Defining polynomial
| $x^{7} + b_{20} \pi^{3} x^{6} + a_{19} \pi^{3} x^{5} + b_{22} \pi^{4} x + \pi$ |
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 $c$: | $25$ |
| Absolute Artin slopes: | $[\frac{55}{36}]$ |
| Swan slopes: | $[\frac{19}{6}]$ |
| Means: | $\langle\frac{19}{7}\rangle$ |
| Rams: | $(\frac{19}{6})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $1$ |
| Mass: | $294$ |
| Absolute Mass: | $49$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.