Defining polynomial
| $x^{7} + b_{41} \pi^{6} x^{6} + b_{40} \pi^{6} x^{5} + b_{39} \pi^{6} x^{4} + b_{38} \pi^{6} x^{3} + b_{37} \pi^{6} x^{2} + a_{36} \pi^{6} x + c_{42} \pi^{7} + \pi$ |
Invariants
| Residue field characteristic: | $7$ |
| Degree: | $7$ |
| Base field: | 7.1.6.5a1.6 |
| Ramification index $e$: | $7$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $42$ |
| Absolute Artin slopes: | $[2]$ |
| Swan slopes: | $[6]$ |
| Means: | $\langle\frac{36}{7}\rangle$ |
| Rams: | $(6)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $7$ |
| Mass: | $100842$ |
| Absolute Mass: | $16807$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.