Defining polynomial over unramified subextension
| $x^{18} + 9 b_{35} x^{17} + 9 b_{34} x^{16} + 3 b_{15} x^{15} + 9 b_{32} x^{14} + 9 b_{31} x^{13} + 3 a_{12} x^{12} + 27 c_{39} x^{3} + 27 b_{38} x^{2} + 27 b_{37} x + 3 d_{0} + 9 c_{18}$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $36$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $18$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $94$ |
| Artin slopes: | $[2,\frac{19}{6}]$ |
| Swan slopes: | $[1,\frac{13}{6}]$ |
| Means: | $\langle\frac{2}{3},\frac{5}{3}\rangle$ |
| Rams: | $(2,9)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $36$ |
| Mass: | $38263752$ |
| Absolute Mass: | $19131876$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.