Defining polynomial
| $x^{45} + 9 b_{67} x^{22} + 9 b_{65} x^{20} + 9 b_{64} x^{19} + 9 b_{62} x^{17} + 9 b_{61} x^{16} + 9 b_{59} x^{14} + 9 b_{58} x^{13} + 9 b_{56} x^{11} + 9 b_{55} x^{10} + 3 c_{9} x^{9} + 9 b_{53} x^{8} + 9 b_{52} x^{7} + 3 a_{6} x^{6} + 9 b_{50} x^{5} + 9 b_{49} x^{4} + 9 a_{47} x^{2} + 3$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $45$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $45$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $91$ |
| Artin slopes: | $[\frac{6}{5},\frac{5}{2}]$ |
| Swan slopes: | $[\frac{1}{5},\frac{3}{2}]$ |
| Means: | $\langle\frac{2}{15},\frac{47}{45}\rangle$ |
| Rams: | $(1,\frac{41}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $3$ |
| Mass: | $6377292$ |
| Absolute Mass: | $6377292$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.