Defining polynomial
| $x^{6} + \left(b_{23} \pi^{4} + b_{17} \pi^{3}\right) x^{5} + \left(b_{21} \pi^{4} + b_{15} \pi^{3}\right) x^{3} + \left(b_{19} \pi^{4} + b_{13} \pi^{3}\right) x + c_{24} \pi^{5} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $6$ |
| Base field: | 2.3.2.9a1.6 |
| Ramification index $e$: | $6$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $17$ |
| Absolute Artin slopes: | $[3,4]$ |
| Swan slopes: | $[4]$ |
| Means: | $\langle2\rangle$ |
| Rams: | $(12)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $2$ |
| Mass: | $262144$ |
| Absolute Mass: | $131072/3$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.