Defining polynomial
| $x^{6} + b_{10} \pi^{2} x^{4} + b_{8} \pi^{2} x^{2} + a_{7} \pi^{2} x + d_{0} \pi$ |
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 $c$: | $12$ |
| Absolute Artin slopes: | $[\frac{15}{8},\frac{5}{2}]$ |
| Swan slopes: | $[\frac{7}{4}]$ |
| Means: | $\langle\frac{7}{6}\rangle$ |
| Rams: | $(\frac{7}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $2$ |
| Mass: | $18$ |
| Absolute Mass: | $6$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.