Defining polynomial
| $x^{7} + b_{9} \pi^{2} x^{2} + a_{8} \pi^{2} x + \pi$ |
Invariants
| Residue field characteristic: | $7$ |
| Degree: | $7$ |
| Base field: | 7.1.6.5a1.6 |
| Ramification index $e$: | $7$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $14$ |
| Absolute Artin slopes: | $[\frac{11}{9}]$ |
| Swan slopes: | $[\frac{4}{3}]$ |
| Means: | $\langle\frac{8}{7}\rangle$ |
| Rams: | $(\frac{4}{3})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $1$ |
| Mass: | $42$ |
| Absolute Mass: | $7$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.