History of Class polynomials of $\gamma_2=\sqrt[3]{j}$

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2026-09-17 18:29 zeta3 table-repair@2.0+dc0f96a0 shorten gamma2 definition current reviewed
2026-09-17 18:27 zeta3 table-repair@2.0+dc0f96a0 clarify gamma2 class polynomial prose
2026-09-17 18:03 zeta3 table-build@2.0+395f185d shorten gamma2 class polynomial definition
2026-09-17 18:02 zeta3 with Codex CLI, table-bui table-build@2.0+395f185d gamma2 class polynomials for |Delta| <= 300
2026-09-17 18:00 zeta3 table-build@2.0+395f185d claim gamma2 class polynomial draft

What changed between 2026-09-17 18:27 and 2026-09-17 18:29

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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:
from line 24 (6 lines, 1 more than before) @@ -26,5 +24,6 @@
   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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