Defining polynomial over unramified subextension
| $x^{12} + 9 c_{18} x^{6} + 9 b_{17} x^{5} + 9 b_{16} x^{4} + 9 b_{14} x^{2} + 9 b_{13} x + 3 d_{0}$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $24$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $12$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $46$ |
| Artin slopes: | $[\frac{5}{2}]$ |
| Swan slopes: | $[\frac{3}{2}]$ |
| Means: | $\langle1\rangle$ |
| Rams: | $(6)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $24$ |
| Mass: | $6561$ |
| Absolute Mass: | $6561/2$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.