Defining polynomial
| $x^{6} + 2 a_{5} x^{5} + 4 c_{10} x^{4} + 4 b_{9} x^{3} + 4 b_{7} x + 2$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $6$ |
| Base field: | 2.7.1.0a1.1 |
| Ramification index $e$: | $6$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $10$ |
| Absolute Artin slopes: | $[\frac{8}{3}]$ |
| Swan slopes: | $[\frac{5}{3}]$ |
| Means: | $\langle\frac{5}{6}\rangle$ |
| Rams: | $(5)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $2$ |
| Mass: | $2080768$ |
| Absolute Mass: | $2080768/7$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.