Gaussian hypergeometric evaluations of traces of Frobenius for elliptic curves

DOI10.1090/S0002-9939-2010-10609-3zbMATH Open1281.11104arXiv1003.4421MaRDI QIDQ3005603

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Publication date: 9 June 2011

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Abstract: We present here a formula for expressing the trace of the Frobenius endomorphism of an elliptic curve $E$ over $mathbb{F}_q$ satisfying $j(E)eq0,1728$ and $qequiv1pmod12$ in terms of special values of Gaussian hypergeometric series. This paper uses methods introduced in Fuselier's work for one parameter families of curves to express the trace of Frobenius of $E$ as a function of its $j$-invariant and discriminant instead of a parameter, which are more intrinsic characteristics of the curve.

Full work available at URL: https://arxiv.org/abs/1003.4421

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