Defining polynomial
| $x^{2} + \left(b_{37} \pi^{19} + b_{35} \pi^{18} + b_{33} \pi^{17} + b_{31} \pi^{16} + b_{29} \pi^{15} + b_{27} \pi^{14} + b_{25} \pi^{13} + b_{23} \pi^{12} + b_{21} \pi^{11} + a_{19} \pi^{10}\right) x + c_{38} \pi^{20} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $2$ |
| Base field: | 2.1.14.22a1.11 |
| Ramification index $e$: | $2$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $20$ |
| Absolute Artin slopes: | $[\frac{16}{7},3]$ |
| Swan slopes: | $[19]$ |
| Means: | $\langle\frac{19}{2}\rangle$ |
| Rams: | $(19)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $2$ |
| Mass: | $512$ |
| Absolute Mass: | $256$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.