Defining polynomial
| $x^{27} + 3 c_{15} x^{15} + 3 b_{14} x^{14} + 3 b_{13} x^{13} + 3 a_{11} x^{11} + 3 a_{3} x^{3} + 3$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $27$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $27$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $37$ |
| Artin slopes: | $[\frac{9}{8},\frac{9}{8},\frac{14}{9}]$ |
| Swan slopes: | $[\frac{1}{8},\frac{1}{8},\frac{5}{9}]$ |
| Means: | $\langle\frac{1}{12},\frac{1}{9},\frac{11}{27}\rangle$ |
| Rams: | $(\frac{1}{8},\frac{1}{8},4)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $3$ |
| Mass: | $36$ |
| Absolute Mass: | $36$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.