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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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


Authors: San Ling, Enver Ozdemir and Chaoping Xing
Journal: Math. Comp.
MSC (2010): Primary 11R11, 11R29, 11G15, 11G05
Published electronically: May 9, 2014
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Abstract: In this paper, we describe a relation between the embedding degree of an elliptic curve over a prime field $ \mathbb{F}_p$ 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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Additional Information

San Ling
Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore
Email: lingsan@ntu.edu.sg

Enver Ozdemir
Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore
Address at time of publication: Informatics Institute, Istanbul Technical University, 34469 Istanbul, Turkey
Email: ozdemiren@itu.edu.tr

Chaoping Xing
Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore
Email: xingcp@ntu.edu.sg

DOI: http://dx.doi.org/10.1090/S0025-5718-2014-02831-7
PII: S 0025-5718(2014)02831-7
Keywords: Imaginary quadratic fields, class number, elliptic curves, embedding degree
Received by editor(s): December 11, 2012
Received by editor(s) in revised form: April 1, 2013
Published electronically: May 9, 2014
Additional Notes: This research was partially supported by the Singapore National Research Foundation Competitive Research Program grant NRF-CRP2-2007-03 and the Singapore Ministry of Education under Research Grant T208B2206.
Article copyright: © Copyright 2014 American Mathematical Society