Defining polynomial over unramified subextension
| $x^{18} + 3 b_{17} x^{17} + 3 b_{16} x^{16} + 3 a_{14} x^{14} + 3 c_{9} x^{9} + 3 a_{6} x^{6} + 3 d_{0} + 9 c_{18}$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $36$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $18$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $62$ |
| Artin slopes: | $[\frac{3}{2},2]$ |
| Swan slopes: | $[\frac{1}{2},1]$ |
| Means: | $\langle\frac{1}{3},\frac{7}{9}\rangle$ |
| Rams: | $(1,4)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $36$ |
| Mass: | $5184$ |
| Absolute Mass: | $2592$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.