\(x^{14} + 4 x^{8} + 35 x^{7} + 35 x^{6} + x^{5} + 32 x^{4} + 16 x^{3} + x^{2} + 9 x + 2\)
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Fields in the database are given up to isomorphism. Isomorphic
intermediate fields are shown with their multiplicities.
Unramified subfield: | 37.14.0.1 $\cong \Q_{37}(t)$ where $t$ is a root of
\( x^{14} + 4 x^{8} + 35 x^{7} + 35 x^{6} + x^{5} + 32 x^{4} + 16 x^{3} + x^{2} + 9 x + 2 \)
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Relative Eisenstein polynomial: |
\( x - 37 \)
$\ \in\Q_{37}(t)[x]$
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The ramification polygon is trivial for unramified extensions.