Division polynomials
= Division polynomials
{title2=$\psi_n$}
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= Division polynomial of an elliptic curve
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= Division polynomials of an elliptic curve
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The division polynomial $\psi_n$ has roots at the nonzero $n$-torsion points of an elliptic curve, with the two points sharing an $x$-coordinate represented by the same root when $n$ is odd.