Defining polynomial over unramified subextension
| $x^{7} + 7 a_{6} x^{6} + 49 c_{7} + 7$ |
Invariants
| Residue field characteristic: | $7$ |
| Degree: | $28$ |
| Base field: | $\Q_{7}$ |
| Ramification index $e$: | $7$ |
| Residue field degree $f$: | $4$ |
| Discriminant exponent $c$: | $48$ |
| Artin slopes: | $[2]$ |
| Swan slopes: | $[1]$ |
| Means: | $\langle\frac{6}{7}\rangle$ |
| Rams: | $(1)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $28$ |
| Mass: | $2400$ |
| Absolute Mass: | $600$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.