A relation between embedding degrees and class numbers of binary quadratic forms
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- by San Ling, Enver Ozdemir and Chaoping Xing PDF
- Math. Comp. 83 (2014), 3001-3004 Request permission
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.References
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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
- 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.
- © Copyright 2014 American Mathematical Society
- 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
- MathSciNet review: 3246820