Defining polynomial
| $x^{4} + a_{3} \pi x^{3} + b_{2} \pi x^{2} + c_{4} \pi^{2} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.5.2.10a4.2 |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $6$ |
| Absolute Artin slopes: | $[2,2,2]$ |
| Swan slopes: | $[1,1]$ |
| Means: | $\langle\frac{1}{2},\frac{3}{4}\rangle$ |
| Rams: | $(1,1)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $992$ |
| Absolute Mass: | $496$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.