%0 Journal Article
%T An explicit height bound for the classical modular polynomial
%A Reinier Broker
%A Andrew V. Sutherland
%J Mathematics
%D 2009
%I arXiv
%R 10.1007/s11139-010-9231-8
%X For a prime m, let Phi_m be the classical modular polynomial, and let h(Phi_m) denote its logarithmic height. By specializing a theorem of Cohen, we prove that h(Phi_m) <= 6 m log m + 16 m + 14 sqrt m log m. As a corollary, we find that h(Phi_m) <= 6 m log m + 18 m also holds. A table of h(Phi_m) values is provided for m <= 3607.
%U http://arxiv.org/abs/0909.3442v2