Defining polynomial over unramified subextension
| $x^{18} + 9 c_{33} x^{15} + 9 b_{32} x^{14} + 9 b_{31} x^{13} + 9 b_{29} x^{11} + 9 b_{28} x^{10} + 3 c_{9} x^{9} + 9 b_{26} x^{8} + 9 b_{25} x^{7} + 3 a_{6} x^{6} + 3 d_{0}$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $36$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $18$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $82$ |
| Artin slopes: | $[\frac{3}{2},\frac{17}{6}]$ |
| Swan slopes: | $[\frac{1}{2},\frac{11}{6}]$ |
| Means: | $\langle\frac{1}{3},\frac{4}{3}\rangle$ |
| Rams: | $(1,9)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $36$ |
| Mass: | $4251528$ |
| Absolute Mass: | $2125764$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.