Defining polynomial over unramified subextension
| $x^{3} + \left(b_{26} \pi^{9} + b_{23} \pi^{8} + b_{20} \pi^{7}\right) x^{2} + \left(b_{25} \pi^{9} + b_{22} \pi^{8} + b_{19} \pi^{7}\right) x + c_{27} \pi^{10} + \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $6$ |
| Base field: | 3.1.6.11a1.7 |
| Ramification index $e$: | $3$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $40$ |
| Absolute Artin slopes: | $[\frac{5}{2},\frac{7}{2}]$ |
| Swan slopes: | $[9]$ |
| Means: | $\langle6\rangle$ |
| Rams: | $(9)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $6$ |
| Mass: | $531441$ |
| Absolute Mass: | $177147/2$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.