Reduction of CM elliptic curves and modular function congruences (original) (raw)

Abstract

Here we investigate congruences for the coefficients of modular functions on SL 2 (ℤ). We obtain a simple criterion, in terms of the locus of supersingular j -invariants, which guarantees certain congruences. We implement this criterion in the case of modular functions obtained from Hilbert class polynomials.

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