Schoof's algorithm: Difference between revisions

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m Hasse's theorem: replace \sharp with \#
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'''Theorem:''' The Frobenius endomorphism given by <math>\phi</math> satisfies the characteristic equation
 
: <math> \phi ^2 - t\phi + q = 0,</math> where <math> t = q + 1 - \sharp# E(\mathbb{F}_q) </math>
 
Thus we have for all <math>P=(x, y) \in E</math> that <math>(x^{q^{2}}, y^{q^{2}} ) + q(x, y) = t(x^{q}, y^{q})</math>, where + denotes addition on the elliptic curve and <math>q(x,y)</math> and <math>t(x^{q},y^{q})</math>