In mathematics, Hasse's theorem on elliptic curves bounds the number of points on an elliptic curve over a finite field. If N is the number of points on an elliptic curve E over a finite field of q elements, then

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The result is due to Helmut Hasse; it had been a conjecture of Emil Artin. It is equivalent to the determination of the absolute value of the roots of the local zeta-function of E.