A relation between embedding degrees and class numbers of binary quadratic forms

San Ling; Enver Ozdemir; Chaoping Xing

doi:10.1090/S0025-5718-2014-02831-7

A relation between embedding degrees and class numbers of binary quadratic forms

San Ling, Enver Ozdemir, Chaoping Xing

Informatics Institute

Nanyang Technological University

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we describe a relation between the embedding degree of an elliptic curve over a prime field Fp and the inertial degree of the primes above p in a certain ring class field. From this relation, we conclude that the embedding degree divides the class number of a group of binary quadratic forms of a fixed discriminant.

Original language	English
Pages (from-to)	3001-3004
Number of pages	4
Journal	Mathematics of Computation
Volume	83
Issue number	290
DOIs	https://doi.org/10.1090/S0025-5718-2014-02831-7
Publication status	Published - 2014

Bibliographical note

Publisher Copyright:
© 2014 American Mathematical Society.

Keywords

Class number
Elliptic curves
Embedding degree
Imaginary quadratic fields

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10.1090/S0025-5718-2014-02831-7

Cite this

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abstract = "In this paper, we describe a relation between the embedding degree of an elliptic curve over a prime field Fp and the inertial degree of the primes above p in a certain ring class field. From this relation, we conclude that the embedding degree divides the class number of a group of binary quadratic forms of a fixed discriminant.",

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AB - In this paper, we describe a relation between the embedding degree of an elliptic curve over a prime field Fp and the inertial degree of the primes above p in a certain ring class field. From this relation, we conclude that the embedding degree divides the class number of a group of binary quadratic forms of a fixed discriminant.

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KW - Elliptic curves

KW - Embedding degree

KW - Imaginary quadratic fields

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A relation between embedding degrees and class numbers of binary quadratic forms

Abstract

Bibliographical note

Keywords

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