Defining polynomial over unramified subextension
| $x^{20} + 4 b_{39} x^{19} + 4 b_{38} x^{18} + 4 b_{37} x^{17} + 4 a_{35} x^{15} + 4 b_{34} x^{14} + \left(4 b_{30} + 8 c_{50}\right) x^{10} + 8 b_{49} x^{9} + 8 b_{47} x^{7} + 4 b_{26} x^{6} + 8 b_{45} x^{5} + 8 b_{43} x^{3} + 4 b_{22} x^{2} + 8 b_{41} x + 8 c_{40} + 2$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $40$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $20$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $108$ |
| Artin slopes: | $[3,\frac{7}{2}]$ |
| Swan slopes: | $[2,\frac{5}{2}]$ |
| Means: | $\langle1,\frac{7}{4}\rangle$ |
| Rams: | $(10,15)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $8$ |
| Mass: | $50331648$ |
| Absolute Mass: | $25165824$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.