 Elliptic-curve point count over a finite field

ID: elliptic-curve-point-count-over-a-finite-field

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

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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