Defining polynomial over unramified subextension
| $x^{2} + \left(b_{31} \pi^{16} + b_{29} \pi^{15} + b_{27} \pi^{14} + b_{25} \pi^{13} + b_{23} \pi^{12} + b_{21} \pi^{11} + b_{19} \pi^{10} + b_{17} \pi^{9}\right) x + c_{32} \pi^{17} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.1.8.28b1.16 |
| Ramification index $e$: | $2$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $34$ |
| Absolute Artin slopes: | $[3,4,\frac{17}{4},\frac{45}{8}]$ |
| Swan slopes: | $[16]$ |
| Means: | $\langle8\rangle$ |
| Rams: | $(16)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $65536$ |
| Absolute Mass: | $16384$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.