Elliptic-curve point count over a finite field

If

α, β

are the roots of

T^{2} - a T + q

, where

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

, then

# E (F_{q^{r}}) = q^{r} + 1 - α^{r} - β^{r} .

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Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 125 / 1 / b / Solution
Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 125 / 2 / b / Solution

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