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Properties

Label 2.1.4.11a1.5-1.4.28b
Base 2.1.4.11a1.5
Degree \(4\)
e \(4\)
f \(1\)
c \(28\)

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Defining polynomial

$x^{4} + \left(b_{35} \pi^{9} + b_{31} \pi^{8} + b_{27} \pi^{7}\right) x^{3} + \left(b_{26} \pi^{7} + b_{22} \pi^{6} + b_{18} \pi^{5} + a_{14} \pi^{4}\right) x^{2} + \left(b_{33} \pi^{9} + b_{29} \pi^{8} + a_{25} \pi^{7}\right) x + c_{36} \pi^{10} + c_{28} \pi^{8} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $4$
Base field: 2.1.4.11a1.5
Ramification index $e$: $4$
Residue field degree $f$: $1$
Discriminant exponent $c$: $28$
Absolute Artin slopes: $[3,4,\frac{19}{4},\frac{21}{4}]$
Swan slopes: $[7,9]$
Means: $\langle\frac{7}{2},\frac{25}{4}\rangle$
Rams: $(7,11)$
Field count: $256$ (complete)
Ambiguity: $4$
Mass: $256$
Absolute Mass: $128$

Diagrams

Varying

These invariants are all associated to absolute extensions of $\Q_{ 2 }$ within this relative family, not the relative extension.

Galois group: $C_2^6:\SD_{16}$ (show 32), $(C_2^2\times C_4^2):\SD_{16}$ (show 32), $C_2^6:D_8$ (show 32), $(C_2^2\times C_4^2):D_8$ (show 32), $C_2^4.C_2\wr D_4$ (show 128) (incomplete)
Hidden Artin slopes: $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ (show 96), $[2,2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ (show 16), not computed (show 112), $[\frac{17}{4},2,\frac{39}{8},\frac{7}{2},\frac{9}{2}]_{2}$ (show 32) (incomplete)
Indices of inseparability: $[57,46,32,16,0]$
Associated inertia: $[1,1,1,1]$
Jump Set: $[1,3,7,15,31]$

Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set
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Showing 1-50 of 256

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Label Polynomial $/ \Q_p$ Galois group $/ \Q_p$ Galois degree $/ \Q_p$ $\#\Aut(K/\Q_p)$ Artin slope content $/ \Q_p$ Swan slope content $/ \Q_p$ Hidden Artin slopes $/ \Q_p$ Hidden Swan slopes $/ \Q_p$ Ind. of Insep. $/ \Q_p$ Assoc. Inertia $/ \Q_p$ Resid. Poly Jump Set
2.1.16.72d1.1025 $x^{16} + 8 x^{14} + 16 x^{9} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1276) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1026 $x^{16} + 8 x^{14} + 16 x^{9} + 32 x^{4} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1276) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1027 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{9} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1276) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1028 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{9} + 32 x^{3} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1276) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1029 $x^{16} + 8 x^{14} + 16 x^{13} + 16 x^{9} + 10$ $C_2^4.C_2\wr D_4$ (as 16T1456) $2048$ $2$ not computed not computed not computed not computed $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1030 $x^{16} + 8 x^{14} + 16 x^{13} + 16 x^{9} + 32 x^{4} + 10$ $C_2^4.C_2\wr D_4$ (as 16T1456) $2048$ $2$ not computed not computed not computed not computed $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1031 $x^{16} + 8 x^{14} + 16 x^{13} + 16 x^{9} + 32 x^{3} + 10$ $C_2^4.C_2\wr D_4$ (as 16T1456) $2048$ $2$ not computed not computed not computed not computed $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1032 $x^{16} + 8 x^{14} + 16 x^{13} + 16 x^{9} + 32 x^{4} + 32 x^{3} + 10$ $C_2^4.C_2\wr D_4$ (as 16T1456) $2048$ $2$ not computed not computed not computed not computed $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1033 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 16 x^{9} + 10$ $C_2^4.C_2\wr D_4$ (as 16T1456) $2048$ $2$ not computed not computed not computed not computed $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1034 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 16 x^{9} + 32 x^{4} + 10$ $C_2^4.C_2\wr D_4$ (as 16T1456) $2048$ $2$ not computed not computed not computed not computed $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1035 $x^{16} + 8 x^{14} + 16 x^{12} + 16 x^{9} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1276) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1036 $x^{16} + 8 x^{14} + 16 x^{12} + 16 x^{9} + 32 x^{4} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1276) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1037 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{12} + 16 x^{9} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1276) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1038 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{12} + 16 x^{9} + 32 x^{3} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1276) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1039 $x^{16} + 8 x^{14} + 16 x^{13} + 16 x^{12} + 16 x^{9} + 10$ $C_2^4.C_2\wr D_4$ (as 16T1456) $2048$ $2$ not computed not computed not computed not computed $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1040 $x^{16} + 8 x^{14} + 16 x^{13} + 16 x^{12} + 16 x^{9} + 32 x^{4} + 10$ $C_2^4.C_2\wr D_4$ (as 16T1456) $2048$ $2$ not computed not computed not computed not computed $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1041 $x^{16} + 8 x^{14} + 16 x^{13} + 16 x^{12} + 16 x^{9} + 32 x^{3} + 10$ $C_2^4.C_2\wr D_4$ (as 16T1456) $2048$ $2$ not computed not computed not computed not computed $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1042 $x^{16} + 8 x^{14} + 16 x^{13} + 16 x^{12} + 16 x^{9} + 32 x^{4} + 32 x^{3} + 10$ $C_2^4.C_2\wr D_4$ (as 16T1456) $2048$ $2$ not computed not computed not computed not computed $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1043 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 16 x^{12} + 16 x^{9} + 10$ $C_2^4.C_2\wr D_4$ (as 16T1456) $2048$ $2$ not computed not computed not computed not computed $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1044 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 16 x^{12} + 16 x^{9} + 32 x^{4} + 10$ $C_2^4.C_2\wr D_4$ (as 16T1456) $2048$ $2$ not computed not computed not computed not computed $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1045 $x^{16} + 8 x^{14} + 16 x^{11} + 16 x^{9} + 10$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1046 $x^{16} + 8 x^{14} + 16 x^{11} + 16 x^{9} + 32 x^{4} + 10$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1047 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{11} + 16 x^{9} + 10$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1048 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{11} + 16 x^{9} + 32 x^{4} + 10$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1049 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{11} + 16 x^{9} + 32 x^{3} + 10$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1050 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{11} + 16 x^{9} + 32 x^{4} + 32 x^{3} + 10$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1051 $x^{16} + 8 x^{14} + 16 x^{13} + 16 x^{11} + 16 x^{9} + 10$ $C_2^4.C_2\wr D_4$ (as 16T1456) $2048$ $2$ not computed not computed not computed not computed $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1052 $x^{16} + 8 x^{14} + 16 x^{13} + 16 x^{11} + 16 x^{9} + 32 x^{4} + 10$ $C_2^4.C_2\wr D_4$ (as 16T1456) $2048$ $2$ not computed not computed not computed not computed $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1053 $x^{16} + 8 x^{14} + 16 x^{13} + 16 x^{11} + 16 x^{9} + 32 x^{3} + 10$ $C_2^4.C_2\wr D_4$ (as 16T1456) $2048$ $2$ not computed not computed not computed not computed $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1054 $x^{16} + 8 x^{14} + 16 x^{13} + 16 x^{11} + 16 x^{9} + 32 x^{4} + 32 x^{3} + 10$ $C_2^4.C_2\wr D_4$ (as 16T1456) $2048$ $2$ not computed not computed not computed not computed $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1055 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 16 x^{11} + 16 x^{9} + 10$ $C_2^4.C_2\wr D_4$ (as 16T1456) $2048$ $2$ not computed not computed not computed not computed $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1056 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 16 x^{11} + 16 x^{9} + 32 x^{4} + 10$ $C_2^4.C_2\wr D_4$ (as 16T1456) $2048$ $2$ not computed not computed not computed not computed $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1057 $x^{16} + 8 x^{14} + 16 x^{12} + 16 x^{11} + 16 x^{9} + 10$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1058 $x^{16} + 8 x^{14} + 16 x^{12} + 16 x^{11} + 16 x^{9} + 32 x^{4} + 10$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1059 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{12} + 16 x^{11} + 16 x^{9} + 10$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1060 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{12} + 16 x^{11} + 16 x^{9} + 32 x^{4} + 10$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1061 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{12} + 16 x^{11} + 16 x^{9} + 32 x^{3} + 10$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1062 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{12} + 16 x^{11} + 16 x^{9} + 32 x^{4} + 32 x^{3} + 10$ $C_2^6:D_8$ (as 16T1275) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1063 $x^{16} + 8 x^{14} + 16 x^{13} + 16 x^{12} + 16 x^{11} + 16 x^{9} + 10$ $C_2^4.C_2\wr D_4$ (as 16T1456) $2048$ $2$ not computed not computed not computed not computed $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1064 $x^{16} + 8 x^{14} + 16 x^{13} + 16 x^{12} + 16 x^{11} + 16 x^{9} + 32 x^{4} + 10$ $C_2^4.C_2\wr D_4$ (as 16T1456) $2048$ $2$ not computed not computed not computed not computed $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1065 $x^{16} + 8 x^{14} + 16 x^{13} + 16 x^{12} + 16 x^{11} + 16 x^{9} + 32 x^{3} + 10$ $C_2^4.C_2\wr D_4$ (as 16T1456) $2048$ $2$ not computed not computed not computed not computed $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1066 $x^{16} + 8 x^{14} + 16 x^{13} + 16 x^{12} + 16 x^{11} + 16 x^{9} + 32 x^{4} + 32 x^{3} + 10$ $C_2^4.C_2\wr D_4$ (as 16T1456) $2048$ $2$ not computed not computed not computed not computed $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1067 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 16 x^{12} + 16 x^{11} + 16 x^{9} + 10$ $C_2^4.C_2\wr D_4$ (as 16T1456) $2048$ $2$ not computed not computed not computed not computed $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1068 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 16 x^{12} + 16 x^{11} + 16 x^{9} + 32 x^{4} + 10$ $C_2^4.C_2\wr D_4$ (as 16T1456) $2048$ $2$ not computed not computed not computed not computed $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1069 $x^{16} + 8 x^{14} + 16 x^{10} + 16 x^{9} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1276) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1070 $x^{16} + 8 x^{14} + 16 x^{10} + 16 x^{9} + 32 x^{4} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1276) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1071 $x^{16} + 8 x^{14} + 16 x^{10} + 16 x^{9} + 32 x^{3} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1276) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1072 $x^{16} + 8 x^{14} + 16 x^{10} + 16 x^{9} + 32 x^{4} + 32 x^{3} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1276) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1073 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{10} + 16 x^{9} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1276) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72d1.1074 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{10} + 16 x^{9} + 32 x^{4} + 10$ $(C_2^2\times C_4^2):D_8$ (as 16T1276) $1024$ $2$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,\frac{7}{2},\frac{17}{4},\frac{9}{2},\frac{39}{8}]^{2}$ $[1,\frac{5}{2},\frac{13}{4},\frac{7}{2},\frac{31}{8}]^{2}$ $[57, 46, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
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