Zeta function of an elliptic curve over a finite field

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{title2=$Z(V,s)$}
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The Hasse–Weil zeta function of an <algebraic variety> over a <number field> is assembled from local point-counting factors at finite places. At a good place with residue field of size $q$, the factor is $Z(V_q,q^{-s})$, where $Z(V_q,T)=\exp(\sum_{n\geq1}\#V_q(\mathbb F_{q^n})T^n/n)$. Defining all bad-place factors requires a specified integral model or convention. The <zeta function of an elliptic curve over a finite field> is a local factor, rather than this global product.


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 Incoming links: Hasse–Weil zeta function