When the value of modular $j$ function is cubic number

Asked Jun 14 '19 at 14:37

Active Jun 16 '19 at 23:56

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It seems to be well known that when the class number of $K=\mathbb{Q}(\sqrt{-d})$ is one, the value of modular $j$ function at $\mathbb{Z}$ basis of integer ring of $K$ is cubic number.

But I couldn't find the available proof. I'll appreciate if someone tell me the proof or paper.

edited Jun 14 '19 at 15:52

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asked Jun 14 '19 at 14:37

user682141

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Do you have a link to such a statement? I find the modular $J$-function in other contexts, and in wikipedia, but no such statement right now. – Dietrich Burde Jun 14 '19 at 14:43
I found it now here, with references. This is for $d=-1, -2, -3, -7, -11, -19, -43, -67, -163$. – Dietrich Burde Jun 14 '19 at 14:53

When the value of modular $j$ function is cubic number

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