Defining polynomial
| $x^{3} + b_{8} \pi^{3} x^{2} + \left(b_{10} \pi^{4} + a_{7} \pi^{3}\right) x + \pi$ |
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 $c$: | $9$ |
| Absolute Artin slopes: | $[\frac{17}{10},\frac{5}{2}]$ |
| Swan slopes: | $[\frac{7}{2}]$ |
| Means: | $\langle\frac{7}{3}\rangle$ |
| Rams: | $(\frac{7}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $1$ |
| Mass: | $18$ |
| Absolute Mass: | $18$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.