Defining polynomial
| $x^{42} + 7 a_{3} x^{3} + 7 d_{0}$ |
Invariants
| Residue field characteristic: | $7$ |
| Degree: | $42$ |
| Base field: | $\Q_{7}$ |
| Ramification index $e$: | $42$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $44$ |
| Artin slopes: | $[\frac{13}{12}]$ |
| Swan slopes: | $[\frac{1}{12}]$ |
| Means: | $\langle\frac{1}{14}\rangle$ |
| Rams: | $(\frac{1}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $6$ |
| Mass: | $6$ |
| Absolute Mass: | $6$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.