Defining polynomial
| $x^{7} + a_{27} \pi^{4} x^{6} + b_{31} \pi^{5} x^{3} + b_{30} \pi^{5} x^{2} + b_{29} \pi^{5} x + \pi$ |
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 $c$: | $33$ |
| Absolute Artin slopes: | $[\frac{7}{4}]$ |
| Swan slopes: | $[\frac{9}{2}]$ |
| Means: | $\langle\frac{27}{7}\rangle$ |
| Rams: | $(\frac{9}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $1$ |
| Mass: | $2058$ |
| Absolute Mass: | $343$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.