Defining polynomial
| $x^{45} + 3 b_{42} x^{42} + 3 a_{39} x^{39} + 9 b_{67} x^{22} + 9 b_{65} x^{20} + 9 b_{64} x^{19} + 9 b_{62} x^{17} + 9 b_{61} x^{16} + 9 b_{59} x^{14} + 9 a_{58} x^{13} + 9 b_{57} x^{12} + 9 b_{51} x^{6} + 9 b_{48} x^{3} + 3$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $45$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $45$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $102$ |
| Artin slopes: | $[\frac{23}{10},\frac{5}{2}]$ |
| Swan slopes: | $[\frac{13}{10},\frac{3}{2}]$ |
| Means: | $\langle\frac{13}{15},\frac{58}{45}\rangle$ |
| Rams: | $(\frac{13}{2},\frac{19}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $1$ |
| Mass: | $236196$ |
| Absolute Mass: | $236196$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.