Defining polynomial over unramified subextension
| $x^{18} + \left(3 c_{9} + 9 c_{27}\right) x^{9} + 9 b_{26} x^{8} + 9 b_{25} x^{7} + 3 a_{6} x^{6} + 9 b_{23} x^{5} + 9 b_{22} x^{4} + 9 a_{20} x^{2} + 3 d_{0}$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $36$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $18$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $74$ |
| Artin slopes: | $[\frac{3}{2},\frac{5}{2}]$ |
| Swan slopes: | $[\frac{1}{2},\frac{3}{2}]$ |
| Means: | $\langle\frac{1}{3},\frac{10}{9}\rangle$ |
| Rams: | $(1,7)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $36$ |
| Mass: | $419904$ |
| Absolute Mass: | $209952$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.