Defining polynomial
| $x^{6} + \left(b_{41} \pi^{7} + b_{35} \pi^{6}\right) x^{5} + \left(b_{40} \pi^{7} + b_{34} \pi^{6}\right) x^{4} + c_{45} \pi^{8} x^{3} + \left(b_{44} \pi^{8} + b_{38} \pi^{7} + b_{32} \pi^{6}\right) x^{2} + \left(b_{43} \pi^{8} + b_{37} \pi^{7} + b_{31} \pi^{6}\right) x + d_{0} \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $6$ |
| Base field: | 3.1.5.4a1.1 |
| Ramification index $e$: | $6$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $35$ |
| Absolute Artin slopes: | $[\frac{5}{2}]$ |
| Swan slopes: | $[\frac{15}{2}]$ |
| Means: | $\langle5\rangle$ |
| Rams: | $(15)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $6$ |
| Mass: | $59049$ |
| Absolute Mass: | $59049$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.