Defining polynomial
| $x^{27} + 3 a_{13} x^{13} + 3 b_{12} x^{12} + 3 b_{9} x^{9} + 3$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $27$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $27$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $39$ |
| Artin slopes: | $[\frac{3}{2},\frac{3}{2},\frac{3}{2}]$ |
| Swan slopes: | $[\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
| Means: | $\langle\frac{1}{3},\frac{4}{9},\frac{13}{27}\rangle$ |
| Rams: | $(\frac{1}{2},\frac{1}{2},\frac{1}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $1$ |
| Mass: | $18$ |
| Absolute Mass: | $18$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.