Defining polynomial
| \( x^{11} - 5 \) |
Invariants
| Base field: | $\Q_{5}$ |
| Degree $d$ : | $11$ |
| Ramification exponent $e$ : | $11$ |
| Residue field degree $f$ : | $1$ |
| Discriminant exponent $c$ : | $10$ |
| Discriminant root field: | $\Q_{5}$ |
| Root number: | $1$ |
| $|\Aut(K/\Q_{ 5 })|$: | $1$ |
| This field is not Galois over $\Q_{5}$. | |
Intermediate fields
| The extension is primitive: there are no intermediate fields between this field and $\Q_{ 5 }$. |
Unramified/totally ramified tower
| Unramified subfield: | $\Q_{5}$ |
| Relative Eisenstein polynomial: | \( x^{11} - 5 \) |