Defining polynomial
| $x^{6} + \left(b_{17} \pi^{3} + b_{11} \pi^{2}\right) x^{5} + \left(b_{15} \pi^{3} + a_{9} \pi^{2}\right) x^{3} + b_{13} \pi^{3} x + c_{18} \pi^{4} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $6$ |
| Base field: | 2.2.2.6a1.4 |
| Ramification index $e$: | $6$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $14$ |
| Absolute Artin slopes: | $[3,\frac{7}{2}]$ |
| Swan slopes: | $[3]$ |
| Means: | $\langle\frac{3}{2}\rangle$ |
| Rams: | $(9)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $6$ |
| Mass: | $768$ |
| Absolute Mass: | $384$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.