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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
收藏
页码：89 / 98
页数：10
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