| $x^{8} + \left(b_{55} \pi^{7} + b_{47} \pi^{6}\right) x^{7} + \left(b_{54} \pi^{7} + b_{46} \pi^{6} + b_{38} \pi^{5} + b_{30} \pi^{4}\right) x^{6} + \left(b_{53} \pi^{7} + b_{45} \pi^{6}\right) x^{5} + a_{4} \pi x^{4} + \left(b_{51} \pi^{7} + a_{43} \pi^{6}\right) x^{3} + \left(b_{50} \pi^{7} + b_{42} \pi^{6} + b_{34} \pi^{5}\right) x^{2} + b_{49} \pi^{7} x + c_{56} \pi^{8} + c_{8} \pi^{2} + \pi$ |
| Residue field characteristic: | $2$ |
| Degree: | $8$ |
| Base field: | 2.1.4.8b1.6 |
| Ramification index $e$: | $8$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $50$ |
| Absolute Artin slopes: | $[2,2,3,4,4]$ |
| Swan slopes: | $[1,7,7]$ |
| Means: | $\langle\frac{1}{2},\frac{15}{4},\frac{43}{8}\rangle$ |
| Rams: | $(1,13,13)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $8192$ |
| Absolute Mass: | $2048$ ($0$ currently in the LMFDB) |
The LMFDB does not contain any fields from this family.
