Small discriminants of complex multiplication fields of elliptic curves over finite fields

被引：0

作者：

Shparlinski, Igor E. ^{[1
]}

机构：

[1] Univ New S Wales, Dept Pure Math, Sch Math & Stat, Sydney, NSW 2052, Australia

来源：

CZECHOSLOVAK MATHEMATICAL JOURNAL | 2015年 / 65卷 / 02期

关键词：

elliptic curve; complex multiplication field; Frobenius discriminant; REDUCTIONS;

D O I：

10.1007/s10587-015-0183-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain a conditional, under the Generalized Riemann Hypothesis, lower bound on the number of distinct elliptic curves E over a prime finite field of p elements, such that the discriminant D(E) of the quadratic number field containing the endomorphism ring of E over is small. For almost all primes we also obtain a similar unconditional bound. These lower bounds complement an upper bound of F. Luca and I.E. Shparlinski (2007).

引用

页码：381 / 388

页数：8

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