Defining polynomial
| $x^{27} + 9 b_{51} x^{24} + 9 b_{48} x^{21} + 3 a_{18} x^{18} + 27 b_{70} x^{16} + 9 a_{42} x^{15} + 27 b_{68} x^{14} + 27 b_{67} x^{13} + 27 b_{65} x^{11} + 27 b_{64} x^{10} + 27 b_{62} x^{8} + 27 a_{61} x^{7} + 9 c_{27} + 27 c_{54} + 3$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $27$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $27$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $87$ |
| Artin slopes: | $[2,3,\frac{65}{18}]$ |
| Swan slopes: | $[1,2,\frac{47}{18}]$ |
| Means: | $\langle\frac{2}{3},\frac{14}{9},\frac{61}{27}\rangle$ |
| Rams: | $(1,4,\frac{19}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $9$ |
| Mass: | $52488$ |
| Absolute Mass: | $52488$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.