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arXiv · 0909.3442

An explicit height bound for the classical modular polynomial

Reinier Broker·Andrew V. Sutherland
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Abstract

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.

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Reinier Broker, Andrew V. Sutherland. 2010-04-10. An explicit height bound for the classical modular polynomial. https://doi.org/10.1007/s11139-010-9231-8

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