| $x^{32} + 16 b_{127} x^{31} + 8 b_{94} x^{30} + 16 b_{125} x^{29} + 8 b_{92} x^{28} + 16 b_{123} x^{27} + 8 a_{90} x^{26} + 16 b_{121} x^{25} + 4 a_{56} x^{24} + 16 b_{119} x^{23} + 16 b_{117} x^{21} + 8 b_{84} x^{20} + 16 b_{115} x^{19} + 16 b_{113} x^{17} + \left(4 b_{48} + 8 c_{80}\right) x^{16} + 16 b_{111} x^{15} + 16 a_{109} x^{13} + 8 a_{76} x^{12} + \left(8 b_{72} + 16 c_{104}\right) x^{8} + 16 b_{102} x^{6} + 16 b_{98} x^{2} + 8 c_{64} + 16 c_{96} + 32 c_{128} + 2$ |
| Residue field characteristic: | $2$ |
| Degree: | $32$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $32$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $140$ |
| Artin slopes: | $[3,\frac{7}{2},4,\frac{17}{4},5]$ |
| Swan slopes: | $[2,\frac{5}{2},3,\frac{13}{4},4]$ |
| Means: | $\langle1,\frac{7}{4},\frac{19}{8},\frac{45}{16},\frac{109}{32}\rangle$ |
| Rams: | $(2,3,5,7,19)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $32$ |
| Mass: | $65536$ |
| Absolute Mass: | $65536$ ($0$ currently in the LMFDB) |
The LMFDB does not contain any fields from this family.
