Abstract
We present here a formula for expressing the trace of the Frobenius endomorphism of an elliptic curve E over F q satisfying j(E) ≠ 0,1728 and q ≡ 1 (mod 12) 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 E as a function of its j-invariant and discriminant instead of a parameter, which are more intrinsic characteristics of the curve.
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