Defining polynomial
| $x^{45} + 3 b_{11} x^{11} + 3 a_{10} x^{10} + 3$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $45$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $45$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $54$ |
| Artin slopes: | $[\frac{5}{4},\frac{5}{4}]$ |
| Swan slopes: | $[\frac{1}{4},\frac{1}{4}]$ |
| Means: | $\langle\frac{1}{6},\frac{2}{9}\rangle$ |
| Rams: | $(\frac{5}{4},\frac{5}{4})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $1$ |
| Mass: | $6$ |
| Absolute Mass: | $6$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.