Defining polynomial
| $x^{45} + 9 b_{89} x^{44} + 9 b_{88} x^{43} + 9 b_{86} x^{41} + 9 b_{85} x^{40} + 9 b_{83} x^{38} + 9 b_{82} x^{37} + 9 b_{80} x^{35} + 9 b_{79} x^{34} + 9 a_{77} x^{32} + 9 b_{66} x^{21} + 9 b_{60} x^{15} + 9 b_{57} x^{12} + 9 b_{51} x^{6} + \left(9 b_{48} + 27 c_{93}\right) x^{3} + 27 b_{92} x^{2} + 27 b_{91} x + 3$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $45$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $45$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $121$ |
| Artin slopes: | $[\frac{5}{2},\frac{46}{15}]$ |
| Swan slopes: | $[\frac{3}{2},\frac{31}{15}]$ |
| Means: | $\langle1,\frac{77}{45}\rangle$ |
| Rams: | $(\frac{15}{2},16)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $3$ |
| Mass: | $28697814$ |
| Absolute Mass: | $28697814$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.