Defining polynomial
| $x^{36} + 3 b_{35} x^{35} + 3 b_{34} x^{34} + 3 b_{32} x^{32} + 3 b_{31} x^{31} + 3 b_{29} x^{29} + 3 b_{28} x^{28} + 3 b_{26} x^{26} + 3 a_{25} x^{25} + 3 a_{3} x^{3} + 3 d_{0} + 9 c_{36}$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $36$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $36$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $60$ |
| Artin slopes: | $[\frac{9}{8},2]$ |
| Swan slopes: | $[\frac{1}{8},1]$ |
| Means: | $\langle\frac{1}{12},\frac{25}{36}\rangle$ |
| Rams: | $(\frac{1}{2},11)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $6$ |
| Mass: | $8748$ |
| Absolute Mass: | $8748$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.