Defining polynomial
| $x^{45} + 9 c_{69} x^{24} + 9 b_{68} x^{23} + 9 b_{67} x^{22} + 9 b_{66} x^{21} + 9 b_{65} x^{20} + 9 b_{64} x^{19} + 9 b_{62} x^{17} + 9 a_{61} x^{16} + 9 b_{60} x^{15} + 9 b_{57} x^{12} + 9 b_{51} x^{6} + 9 b_{48} x^{3} + 3$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $45$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $45$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $105$ |
| Artin slopes: | $[\frac{5}{2},\frac{38}{15}]$ |
| Swan slopes: | $[\frac{3}{2},\frac{23}{15}]$ |
| Means: | $\langle1,\frac{61}{45}\rangle$ |
| Rams: | $(\frac{15}{2},8)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $3$ |
| Mass: | $118098$ |
| Absolute Mass: | $118098$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.