Defining polynomial over unramified subextension
| $x^{12} + 2 b_{11} x^{11} + 2 a_{9} x^{9} + \left(2 c_{4} + 4 c_{16}\right) x^{4} + 4 b_{15} x^{3} + 2 a_{2} x^{2} + 4 b_{13} x + 2$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $36$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $12$ |
| Residue field degree $f$: | $3$ |
| Discriminant exponent $c$: | $60$ |
| Artin slopes: | $[\frac{4}{3},\frac{7}{3}]$ |
| Swan slopes: | $[\frac{1}{3},\frac{4}{3}]$ |
| Means: | $\langle\frac{1}{6},\frac{3}{4}\rangle$ |
| Rams: | $(1,7)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $12$ |
| Mass: | $25088$ |
| Absolute Mass: | $25088/3$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.