\(x^{12} + 120 x^{7} + 75 x^{6} + 41 x^{5} + 77 x^{4} + 106 x^{3} + 8 x^{2} + 10 x + 2\)
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Fields in the database are given up to isomorphism. Isomorphic
intermediate fields are shown with their multiplicities.
Unramified subfield: | 139.12.0.1 $\cong \Q_{139}(t)$ where $t$ is a root of
\( x^{12} + 120 x^{7} + 75 x^{6} + 41 x^{5} + 77 x^{4} + 106 x^{3} + 8 x^{2} + 10 x + 2 \)
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Relative Eisenstein polynomial: |
\( x - 139 \)
$\ \in\Q_{139}(t)[x]$
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The ramification polygon is trivial for unramified extensions.