Beyond two criteria for supersingularity: coefficients of division polynomials
Christophe Debry (2014)
Journal de Théorie des Nombres de Bordeaux
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Let be a cubic, monic and separable polynomial over a field of characteristic and let be the elliptic curve given by . In this paper we prove that the coefficient at in the –th division polynomial of equals the coefficient at in . For elliptic curves over a finite field of characteristic , the first coefficient is zero if and only if is supersingular, which by a classical criterion of Deuring (1941) is also equivalent to the vanishing of the second coefficient. So the...