Elliptic-curve point count over a finite field
= Elliptic-curve point count over a finite field
If $\alpha,\beta$ are the roots of $T^2-aT+q$, where $a=q+1-\#E(\mathbb F_q)$, then
$$
\#E(\mathbb F_{q^r})=q^r+1-\alpha^r-\beta^r.
$$
= Elliptic-curve point count over a finite field
If $\alpha,\beta$ are the roots of $T^2-aT+q$, where $a=q+1-\#E(\mathbb F_q)$, then
$$
\#E(\mathbb F_{q^r})=q^r+1-\alpha^r-\beta^r.
$$