Defining polynomial
| $x^{7} + b_{27} \pi^{4} x^{6} + b_{26} \pi^{4} x^{5} + b_{25} \pi^{4} x^{4} + a_{24} \pi^{4} x^{3} + c_{28} \pi^{5} + \pi$ |
Invariants
| Residue field characteristic: | $7$ |
| Degree: | $7$ |
| Base field: | 7.1.5.4a1.1 |
| Ramification index $e$: | $7$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $30$ |
| Absolute Artin slopes: | $[\frac{9}{5}]$ |
| Swan slopes: | $[4]$ |
| Means: | $\langle\frac{24}{7}\rangle$ |
| Rams: | $(4)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $7$ |
| Mass: | $2058$ |
| Absolute Mass: | $2058$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.