| $x^{8} + \left(b_{63} \pi^{8} + b_{55} \pi^{7} + a_{47} \pi^{6}\right) x^{7} + \left(b_{38} \pi^{5} + a_{30} \pi^{4}\right) x^{6} + \left(b_{61} \pi^{8} + b_{53} \pi^{7}\right) x^{5} + \left(b_{36} \pi^{5} + b_{28} \pi^{4} + b_{20} \pi^{3}\right) x^{4} + \left(b_{59} \pi^{8} + b_{51} \pi^{7}\right) x^{3} + b_{34} \pi^{5} x^{2} + \left(b_{57} \pi^{8} + b_{49} \pi^{7}\right) x + c_{64} \pi^{9} + c_{40} \pi^{6} + \pi$ |
| Residue field characteristic: | $2$ |
| Degree: | $8$ |
| Base field: | 2.1.4.11a1.14 |
| Ramification index $e$: | $8$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $54$ |
| Absolute Artin slopes: | $[3,4,\frac{17}{4},\frac{17}{4},5]$ |
| Swan slopes: | $[5,5,8]$ |
| Means: | $\langle\frac{5}{2},\frac{15}{4},\frac{47}{8}\rangle$ |
| Rams: | $(5,5,17)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $8192$ |
| Absolute Mass: | $4096$ ($0$ currently in the LMFDB) |
The LMFDB does not contain any fields from this family.
