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The Frobenius eigenspace of $-1$ is, by definition, the kernel of the map $π+1$. Typically, this is further restricted to some torsion group $E[ℓ]$, so we are really talking about $E[ℓ] ∩ E[π+1]$, i.e., those points of $E[ℓ]$ such that $π(P)=-P$. If the curve is expressed in Weierstrass form $y^2=f(x)$ (or Montgomery, or similar), letting $P=(x,y)$ we have $...

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