Defining polynomial
| $x^{9} + b_{8} \pi x^{8} + a_{7} \pi x^{7} + a_{3} \pi x^{3} + c_{9} \pi^{2} + \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $9$ |
| Base field: | 3.2.2.2a1.1 |
| Ramification index $e$: | $9$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $15$ |
| Absolute Artin slopes: | $[\frac{5}{4},\frac{3}{2}]$ |
| Swan slopes: | $[\frac{1}{2},1]$ |
| Means: | $\langle\frac{1}{3},\frac{7}{9}\rangle$ |
| Rams: | $(\frac{1}{2},2)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $3$ |
| Mass: | $576$ |
| Absolute Mass: | $144$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.