Gaussian hypergeometric evaluations of traces of Frobenius for elliptic curves

Author:
Catherine Lennon

Journal:
Proc. Amer. Math. Soc. **139** (2011), 1931-1938

MSC (2010):
Primary 11T24, 11G20

DOI:
https://doi.org/10.1090/S0002-9939-2010-10609-3

Published electronically:
November 3, 2010

MathSciNet review:
2775369

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Abstract | References | Similar Articles | Additional Information

Abstract: We present here a formula for expressing the trace of the Frobenius endomorphism of an elliptic curve over satisfying and in terms of special values of Gaussian hypergeometric series. This paper uses methods introduced by Fuselier for one-parameter families of curves to express the trace of Frobenius of as a function of its -invariant and discriminant instead of a parameter, which are more intrinsic characteristics of the curve.

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Additional Information

**Catherine Lennon**

Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139

Email:
clennon@math.mit.edu

DOI:
https://doi.org/10.1090/S0002-9939-2010-10609-3

Received by editor(s):
March 22, 2010

Received by editor(s) in revised form:
May 28, 2010

Published electronically:
November 3, 2010

Additional Notes:
This work was supported by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program.

Communicated by:
Matthew A. Papanikolas

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.