Defining polynomial
| $x^{4} + \left(b_{31} \pi^{8} + b_{27} \pi^{7} + b_{23} \pi^{6} + a_{19} \pi^{5}\right) x^{3} + \left(b_{10} \pi^{3} + a_{6} \pi^{2}\right) x^{2} + \left(b_{29} \pi^{8} + b_{25} \pi^{7} + b_{21} \pi^{6}\right) x + c_{32} \pi^{9} + c_{12} \pi^{4} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.1.8.12b1.3 |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $22$ |
| Absolute Artin slopes: | $[\frac{4}{3},\frac{4}{3},2,2,\frac{21}{8}]$ |
| Swan slopes: | $[3,8]$ |
| Means: | $\langle\frac{3}{2},\frac{19}{4}\rangle$ |
| Rams: | $(3,13)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $128$ |
| Absolute Mass: | $64$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.