Defining polynomial
| $x^{8} + \left(b_{39} \pi^{5} + b_{31} \pi^{4}\right) x^{7} + \left(b_{22} \pi^{3} + a_{14} \pi^{2}\right) x^{6} + \left(b_{37} \pi^{5} + b_{29} \pi^{4}\right) x^{5} + a_{4} \pi x^{4} + \left(b_{35} \pi^{5} + a_{27} \pi^{4}\right) x^{3} + b_{18} \pi^{3} x^{2} + b_{33} \pi^{5} x + c_{40} \pi^{6} + c_{24} \pi^{4} + c_{8} \pi^{2} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $8$ |
| Base field: | 2.2.2.4a2.1 |
| Ramification index $e$: | $8$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $34$ |
| Absolute Artin slopes: | $[2,2,3,4]$ |
| Swan slopes: | $[1,3,5]$ |
| Means: | $\langle\frac{1}{2},\frac{7}{4},\frac{27}{8}\rangle$ |
| Rams: | $(1,5,13)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $8$ |
| Mass: | $1769472$ |
| Absolute Mass: | $884736$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.