Defining polynomial over unramified subextension
| $x^{4} + \left(b_{31} \pi^{8} + b_{27} \pi^{7} + b_{23} \pi^{6} + b_{19} \pi^{5}\right) x^{3} + a_{2} \pi x^{2} + \left(b_{29} \pi^{8} + b_{25} \pi^{7} + b_{21} \pi^{6} + a_{17} \pi^{5}\right) x + c_{32} \pi^{9} + c_{4} \pi^{2} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $8$ |
| Base field: | 2.1.4.10a1.2 |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $40$ |
| Absolute Artin slopes: | $[2,3,\frac{7}{2},\frac{19}{4}]$ |
| Swan slopes: | $[1,8]$ |
| Means: | $\langle\frac{1}{2},\frac{17}{4}\rangle$ |
| Rams: | $(1,15)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $8$ |
| Mass: | $147456$ |
| Absolute Mass: | $36864$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.