Ordinary elliptic curves of high rank over (F)over-barp(x) with constant j-invariant

被引：6
|
作者：
Bouw, II
Diem, C
Scholten, J
机构：
[1] Univ Duisburg Essen, Inst Expt Math, D-45326 Essen, Germany
[2] Katholieke Univ Leuven, COSIC, ESAT, B-3001 Louvain, Belgium
来源：
MANUSCRIPTA MATHEMATICA | 2004年 / 114卷 / 04期
关键词：
D O I：
10.1007/s00229-004-0476-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that under the assumption of Artin's Primitive Root Conjecture, for all primes p there exist ordinary elliptic curves over (F) over bar (p)(x) with arbitrarily high rank and constant j-invariant. For odd primes p, this result follows from a theorem we prove which states that whenever p is a generator of (Z/lZ)*/<-1> (l an odd prime) there exists a hyperelliptic curve over (D) over bar (p) whose Jacobian is isogenous to a power of one ordinary elliptic curve.
引用
收藏
页码：487 / 501
页数：15
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