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I have the elliptic curve $E: y^2=x^3+x$ defined over a field $F_q$ with $q=p^2$ for a certain prime $p$, and want to calculate the $l$-torsion points, or in other words $E[l]$, for an integer $l$ (probably a prime different from $p$.)

I have the elliptic curve $E: y^2=x^3+x$ defined over a field $F_q$ with $q=p^2$ for a certain prime $p$, and want to calculate the $l$-torsion points, or in other words $E[l]$, for an integer $l$ (probably a prime different from $p$.)