$( x^{2} + x + 1 )^{8} + \left(-8 x + 20\right) ( x^{2} + x + 1 )^{7} + \left(-28 x - 34\right) ( x^{2} + x + 1 )^{6} + \left(44 x + 42\right) ( x^{2} + x + 1 )^{5} + \left(-130 x + 99\right) ( x^{2} + x + 1 )^{4} + \left(-140 x - 82\right) ( x^{2} + x + 1 )^{3} + \left(118 x - 241\right) ( x^{2} + x + 1 )^{2} + \left(310 x + 111\right) ( x^{2} + x + 1 ) - 99 x + 280$
![Copy content]()
![Toggle raw display]()
|
|
$\Q_{2}(\sqrt{-5})$, $\Q_{2}(\sqrt{5})$, $\Q_{2}(\sqrt{-2})$, $\Q_{2}(\sqrt{-1})$, $\Q_{2}(\sqrt{2\cdot 5})$, $\Q_{2}(\sqrt{-2\cdot 5})$, $\Q_{2}(\sqrt{2})$, 2.4.6.6 x2, 2.4.4.4 x2, 2.4.8.2, 2.4.6.1, 2.4.6.2, 2.4.4.1, 2.4.6.9 x2, 2.4.8.5 x2, 2.4.8.4, 2.4.8.1, 2.4.8.3, 2.8.16.10 x2, 2.8.16.16 x2, 2.8.16.6, 2.8.16.5, 2.8.18.54 x2, 2.8.12.14, 2.8.18.56 x2
|
Fields in the database are given up to isomorphism. Isomorphic
intermediate fields are shown with their multiplicities.
| Unramified subfield: | $\Q_{2}(\sqrt{5})$ $\cong \Q_{2}(t)$ where $t$ is a root of
\( x^{2} + x + 1 \)
![Copy content]()
![Toggle raw display]()
|
| Relative Eisenstein polynomial: |
\( x^{8} + \left(4 t + 2\right) x^{6} + 4 t x^{4} + 4 x^{3} + 14 \)
$\ \in\Q_{2}(t)[x]$
![Copy content]()
![Toggle raw display]()
|
Not computed
