Defining polynomial
| $x^{4} + \left(b_{27} \pi^{7} + b_{23} \pi^{6} + a_{19} \pi^{5}\right) x^{3} + \left(b_{18} \pi^{5} + b_{14} \pi^{4} + a_{10} \pi^{3}\right) x^{2} + \left(b_{25} \pi^{7} + b_{21} \pi^{6}\right) x + c_{28} \pi^{8} + c_{20} \pi^{6} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.1.8.31a1.168 |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $22$ |
| Absolute Artin slopes: | $[3,4,\frac{17}{4},\frac{19}{4},5]$ |
| Swan slopes: | $[5,7]$ |
| Means: | $\langle\frac{5}{2},\frac{19}{4}\rangle$ |
| Rams: | $(5,9)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $64$ |
| Absolute Mass: | $8$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.