Defining polynomial
| $x^{36} + 9 b_{71} x^{35} + 9 b_{70} x^{34} + 3 b_{33} x^{33} + 9 b_{68} x^{32} + 9 b_{67} x^{31} + 3 a_{30} x^{30} + 9 b_{65} x^{29} + 9 b_{64} x^{28} + 9 b_{62} x^{26} + 9 b_{61} x^{25} + 9 b_{59} x^{23} + 9 a_{58} x^{22} + 9 c_{45} x^{9} + 9 b_{42} x^{6} + 9 b_{39} x^{3} + 3 d_{0} + 27 c_{72}$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $36$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $36$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $93$ |
| Artin slopes: | $[\frac{9}{4},3]$ |
| Swan slopes: | $[\frac{5}{4},2]$ |
| Means: | $\langle\frac{5}{6},\frac{29}{18}\rangle$ |
| Rams: | $(5,14)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $18$ |
| Mass: | $2125764$ |
| Absolute Mass: | $2125764$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.