Defining polynomial over unramified subextension
| $x^{6} + 4 b_{11} x^{5} + 4 b_{9} x^{3} + 4 b_{7} x + 2 d_{0} + 8 c_{12}$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $36$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $6$ |
| Residue field degree $f$: | $6$ |
| Discriminant exponent $c$: | $66$ |
| Artin slopes: | $[3]$ |
| Swan slopes: | $[2]$ |
| Means: | $\langle1\rangle$ |
| Rams: | $(6)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $36$ |
| Mass: | $262144$ |
| Absolute Mass: | $131072/3$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.