Defining polynomial over unramified subextension
| $x^{12} + 4 b_{23} x^{11} + 4 b_{22} x^{10} + 4 b_{21} x^{9} + 4 a_{19} x^{7} + 4 b_{18} x^{6} + \left(4 b_{14} + 8 c_{26}\right) x^{2} + 8 b_{25} x + 8 c_{24} + 2$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $36$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $12$ |
| Residue field degree $f$: | $3$ |
| Discriminant exponent $c$: | $90$ |
| Artin slopes: | $[3,\frac{19}{6}]$ |
| Swan slopes: | $[2,\frac{13}{6}]$ |
| Means: | $\langle1,\frac{19}{12}\rangle$ |
| Rams: | $(6,7)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $12$ |
| Mass: | $1835008$ |
| Absolute Mass: | $1835008/3$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.