Defining polynomial
| $x^{28} + 2 b_{27} x^{27} + 2 b_{25} x^{25} + 2 b_{23} x^{23} + 2 a_{21} x^{21} + 4 c_{40} x^{12} + 4 b_{39} x^{11} + 4 b_{37} x^{9} + 4 b_{35} x^{7} + 4 b_{33} x^{5} + 2 c_{4} x^{4} + 4 b_{31} x^{3} + 2 a_{2} x^{2} + 4 b_{29} x + 2$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $28$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $28$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $48$ |
| Artin slopes: | $[\frac{8}{7},\frac{17}{7}]$ |
| Swan slopes: | $[\frac{1}{7},\frac{10}{7}]$ |
| Means: | $\langle\frac{1}{14},\frac{3}{4}\rangle$ |
| Rams: | $(1,19)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $512$ |
| Absolute Mass: | $512$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.