Defining polynomial
| $x^{6} + b_{11} \pi^{2} x^{5} + a_{10} \pi^{2} x^{4} + c_{15} \pi^{3} x^{3} + b_{14} \pi^{3} x^{2} + b_{13} \pi^{3} x + d_{0} \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $6$ |
| Base field: | 3.1.6.10a1.1 |
| Ramification index $e$: | $6$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $15$ |
| Absolute Artin slopes: | $[\frac{9}{4},\frac{9}{4}]$ |
| Swan slopes: | $[\frac{5}{2}]$ |
| Means: | $\langle\frac{5}{3}\rangle$ |
| Rams: | $(5)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $6$ |
| Mass: | $54$ |
| Absolute Mass: | $54$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.