Defining polynomial
| \( x^{8} + 26 \) |
Invariants
| Base field: | $\Q_{13}$ |
| Degree $d$ : | $8$ |
| Ramification exponent $e$ : | $8$ |
| Residue field degree $f$ : | $1$ |
| Discriminant exponent $c$ : | $7$ |
| Discriminant root field: | $\Q_{13}(\sqrt{13*})$ |
| Root number: | $-1$ |
| $|\Aut(K/\Q_{ 13 })|$: | $4$ |
| This field is not Galois over $\Q_{13}$. | |
Intermediate fields
| $\Q_{13}(\sqrt{13*})$, 13.4.3.3 |
Fields in the database are given up to isomorphism. Isomorphic intermediate fields are shown with their multiplicities.
Unramified/totally ramified tower
| Unramified subfield: | $\Q_{13}$ |
| Relative Eisenstein polynomial: | \( x^{8} + 26 \) |