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Let $K=\mathbb{Q}(\alpha)$, where $\alpha$ is a root of $f(x)=x^3+x+1$. If $p$ is a rational prime. What can you say about factorization of $p\mathcal{O}_K$ in $\mathcal{O}_K$?

I have this: The discriminant is -31 and the minkowski bound, $M_K \leq 1.57$. Then $N(\mathcal{A})=1$, $\mathcal{A}$ a ideal class. I can say anything about the question?

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    Have you ever done anything with the Minkowski bound? If so, please tell us, because the fact that the bound is less than 2 and you don't notice anything from that seems unusual.2012-12-19
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    @KCd, see http://math.stackexchange.com/questions/261828/class-group-of-mathbbq-sqrt-47 from a few minutes ago. No response from the OP before posting this new question. Lord, there is yet another one after.2012-12-19

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