Defining polynomial
| \( x^{5} + 8856 \) |
Invariants
| Base field: | $\Q_{41}$ |
| Degree $d$ : | $5$ |
| Ramification exponent $e$ : | $5$ |
| Residue field degree $f$ : | $1$ |
| Discriminant exponent $c$ : | $4$ |
| Discriminant root field: | $\Q_{41}$ |
| Root number: | $1$ |
| $|\Gal(K/\Q_{ 41 })|$: | $5$ |
| This field is Galois and abelian over $\Q_{41}$. | |
Intermediate fields
| The extension is primitive: there are no intermediate fields between this field and $\Q_{ 41 }$. |
Unramified/totally ramified tower
| Unramified subfield: | $\Q_{41}$ |
| Relative Eisenstein polynomial: | \( x^{5} + 8856 \) |