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Consider the number field $L/\mathbb{Q}$. I know that the only primes $p$ that ramify over $L$ are the ones that divide $\Delta_{L}$, the discriminant of $L$. But what if I can't compute $\Delta_{L}$? Are there other ways to determine which primes ramify over $L$?

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    If $f(x)\in \mathbb Q[x]$ is the minimal polynomial of a generator of $L$, then $L/\mathbb Q$ is unramified at all $p$ such that $f(x)\in \mathbb Z[1/p][x]$ and $\bar{f}(x)$ is separable in $\mathbb F_p[x]$. However you can miss some unramified primes this way.2011-11-30

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