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

Ling, San; Ozdemir, Enver; Xing, Chaoping

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

A relation between embedding degrees and class numbers of binary quadratic forms
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by San Ling, Enver Ozdemir and Chaoping Xing;

Math. Comp. 83 (2014), 3001-3004

DOI: https://doi.org/10.1090/S0025-5718-2014-02831-7

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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