Defining polynomial over unramified subextension
| $x^{18} + \left(9 c_{27} + 27 c_{45}\right) x^{9} + 27 b_{44} x^{8} + 27 b_{43} x^{7} + 9 b_{24} x^{6} + 27 b_{41} x^{5} + 27 b_{40} x^{4} + 9 b_{21} x^{3} + 27 b_{38} x^{2} + 27 b_{37} x + 3 d_{0}$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $36$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $18$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $106$ |
| Artin slopes: | $[\frac{5}{2},\frac{7}{2}]$ |
| Swan slopes: | $[\frac{3}{2},\frac{5}{2}]$ |
| Means: | $\langle1,2\rangle$ |
| Rams: | $(3,9)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $36$ |
| Mass: | $43046721$ |
| Absolute Mass: | $43046721/2$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.