| $x^{32} + 8 a_{95} x^{31} + 8 b_{94} x^{30} + 4 a_{60} x^{28} + 8 b_{90} x^{26} + 4 b_{56} x^{24} + 8 b_{86} x^{22} + 8 a_{82} x^{18} + \left(2 a_{16} + 8 c_{80}\right) x^{16} + \left(8 b_{76} + 16 c_{108}\right) x^{12} + 16 b_{107} x^{11} + 16 b_{105} x^{9} + \left(4 a_{40} + 16 c_{104}\right) x^{8} + 16 b_{103} x^{7} + 16 b_{102} x^{6} + 16 b_{101} x^{5} + 8 b_{68} x^{4} + 16 b_{99} x^{3} + 16 b_{98} x^{2} + 16 b_{97} x + 4 c_{32} + 8 c_{64} + 2$ |
| Residue field characteristic: | $2$ |
| Degree: | $32$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $32$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $126$ |
| Artin slopes: | $[2,3,\frac{7}{2},\frac{17}{4},\frac{35}{8}]$ |
| Swan slopes: | $[1,2,\frac{5}{2},\frac{13}{4},\frac{27}{8}]$ |
| Means: | $\langle\frac{1}{2},\frac{5}{4},\frac{15}{8},\frac{41}{16},\frac{95}{32}\rangle$ |
| Rams: | $(1,3,5,11,13)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $32$ |
| Mass: | $16384$ |
| Absolute Mass: | $16384$ ($0$ currently in the LMFDB) |
The LMFDB does not contain any fields from this family.
