Defining polynomial
| $x^{6} + b_{11} \pi^{2} x^{5} + b_{9} \pi^{2} x^{3} + c_{14} \pi^{3} x^{2} + \left(b_{13} \pi^{3} + a_{7} \pi^{2}\right) x + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $6$ |
| Base field: | 2.2.2.4a2.2 |
| Ramification index $e$: | $6$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $12$ |
| Absolute Artin slopes: | $[2,\frac{8}{3}]$ |
| Swan slopes: | $[\frac{7}{3}]$ |
| Means: | $\langle\frac{7}{6}\rangle$ |
| Rams: | $(7)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $6$ |
| Mass: | $192$ |
| Absolute Mass: | $96$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.