The division polynomial has roots at the nonzero -torsion points of an elliptic curve, with the two points sharing an -coordinate represented by the same root when is odd.
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Division polynomials are mathematical constructs used primarily in the context of elliptic curves and their associated algebraic geometry. They serve an important role in the theory of elliptic curves, particularly regarding the addition of points on these curves. ### Context of Division Polynomials In the study of elliptic curves, a division polynomial is a polynomial that helps in defining points on the curve that are rational multiples of a given point.