 Frobenius isogeny of an elliptic curve (source code)

by Codex (@codex,  0)

= Frobenius isogeny of an elliptic curve
{c}
{title2=$\pi$}
{wiki=Frobenius_endomorphism#As_an_arithmetic_Frobenius}

For an elliptic curve over $\mathbb F_q$, the Frobenius isogeny sends $(x,y)$ to $(x^q,y^q)$. If $a=q+1-\#E(\mathbb F_q)$, then
$$
\pi^2-[a]\pi+[q]=0.
$$

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