Defining polynomial
| $x^{40} + 4 b_{79} x^{39} + 4 b_{77} x^{37} + 4 b_{75} x^{35} + 4 b_{73} x^{33} + 4 b_{71} x^{31} + 4 b_{69} x^{29} + 2 b_{28} x^{28} + 4 b_{67} x^{27} + 2 b_{26} x^{26} + 4 b_{65} x^{25} + 4 b_{63} x^{23} + 2 a_{22} x^{22} + 4 b_{61} x^{21} + 2 b_{20} x^{20} + 4 b_{59} x^{19} + 4 b_{57} x^{17} + 4 b_{55} x^{15} + 4 b_{53} x^{13} + 4 a_{51} x^{11} + 8 c_{80} + 2$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $40$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $40$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $90$ |
| Artin slopes: | $[\frac{26}{15},\frac{26}{15},3]$ |
| Swan slopes: | $[\frac{11}{15},\frac{11}{15},2]$ |
| Means: | $\langle\frac{11}{30},\frac{11}{20},\frac{51}{40}\rangle$ |
| Rams: | $(\frac{11}{3},\frac{11}{3},29)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $2$ |
| Mass: | $131072$ |
| Absolute Mass: | $131072$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.