Defining polynomial
| $x^{36} + 9 b_{71} x^{35} + 9 b_{70} x^{34} + 3 a_{33} x^{33} + 9 b_{68} x^{32} + 9 a_{67} x^{31} + \left(9 b_{48} + 27 c_{84}\right) x^{12} + 27 b_{83} x^{11} + 27 b_{82} x^{10} + 27 b_{80} x^{8} + 27 b_{79} x^{7} + 9 b_{42} x^{6} + 27 b_{77} x^{5} + 27 b_{76} x^{4} + 9 b_{39} x^{3} + 27 b_{74} x^{2} + 27 b_{73} x + 3 d_{0}$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $36$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $36$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $102$ |
| Artin slopes: | $[\frac{19}{8},\frac{10}{3}]$ |
| Swan slopes: | $[\frac{11}{8},\frac{7}{3}]$ |
| Means: | $\langle\frac{11}{12},\frac{67}{36}\rangle$ |
| Rams: | $(\frac{11}{2},17)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $6$ |
| Mass: | $19131876$ |
| Absolute Mass: | $19131876$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.