Defining polynomial
| \( x^{6} + 296 \) |
Invariants
| Base field: | $\Q_{37}$ |
| Degree $d$ : | $6$ |
| Ramification exponent $e$ : | $6$ |
| Residue field degree $f$ : | $1$ |
| Discriminant exponent $c$ : | $5$ |
| Discriminant root field: | $\Q_{37}(\sqrt{37*})$ |
| Root number: | $-1$ |
| $|\Gal(K/\Q_{ 37 })|$: | $6$ |
| This field is Galois and abelian over $\Q_{37}$. | |
Intermediate fields
| $\Q_{37}(\sqrt{37*})$, 37.3.2.1 |
Fields in the database are given up to isomorphism. Isomorphic intermediate fields are shown with their multiplicities.
Unramified/totally ramified tower
| Unramified subfield: | $\Q_{37}$ |
| Relative Eisenstein polynomial: | \( x^{6} + 296 \) |