Defining polynomial
| $x^{2} + \left(b_{15} \pi^{8} + b_{13} \pi^{7} + b_{11} \pi^{6} + b_{9} \pi^{5}\right) x + c_{16} \pi^{9} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $2$ |
| Base field: | 2.3.4.33a1.194 |
| Ramification index $e$: | $2$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $9$ |
| Absolute Artin slopes: | $[3,4,5]$ |
| Swan slopes: | $[8]$ |
| Means: | $\langle4\rangle$ |
| Rams: | $(8)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $2$ |
| Mass: | $4096$ |
| Absolute Mass: | $2048/3$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.