Defining polynomial
| $x^{9} + 9 b_{17} x^{8} + 9 b_{16} x^{7} + 3 a_{6} x^{6} + 9 a_{14} x^{5} + 9 c_{9} + 27 c_{18} + 3$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $9$ |
| Base field: | 3.5.1.0a1.1 |
| Ramification index $e$: | $9$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $22$ |
| Absolute Artin slopes: | $[2,3]$ |
| Swan slopes: | $[1,2]$ |
| Means: | $\langle\frac{2}{3},\frac{14}{9}\rangle$ |
| Rams: | $(1,4)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $9$ |
| Mass: | $3458145636$ |
| Absolute Mass: | $3458145636/5$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.