Defining polynomial
| $x^{2} + \left(b_{21} \pi^{11} + b_{19} \pi^{10} + b_{17} \pi^{9} + b_{15} \pi^{8} + b_{13} \pi^{7} + a_{11} \pi^{6}\right) x + c_{22} \pi^{12} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $2$ |
| Base field: | 2.1.12.30a1.90 |
| Ramification index $e$: | $2$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $12$ |
| Absolute Artin slopes: | $[\frac{8}{3},\frac{10}{3},\frac{7}{2}]$ |
| Swan slopes: | $[11]$ |
| Means: | $\langle\frac{11}{2}\rangle$ |
| Rams: | $(11)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $2$ |
| Mass: | $32$ |
| Absolute Mass: | $16$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.