Defining polynomial
| $x^{9} + b_{26} \pi^{3} x^{8} + b_{25} \pi^{3} x^{7} + a_{6} \pi x^{6} + b_{23} \pi^{3} x^{5} + b_{22} \pi^{3} x^{4} + a_{20} \pi^{3} x^{2} + c_{27} \pi^{4} + c_{9} \pi^{2} + \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $9$ |
| Base field: | 3.2.2.2a1.2 |
| Ramification index $e$: | $9$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $28$ |
| Absolute Artin slopes: | $[\frac{3}{2},\frac{5}{2}]$ |
| Swan slopes: | $[1,3]$ |
| Means: | $\langle\frac{2}{3},\frac{20}{9}\rangle$ |
| Rams: | $(1,7)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $9$ |
| Mass: | $419904$ |
| Absolute Mass: | $104976$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.