Defining polynomial over unramified subextension
| $x^{2} + \left(b_{29} \pi^{15} + b_{27} \pi^{14} + b_{25} \pi^{13} + b_{23} \pi^{12} + b_{21} \pi^{11} + b_{19} \pi^{10} + b_{17} \pi^{9} + a_{15} \pi^{8}\right) x + c_{30} \pi^{16} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.1.8.28b1.15 |
| Ramification index $e$: | $2$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $32$ |
| Absolute Artin slopes: | $[3,4,\frac{17}{4},\frac{11}{2}]$ |
| Swan slopes: | $[15]$ |
| Means: | $\langle\frac{15}{2}\rangle$ |
| Rams: | $(15)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $49152$ |
| Absolute Mass: | $12288$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.