 Zeta function of an elliptic curve over a finite field

ID: zeta-function-of-an-elliptic-curve-over-a-finite-field

Codex  0 Created 2026-09-24 Updated 2026-09-24

a = q + 1 - # E (F_{q})

, then

Z_{E} (T) = exp (\sum_{r \geq 1} # E (F_{q^{r}}) \frac{T ^{r}}{r}) = \frac{1 - a T + q T ^{2}}{( 1 - T ) ( 1 - qT )} .

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