| $x^{32} + 16 b_{127} x^{31} + 8 a_{94} x^{30} + 16 b_{125} x^{29} + 8 b_{92} x^{28} + 16 b_{123} x^{27} + 16 b_{121} x^{25} + \left(4 b_{56} + 16 c_{120}\right) x^{24} + 16 b_{119} x^{23} + 16 b_{118} x^{22} + 16 b_{117} x^{21} + 8 b_{84} x^{20} + 16 b_{115} x^{19} + 16 b_{114} x^{18} + 16 b_{113} x^{17} + 2 a_{16} x^{16} + 16 a_{111} x^{15} + 16 b_{110} x^{14} + 8 b_{76} x^{12} + 16 b_{106} x^{10} + 4 a_{40} x^{8} + 16 b_{102} x^{6} + 8 a_{68} x^{4} + 16 b_{98} x^{2} + 4 c_{32} + 8 c_{64} + 16 c_{96} + 32 c_{128} + 2$ |
| Residue field characteristic: | $2$ |
| Degree: | $32$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $32$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $142$ |
| Artin slopes: | $[2,3,4,\frac{19}{4},5]$ |
| Swan slopes: | $[1,2,3,\frac{15}{4},4]$ |
| Means: | $\langle\frac{1}{2},\frac{5}{4},\frac{17}{8},\frac{47}{16},\frac{111}{32}\rangle$ |
| Rams: | $(1,3,7,13,17)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $32$ |
| Mass: | $262144$ |
| Absolute Mass: | $262144$ ($0$ currently in the LMFDB) |
The LMFDB does not contain any fields from this family.
