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Title: Class polynomials of $\gamma_2=\sqrt[3]{j}$-Definition: Let $\Delta<0$ be a discriminant with $\Delta\equiv0$ or $1 \pmod 4$ and- $3\nmid\Delta$, and let HREF{Hilbert_class_polynomials}[$H_\Delta$] be the Hilbert- class polynomial of the imaginary quadratic order $\mathcal{O}_\Delta$. The $\gamma_2$+Definition: For an admissible $\Delta$, let $H_\Delta$ be the Hilbert class polynomial+ of $\mathcal{O}_\Delta$ and let $j$ be the modular $j$-invariant. The $\gamma_2$ class polynomial $P_\Delta^{\gamma_2}(x)$ is the unique monic factor of $H_\Delta(x^3)$- in $\mathbb{Z}[x]$ of degree $h(\Delta)=\deg H_\Delta$, where $\gamma_2^3=j$ and- $j$ is HREF{Q-expansion_of_the_j-invariant}[the modular $j$-invariant].+ in $\mathbb{Z}[x]$ of degree $\deg H_\Delta$, where $\gamma_2^3=j$. Parameters: Delta:
comment-factor: In the complex multiplication method CITE{WikiCM}, the condition $3\nmid\Delta$ is the one under which $\gamma_2=\sqrt[3]{j}$ gives a class invariant- for $\mathcal{O}_\Delta$ CITE{PARIpolclass} CITE{Cox}. The factor $Q_\Delta$ has+ for $\mathcal{O}_\Delta$, where $j$ is HREF{Q-expansion_of_the_j-invariant}[the+ modular $j$-invariant] CITE{PARIpolclass} CITE{Cox}. The factor $Q_\Delta$ has the roots obtained by multiplying each root of $P_\Delta^{\gamma_2}$ by the two primitive cube roots of unity.
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