# Reduction of CM elliptic curves and modular function congruences

 Title: Reduction of CM elliptic curves and modular function congruences Author: Ono, Ken; Elkies, Noam; Yang, Tonghai Note: Order does not necessarily reflect citation order of authors. Citation: Elkies, Noam D., Ken Ono, and Tonghai Yang. 2005. Reduction of CM elliptic curves and modular function congruences. International Mathematics Research Notices (44): 2695-2707. Full Text & Related Files: Elkies - Reduction of CM elliptic.pdf (190.7Kb; PDF) Abstract: We study congruences of the form F(j(z)) | U(p) = G(j(z)) mod p, where U(p) is the p-th Hecke operator, j is the basic modular invariant 1/q+744+196884q+... for SL2(Z), and F,G are polynomials with integer coefficients. Using the interplay between singular (a.k.a. CM) j-invariants in characteristic zero and supersingular ones in characteristic p, we obtain such congruences in which F is the minimal polynomial of a CM j-invariant, and give a sufficient condition for G to be a constant polynomial in these congruences. Other Sources: http://arxiv.org/abs/math/0512350 Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:2797455 Downloads of this work: