\(x^{12} + x^{8} + 4 x^{7} + 14 x^{6} + 14 x^{5} + 13 x^{4} + 6 x^{3} + 14 x^{2} + 9 x + 3\)
|
Fields in the database are given up to isomorphism. Isomorphic
intermediate fields are shown with their multiplicities.
Unramified subfield: | 17.12.0.1 $\cong \Q_{17}(t)$ where $t$ is a root of
\( x^{12} + x^{8} + 4 x^{7} + 14 x^{6} + 14 x^{5} + 13 x^{4} + 6 x^{3} + 14 x^{2} + 9 x + 3 \)
|
Relative Eisenstein polynomial: |
\( x - 17 \)
$\ \in\Q_{17}(t)[x]$
|
The ramification polygon is trivial for unramified extensions.