A relation between embedding degrees and class numbers of binary quadratic forms
Authors:
San Ling, Enver Ozdemir and Chaoping Xing
Journal:
Math. Comp. 83 (2014), 3001-3004
MSC (2010):
Primary 11R11, 11R29, 11G15, 11G05
DOI:
https://doi.org/10.1090/S0025-5718-2014-02831-7
Published electronically:
May 9, 2014
MathSciNet review:
3246820
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
MR Author ID:
264368
Email:
xingcp@ntu.edu.sg
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
