Discriminants of complex multiplication fields of elliptic curves over finite fields

被引：6
作者：
Luca, Florian [1 ]
Shparlinski, Igor E.
机构：
[1] Univ Nacl Autonoma Mexico, Inst Matemat, Morelia 58089, Michoacan, Mexico
[2] Macquarie Univ, Dept Comp, Sydney, NSW 2109, Australia
来源：
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2007年 / 50卷 / 03期
关键词：
D O I：
10.4153/CMB-2007-039-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that, for most of the elliptic curves E over a prime finite field F-p of p elements, the discriminant D(E) of the quadratic number field containing the endomorphism ring of E over F-p is sufficiently large. We also obtain an asymptotic formula for the number of distinct quadratic number fields generated by the endomorphism rings of all elliptic curves over F-p.
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页码：409 / 417
页数：9
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