Defining polynomial over unramified subextension
| $x^{2} + \left(b_{25} \pi^{13} + b_{23} \pi^{12} + b_{21} \pi^{11} + b_{19} \pi^{10} + b_{17} \pi^{9} + b_{15} \pi^{8} + a_{13} \pi^{7}\right) x + c_{26} \pi^{14} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.1.10.19a1.39 |
| Ramification index $e$: | $2$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $28$ |
| Absolute Artin slopes: | $[3,\frac{33}{10}]$ |
| Swan slopes: | $[13]$ |
| Means: | $\langle\frac{13}{2}\rangle$ |
| Rams: | $(13)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $12288$ |
| Absolute Mass: | $3072$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.