Defining polynomial
| $x^{6} + b_{17} \pi^{3} x^{5} + b_{16} \pi^{3} x^{4} + c_{21} \pi^{4} x^{3} + \left(b_{20} \pi^{4} + a_{14} \pi^{3}\right) x^{2} + b_{19} \pi^{4} x + d_{0} \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $6$ |
| Base field: | 3.1.6.11a1.7 |
| Ramification index $e$: | $6$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $19$ |
| Absolute Artin slopes: | $[\frac{5}{2},\frac{31}{12}]$ |
| Swan slopes: | $[\frac{7}{2}]$ |
| Means: | $\langle\frac{7}{3}\rangle$ |
| Rams: | $(7)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $6$ |
| Mass: | $162$ |
| Absolute Mass: | $54$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.