Defining polynomial
| $x^{2} + \left(b_{53} \pi^{27} + b_{51} \pi^{26} + b_{49} \pi^{25} + b_{47} \pi^{24} + b_{45} \pi^{23} + b_{43} \pi^{22} + b_{41} \pi^{21} + b_{39} \pi^{20} + b_{37} \pi^{19} + b_{35} \pi^{18} + b_{33} \pi^{17} + b_{31} \pi^{16} + b_{29} \pi^{15} + a_{27} \pi^{14}\right) x + c_{54} \pi^{28} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $2$ |
| Base field: | 2.1.14.26a1.19 |
| Ramification index $e$: | $2$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $28$ |
| Absolute Artin slopes: | $[\frac{20}{7},\frac{27}{7}]$ |
| Swan slopes: | $[27]$ |
| Means: | $\langle\frac{27}{2}\rangle$ |
| Rams: | $(27)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $2$ |
| Mass: | $8192$ |
| Absolute Mass: | $4096$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.