Defining polynomial
| $x^{4} + \left(b_{39} \pi^{10} + b_{35} \pi^{9} + b_{31} \pi^{8} + b_{27} \pi^{7}\right) x^{3} + \left(b_{18} \pi^{5} + b_{14} \pi^{4} + a_{10} \pi^{3}\right) x^{2} + \left(b_{37} \pi^{10} + b_{33} \pi^{9} + b_{29} \pi^{8} + a_{25} \pi^{7}\right) x + c_{40} \pi^{11} + c_{20} \pi^{6} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.2.4.22a1.81 |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $28$ |
| Absolute Artin slopes: | $[3,4,\frac{17}{4},\frac{11}{2}]$ |
| Swan slopes: | $[5,10]$ |
| Means: | $\langle\frac{5}{2},\frac{25}{4}\rangle$ |
| Rams: | $(5,15)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $2359296$ |
| Absolute Mass: | $1179648$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.