Defining polynomial
| $x^{3} + \left(b_{29} \pi^{10} + b_{26} \pi^{9} + b_{23} \pi^{8} + a_{20} \pi^{7}\right) x^{2} + \left(b_{28} \pi^{10} + b_{25} \pi^{9} + b_{22} \pi^{8}\right) x + c_{30} \pi^{11} + \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $3$ |
| Base field: | 3.1.12.21a1.18 |
| Ramification index $e$: | $3$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $22$ |
| Absolute Artin slopes: | $[\frac{9}{4},\frac{8}{3}]$ |
| Swan slopes: | $[10]$ |
| Means: | $\langle\frac{20}{3}\rangle$ |
| Rams: | $(10)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $3$ |
| Mass: | $1458$ |
| Absolute Mass: | $729$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.