Defining polynomial
| $x^{4} + a_{11} \pi^{3} x^{3} + \left(b_{14} \pi^{4} + b_{10} \pi^{3}\right) x^{2} + b_{13} \pi^{4} x + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.1.8.12b1.1 |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $14$ |
| Absolute Artin slopes: | $[\frac{4}{3},\frac{4}{3},2,\frac{25}{12},\frac{25}{12}]$ |
| Swan slopes: | $[\frac{11}{3},\frac{11}{3}]$ |
| Means: | $\langle\frac{11}{6},\frac{11}{4}\rangle$ |
| Rams: | $(\frac{11}{3},\frac{11}{3})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $1$ |
| Mass: | $8$ |
| Absolute Mass: | $4$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.