Defining polynomial
| $x^{36} + 3 b_{33} x^{33} + 3 a_{30} x^{30} + 9 b_{49} x^{13} + 9 b_{47} x^{11} + 9 b_{46} x^{10} + 9 c_{45} x^{9} + 9 b_{44} x^{8} + 9 a_{43} x^{7} + 9 b_{42} x^{6} + 9 b_{39} x^{3} + 3 d_{0}$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $36$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $36$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $78$ |
| Artin slopes: | $[\frac{9}{4},\frac{19}{8}]$ |
| Swan slopes: | $[\frac{5}{4},\frac{11}{8}]$ |
| Means: | $\langle\frac{5}{6},\frac{43}{36}\rangle$ |
| Rams: | $(5,\frac{13}{2})$ |
| 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.