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Hasse theorem for elliptic curves

{title2=$Z_E(T)$}
{wiki=Hasse–Weil_zeta_function}

If $a=q+1-\#E(\mathbb F_q)$, then
$$
Z_E(T)=\exp\left(\sum_{r\geq1}\#E(\mathbb F_{q^r})\frac{T^r}{r}\right)
=\frac{1-aT+qT^2}{(1-T)(1-qT)}.
$$


Zeta function of an elliptic curve over a finite field

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 125 / 1 / b / Solution

Zeta function of an elliptic curve over a finite field ( $Z_{E} (T)$ )

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Zeta function of an elliptic curve over a finite field (ZE​(T))

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