Defining polynomial
| $x^{4} + b_{15} \pi^{4} x^{3} + \left(b_{14} \pi^{4} + b_{10} \pi^{3}\right) x^{2} + \left(b_{17} \pi^{5} + a_{13} \pi^{4}\right) x + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.1.8.26b1.1 |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $16$ |
| Absolute Artin slopes: | $[2,\frac{7}{2},\frac{43}{12},\frac{43}{12},\frac{17}{4}]$ |
| Swan slopes: | $[\frac{13}{3},\frac{13}{3}]$ |
| Means: | $\langle\frac{13}{6},\frac{13}{4}\rangle$ |
| Rams: | $(\frac{13}{3},\frac{13}{3})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $1$ |
| Mass: | $16$ |
| Absolute Mass: | $8$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.