| $x^{32} + 8 b_{94} x^{30} + 8 b_{92} x^{28} + 8 a_{90} x^{26} + 4 a_{56} x^{24} + 8 b_{84} x^{20} + \left(4 b_{48} + 8 c_{80} + 16 c_{112}\right) x^{16} + 16 b_{111} x^{15} + 16 b_{109} x^{13} + 8 a_{76} x^{12} + 16 b_{107} x^{11} + 16 b_{105} x^{9} + \left(8 b_{72} + 16 c_{104}\right) x^{8} + 16 b_{103} x^{7} + 16 b_{102} x^{6} + 16 a_{101} x^{5} + 16 b_{98} x^{2} + 8 c_{64} + 16 c_{96} + 2$ |
| Residue field characteristic: | $2$ |
| Degree: | $32$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $32$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $132$ |
| Artin slopes: | $[3,\frac{7}{2},4,\frac{17}{4},\frac{9}{2}]$ |
| Swan slopes: | $[2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2}]$ |
| Means: | $\langle1,\frac{7}{4},\frac{19}{8},\frac{45}{16},\frac{101}{32}\rangle$ |
| Rams: | $(2,3,5,7,11)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $32$ |
| Mass: | $4096$ |
| Absolute Mass: | $4096$ ($0$ currently in the LMFDB) |
The LMFDB does not contain any fields from this family.
