Defining polynomial
| $x^{2} + \left(b_{47} \pi^{24} + b_{45} \pi^{23} + b_{43} \pi^{22} + b_{41} \pi^{21} + b_{39} \pi^{20} + b_{37} \pi^{19} + b_{35} \pi^{18} + b_{33} \pi^{17} + b_{31} \pi^{16} + b_{29} \pi^{15} + b_{27} \pi^{14} + b_{25} \pi^{13}\right) x + c_{48} \pi^{25} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $2$ |
| Base field: | 2.1.12.30a1.121 |
| Ramification index $e$: | $2$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $25$ |
| Absolute Artin slopes: | $[\frac{8}{3},\frac{10}{3},\frac{55}{12}]$ |
| Swan slopes: | $[24]$ |
| Means: | $\langle12\rangle$ |
| Rams: | $(24)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $2$ |
| Mass: | $4096$ |
| Absolute Mass: | $2048$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.