Defining polynomial over unramified subextension
| $x^{14} + 4 b_{27} x^{13} + 4 b_{25} x^{11} + 4 b_{23} x^{9} + 4 b_{21} x^{7} + 4 b_{19} x^{5} + 4 b_{17} x^{3} + 4 b_{15} x + 8 c_{28} + 2$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $28$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $14$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $54$ |
| Artin slopes: | $[3]$ |
| Swan slopes: | $[2]$ |
| Means: | $\langle1\rangle$ |
| Rams: | $(14)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $16384$ |
| Absolute Mass: | $8192$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.