Defining polynomial
| $x^{6} + b_{23} \pi^{4} x^{5} + b_{22} \pi^{4} x^{4} + c_{27} \pi^{5} x^{3} + \left(b_{26} \pi^{5} + b_{20} \pi^{4}\right) x^{2} + \left(b_{25} \pi^{5} + b_{19} \pi^{4}\right) x + d_{0} \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $6$ |
| Base field: | 3.2.3.8a1.2 |
| Ramification index $e$: | $6$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $23$ |
| Absolute Artin slopes: | $[2,\frac{19}{6}]$ |
| Swan slopes: | $[\frac{9}{2}]$ |
| Means: | $\langle3\rangle$ |
| Rams: | $(9)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $6$ |
| Mass: | $531441$ |
| Absolute Mass: | $177147$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.