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

Title:

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

Creator:

Shparlinski, Igor E

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:d66079c0-88b9-4356-af9b-f29f14d6882d
uuid:d66079c0-88b9-4356-af9b-f29f14d6882d
issn:0011-4642

Subject:

matematika, mathematics, elliptic curve, complex multiplication field, Frobenius discriminant, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

We obtain a conditional, under the Generalized Riemann Hypothesis, lower bound on the number of distinct elliptic curves E over a prime finite field F_{p} of p elements, such that the discriminant D(E) of the quadratic number field containing the endomorphism ring of E over F_{p} 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)., Igor E. Shparlinski., and Obsahuje seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

381-388

Source:

Czechoslovak Mathematical Journal | 2015 Volume:65 | Number:2

Harvested from:

CDK

Metadata only:

false