| $x^{32} + 16 b_{127} x^{31} + 8 b_{94} x^{30} + 16 b_{125} x^{29} + 4 a_{60} x^{28} + 16 b_{123} x^{27} + 8 b_{90} x^{26} + 16 b_{121} x^{25} + 4 b_{56} x^{24} + 16 b_{119} x^{23} + 8 b_{86} x^{22} + 16 b_{117} x^{21} + 16 b_{115} x^{19} + 8 b_{82} x^{18} + 16 b_{113} x^{17} + \left(2 a_{16} + 8 c_{80}\right) x^{16} + 16 b_{111} x^{15} + 8 a_{78} x^{14} + 16 b_{109} x^{13} + 8 b_{76} x^{12} + 16 b_{107} x^{11} + 16 b_{105} x^{9} + 4 a_{40} x^{8} + 16 a_{103} x^{7} + 8 b_{68} x^{4} + 4 c_{32} + 8 c_{64} + 16 c_{96} + 32 c_{128} + 2$ |
| Residue field characteristic: | $2$ |
| Degree: | $32$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $32$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $134$ |
| Artin slopes: | $[2,3,\frac{7}{2},4,5]$ |
| Swan slopes: | $[1,2,\frac{5}{2},3,4]$ |
| Means: | $\langle\frac{1}{2},\frac{5}{4},\frac{15}{8},\frac{39}{16},\frac{103}{32}\rangle$ |
| Rams: | $(1,3,5,9,25)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $32$ |
| Mass: | $524288$ |
| Absolute Mass: | $524288$ ($0$ currently in the LMFDB) |
The LMFDB does not contain any fields from this family.
