Defining polynomial
| $x^{6} + b_{17} \pi^{3} x^{5} + b_{16} \pi^{3} x^{4} + b_{14} \pi^{3} x^{2} + \left(b_{19} \pi^{4} + a_{13} \pi^{3}\right) x + d_{0} \pi$ |
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 $c$: | $18$ |
| Absolute Artin slopes: | $[2,\frac{11}{4}]$ |
| Swan slopes: | $[\frac{13}{4}]$ |
| Means: | $\langle\frac{13}{6}\rangle$ |
| Rams: | $(\frac{13}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $2$ |
| Mass: | $52488$ |
| Absolute Mass: | $17496$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.