2 problems

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Lauter's denominator-bound conjecture for quartic CM class polynomials
Lauter's denominator-bound conjecture. Every prime dividing the denominator of a coefficient of $H_i(X)$ is bounded by the discriminant of $K$ .
Conjectureopenclass-polynomials complex-multiplication number-theoryarXiv posted 2 days ago
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Integrality and irreducibility conjecture for level- $N$ class polynomials
Class-polynomial conjecture. The polynomial $H_{D,N,m}(X)$ belongs to $\mathbb{Z}[X]$ and is irreducible. This is proposed as an analogue of the preceding classical class-polynomia…
Conjectureopenclass-polynomials complex-multiplication modular-formsarXiv posted 2 days ago

Lauter's denominator-bound conjecture for quartic CM class polynomials