Defining polynomial
\( x^{8} - 11 \) |
Invariants
Base field: | $\Q_{11}$ |
Degree $d$: | $8$ |
Ramification exponent $e$: | $8$ |
Residue field degree $f$: | $1$ |
Discriminant exponent $c$: | $7$ |
Discriminant root field: | $\Q_{11}(\sqrt{11\cdot 2})$ |
Root number: | $-i$ |
$|\Aut(K/\Q_{ 11 })|$: | $2$ |
This field is not Galois over $\Q_{11}.$ |
Intermediate fields
$\Q_{11}(\sqrt{11})$, 11.4.3.2 |
Fields in the database are given up to isomorphism. Isomorphic intermediate fields are shown with their multiplicities.
Unramified/totally ramified tower
Unramified subfield: | $\Q_{11}$ |
Relative Eisenstein polynomial: | \( x^{8} - 11 \) |