Defining polynomial
| $x^{2} + \left(b_{33} \pi^{17} + b_{31} \pi^{16} + b_{29} \pi^{15} + b_{27} \pi^{14} + b_{25} \pi^{13} + b_{23} \pi^{12} + b_{21} \pi^{11} + b_{19} \pi^{10} + a_{17} \pi^{9}\right) x + c_{34} \pi^{18} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $2$ |
| Base field: | 2.1.12.25a1.89 |
| Ramification index $e$: | $2$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $18$ |
| Absolute Artin slopes: | $[\frac{4}{3},\frac{19}{6},\frac{43}{12}]$ |
| Swan slopes: | $[17]$ |
| Means: | $\langle\frac{17}{2}\rangle$ |
| Rams: | $(17)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $2$ |
| Mass: | $256$ |
| Absolute Mass: | $128$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.