt, Klagenfurt, Austria

来源：

JOURNAL OF NUMBER THEORY | 2017年 / 181卷

基金：

奥地利科学基金会;

关键词：

Elliptic curve; Rational points; Finite field; Field extension; Isomorphism; Isogeny; Valuation;

D O I：

10.1016/j.jnt.2017.05.028

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Consider a pair of ordinary elliptic curves E and E' defined over the same finite field F-q. Suppose they have the same number of F-q-rational points, i.e. vertical bar E(F-q)vertical bar = vertical bar E'(F-q)vertical bar. In this paper we characterise for which finite field extensions F(q)k k >= 1 (if any) the corresponding groups of F(q)k-rational points are isomorphic, i.e. E(F(q)k) congruent to (F(q)k). (C) 2017 The Author(s). Published by Elsevier Inc.

引用

页码：89 / 98

页数：10