Defining polynomial
| $x^{8} + \left(b_{23} \pi^{3} + b_{15} \pi^{2}\right) x^{7} + \left(b_{21} \pi^{3} + a_{13} \pi^{2}\right) x^{5} + b_{19} \pi^{3} x^{3} + a_{2} \pi x^{2} + b_{17} \pi^{3} x + c_{24} \pi^{4} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $8$ |
| Base field: | 2.2.2.4a1.1 |
| Ramification index $e$: | $8$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $20$ |
| Absolute Artin slopes: | $[\frac{4}{3},\frac{4}{3},2,3]$ |
| Swan slopes: | $[\frac{1}{3},\frac{1}{3},3]$ |
| Means: | $\langle\frac{1}{6},\frac{1}{4},\frac{13}{8}\rangle$ |
| Rams: | $(\frac{1}{3},\frac{1}{3},11)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $2$ |
| Mass: | $9216$ |
| Absolute Mass: | $2304$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.