Defining polynomial
| $x^{4} + \left(b_{23} \pi^{6} + b_{19} \pi^{5}\right) x^{3} + \left(b_{18} \pi^{5} + b_{14} \pi^{4} + a_{10} \pi^{3}\right) x^{2} + \left(b_{21} \pi^{6} + a_{17} \pi^{5}\right) x + c_{24} \pi^{7} + c_{20} \pi^{6} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.1.7.6a1.1 |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $20$ |
| Absolute Artin slopes: | $[\frac{12}{7},\frac{13}{7}]$ |
| Swan slopes: | $[5,6]$ |
| Means: | $\langle\frac{5}{2},\frac{17}{4}\rangle$ |
| Rams: | $(5,7)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $32$ |
| Absolute Mass: | $32$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.