Defining polynomial
| $x^{3} + \left(b_{23} \pi^{8} + b_{20} \pi^{7} + b_{17} \pi^{6}\right) x^{2} + \left(b_{22} \pi^{8} + b_{19} \pi^{7} + a_{16} \pi^{6}\right) x + c_{24} \pi^{9} + \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $3$ |
| Base field: | 3.1.15.29a1.32 |
| Ramification index $e$: | $3$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $18$ |
| Absolute Artin slopes: | $[\frac{5}{2},\frac{38}{15}]$ |
| Swan slopes: | $[8]$ |
| Means: | $\langle\frac{16}{3}\rangle$ |
| Rams: | $(8)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $3$ |
| Mass: | $486$ |
| Absolute Mass: | $486$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.