Defining polynomial
| $x^{4} + a_{7} \pi^{2} x^{3} + b_{6} \pi^{2} x^{2} + b_{9} \pi^{3} x + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.1.8.28b1.15 |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $10$ |
| Absolute Artin slopes: | $[3,\frac{19}{6},\frac{19}{6},4,\frac{17}{4}]$ |
| Swan slopes: | $[\frac{7}{3},\frac{7}{3}]$ |
| Means: | $\langle\frac{7}{6},\frac{7}{4}\rangle$ |
| Rams: | $(\frac{7}{3},\frac{7}{3})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $1$ |
| Mass: | $4$ |
| Absolute Mass: | $2$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.