Defining polynomial
| $x^{4} + \left(b_{31} \pi^{8} + b_{27} \pi^{7}\right) x^{3} + \left(c_{34} \pi^{9} + b_{30} \pi^{8} + b_{26} \pi^{7} + b_{22} \pi^{6} + b_{18} \pi^{5}\right) x^{2} + \left(b_{33} \pi^{9} + b_{29} \pi^{8} + a_{25} \pi^{7}\right) x + c_{32} \pi^{9} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.2.4.22a1.48 |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $28$ |
| Absolute Artin slopes: | $[3,4,5,\frac{41}{8}]$ |
| Swan slopes: | $[8,\frac{17}{2}]$ |
| Means: | $\langle4,\frac{25}{4}\rangle$ |
| Rams: | $(8,9)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $196608$ |
| Absolute Mass: | $98304$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.