Defining polynomial
| $x^{45} + 9 b_{89} x^{44} + 9 a_{88} x^{43} + 9 b_{66} x^{21} + 27 b_{109} x^{19} + 27 b_{107} x^{17} + 27 b_{106} x^{16} + 9 b_{60} x^{15} + 27 b_{104} x^{14} + 27 b_{103} x^{13} + 9 b_{57} x^{12} + 27 b_{101} x^{11} + 27 b_{100} x^{10} + 27 b_{98} x^{8} + 27 b_{97} x^{7} + 9 b_{51} x^{6} + 27 b_{95} x^{5} + 27 b_{94} x^{4} + 9 b_{48} x^{3} + 27 b_{92} x^{2} + 27 b_{91} x + 3$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $45$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $45$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $132$ |
| Artin slopes: | $[\frac{5}{2},\frac{103}{30}]$ |
| Swan slopes: | $[\frac{3}{2},\frac{73}{30}]$ |
| Means: | $\langle1,\frac{88}{45}\rangle$ |
| Rams: | $(\frac{15}{2},\frac{43}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $1$ |
| Mass: | $2324522934$ |
| Absolute Mass: | $2324522934$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.