Defining polynomial
| $x^{4} + b_{15} \pi^{4} x^{3} + \left(c_{18} \pi^{5} + b_{14} \pi^{4} + b_{10} \pi^{3}\right) x^{2} + \left(b_{17} \pi^{5} + a_{13} \pi^{4}\right) x + c_{16} \pi^{5} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.5.2.15a1.2 |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $16$ |
| Absolute Artin slopes: | $[3,4,\frac{17}{4}]$ |
| Swan slopes: | $[4,\frac{9}{2}]$ |
| Means: | $\langle2,\frac{13}{4}\rangle$ |
| Rams: | $(4,5)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $32505856$ |
| Absolute Mass: | $16252928/5$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.