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There is an error in this article. The improvement over Schoof is not that you work modulo the smaller modular polynomials, but a factor of the division polynomial. This factor is such that its roots are the x-coordinates of the points in the eigenspace C. The modular polynomials have roots the j-invariants of the cyclic subgroups C of E, and are used merely to determine whether or not l is an Elkies prime or not. —Preceding unsigned comment added by 129.241.66.108 (talk) 14:20, 23 May 2010 (UTC)