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Properties

Label 2.1.16.56l
Base 2.1.1.0a1.1
Degree \(16\)
e \(16\)
f \(1\)
c \(56\)

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Defining polynomial

$x^{16} + 8 b_{47} x^{15} + 8 b_{46} x^{14} + 8 b_{45} x^{13} + 4 b_{28} x^{12} + 8 b_{43} x^{11} + 8 b_{42} x^{10} + 8 a_{41} x^{9} + 2 a_{8} x^{8} + 8 b_{38} x^{6} + 4 a_{20} x^{4} + 8 b_{34} x^{2} + 4 c_{16} + 8 c_{32} + 16 c_{48} + 2$

Invariants

Residue field characteristic: $2$
Degree: $16$
Base field: $\Q_{2}$
Ramification index $e$: $16$
Residue field degree $f$: $1$
Discriminant exponent $c$: $56$
Artin slopes: $[2,3,4,4]$
Swan slopes: $[1,2,3,3]$
Means: $\langle\frac{1}{2},\frac{5}{4},\frac{17}{8},\frac{41}{16}\rangle$
Rams: $(1,3,7,7)$
Field count: $384$ (complete)
Ambiguity: $8$
Mass: $256$
Absolute Mass: $256$

Diagrams

Varying

Indices of inseparability: $[41,34,20,8,0]$ (show 128), $[41,36,20,8,0]$ (show 256)
Associated inertia: $[1,1,2]$ (show 256), $[1,1,3]$ (show 128)
Jump Set: $[1,2,4,8,32]$ (show 192), $[1,2,4,32,48]$ (show 48), $[1,2,25,41,57]$ (show 8), $[1,7,15,31,47]$ (show 96), $[1,9,18,34,50]$ (show 2), $[1,9,27,43,59]$ (show 16), $[1,9,29,45,61]$ (show 8), $[1,9,31,47,63]$ (show 4), $[1,9,32,48,64]$ (show 2), $[1,11,25,41,57]$ (show 8)

Galois groups and Hidden Artin slopes

Select desired size of Galois group. Note that the following data has not all been computed for fields in this family, so the tables below are incomplete.

Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set
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Showing all 48

  displayed columns for results
Label Packet size Polynomial Galois group Galois degree $\#\Aut(K/\Q_p)$ Artin slope content Swan slope content Hidden Artin slopes Hidden Swan slopes Ind. of Insep. Assoc. Inertia Resid. Poly Jump Set
2.1.16.56l1.33 8 $x^{16} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $C_2^4:Q_8$ (as 16T384) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.34 8 $x^{16} + 8 x^{15} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $C_2^4.C_2^3$ (as 16T231) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.35 8 $x^{16} + 8 x^{15} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 26$ $C_2^4.C_2^3$ (as 16T231) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.36 8 $x^{16} + 8 x^{14} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $C_2^4.C_2^3$ (as 16T231) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.37 8 $x^{16} + 8 x^{14} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 26$ $C_2^4.C_2^3$ (as 16T231) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.38 8 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $C_2^4:Q_8$ (as 16T384) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.39 16 $x^{16} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $C_2^4:Q_8$ (as 16T368) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.40 16 $x^{16} + 8 x^{15} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $C_2^4.C_2^3$ (as 16T229) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.41 16 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $C_2^4.C_2^3$ (as 16T229) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.42 16 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $C_2^4:Q_8$ (as 16T368) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.43 32 $x^{16} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $C_2^4.C_2^3$ (as 16T383) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.44 8 $x^{16} + 8 x^{15} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $C_2^4.D_4$ (as 16T284) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.45 8 $x^{16} + 8 x^{15} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 26$ $C_2^4.D_4$ (as 16T284) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.46 8 $x^{16} + 8 x^{14} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $C_2^4.D_4$ (as 16T284) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.47 8 $x^{16} + 8 x^{14} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 26$ $C_2^4.D_4$ (as 16T284) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.48 32 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $C_2^4.C_2^3$ (as 16T383) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.49 32 $x^{16} + 8 x^{13} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $C_2^4.C_2^3$ (as 16T383) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.50 8 $x^{16} + 8 x^{15} + 8 x^{13} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $C_2^4.D_4$ (as 16T318) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.51 8 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $C_2^4.D_4$ (as 16T318) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.52 32 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $C_2^4.C_2^3$ (as 16T383) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.53 16 $x^{16} + 8 x^{10} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $C_2^4:Q_8$ (as 16T368) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.54 16 $x^{16} + 8 x^{15} + 8 x^{10} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $C_2^4.C_2^3$ (as 16T229) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.55 16 $x^{16} + 8 x^{14} + 8 x^{10} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $C_2^4.C_2^3$ (as 16T229) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.56 16 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{10} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $C_2^4:Q_8$ (as 16T368) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.57 32 $x^{16} + 8 x^{11} + 8 x^{10} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $C_2^4.C_2^3$ (as 16T383) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.58 8 $x^{16} + 8 x^{15} + 8 x^{11} + 8 x^{10} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $C_2^4.D_4$ (as 16T318) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.59 8 $x^{16} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $C_2^4.D_4$ (as 16T318) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.60 32 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 8 x^{10} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $C_2^4.C_2^3$ (as 16T383) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.61 32 $x^{16} + 8 x^{15} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 10$ $C_2^4.C_2^3$ (as 16T383) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.62 32 $x^{16} + 8 x^{14} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 10$ $C_2^4.C_2^3$ (as 16T383) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.63 8 $x^{16} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 10$ $C_2^4:Q_8$ (as 16T384) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.64 8 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 10$ $C_2^4:Q_8$ (as 16T384) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l2.17 $x^{16} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 10$ $C_2^8:(C_2\times C_6)$ (as 16T1516) $3072$ $1$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, 4]^{3}$ $[1,1,1,2,2,2,\frac{5}{2},\frac{5}{2},3,3]^{3}$ $[2,2,3,3,\frac{7}{2},\frac{7}{2}]^{3}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2}]^{3}$ $[41, 34, 20, 8, 0]$ $[1, 1, 3]$ $z^8 + 1,z^4 + 1,z^3 + z + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l2.18 $x^{16} + 8 x^{15} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 10$ $C_2^8:(C_2\times C_6)$ (as 16T1516) $3072$ $1$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, 4]^{3}$ $[1,1,1,2,2,2,\frac{5}{2},\frac{5}{2},3,3]^{3}$ $[2,2,3,3,\frac{7}{2},\frac{7}{2}]^{3}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2}]^{3}$ $[41, 34, 20, 8, 0]$ $[1, 1, 3]$ $z^8 + 1,z^4 + 1,z^3 + z + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l2.19 $x^{16} + 8 x^{14} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 10$ $C_2^8:(C_2\times C_6)$ (as 16T1516) $3072$ $1$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, 4]^{3}$ $[1,1,1,2,2,2,\frac{5}{2},\frac{5}{2},3,3]^{3}$ $[2,2,3,3,\frac{7}{2},\frac{7}{2}]^{3}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2}]^{3}$ $[41, 34, 20, 8, 0]$ $[1, 1, 3]$ $z^8 + 1,z^4 + 1,z^3 + z + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l2.20 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 10$ $C_2^8:(C_2\times C_6)$ (as 16T1516) $3072$ $1$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, 4]^{3}$ $[1,1,1,2,2,2,\frac{5}{2},\frac{5}{2},3,3]^{3}$ $[2,2,3,3,\frac{7}{2},\frac{7}{2}]^{3}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2}]^{3}$ $[41, 34, 20, 8, 0]$ $[1, 1, 3]$ $z^8 + 1,z^4 + 1,z^3 + z + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l2.21 $x^{16} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 10$ $C_2^8:(C_2\times C_6)$ (as 16T1516) $3072$ $1$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, 4]^{3}$ $[1,1,1,2,2,2,\frac{5}{2},\frac{5}{2},3,3]^{3}$ $[2,2,3,3,\frac{7}{2},\frac{7}{2}]^{3}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2}]^{3}$ $[41, 34, 20, 8, 0]$ $[1, 1, 3]$ $z^8 + 1,z^4 + 1,z^3 + z + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l2.22 $x^{16} + 8 x^{15} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 10$ $C_2^8:(C_2\times C_6)$ (as 16T1516) $3072$ $1$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, 4]^{3}$ $[1,1,1,2,2,2,\frac{5}{2},\frac{5}{2},3,3]^{3}$ $[2,2,3,3,\frac{7}{2},\frac{7}{2}]^{3}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2}]^{3}$ $[41, 34, 20, 8, 0]$ $[1, 1, 3]$ $z^8 + 1,z^4 + 1,z^3 + z + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l2.23 $x^{16} + 8 x^{14} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 10$ $C_2^8:(C_2\times C_6)$ (as 16T1516) $3072$ $1$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, 4]^{3}$ $[1,1,1,2,2,2,\frac{5}{2},\frac{5}{2},3,3]^{3}$ $[2,2,3,3,\frac{7}{2},\frac{7}{2}]^{3}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2}]^{3}$ $[41, 34, 20, 8, 0]$ $[1, 1, 3]$ $z^8 + 1,z^4 + 1,z^3 + z + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l2.24 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 10$ $C_2^8:(C_2\times C_6)$ (as 16T1516) $3072$ $1$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, 4]^{3}$ $[1,1,1,2,2,2,\frac{5}{2},\frac{5}{2},3,3]^{3}$ $[2,2,3,3,\frac{7}{2},\frac{7}{2}]^{3}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2}]^{3}$ $[41, 34, 20, 8, 0]$ $[1, 1, 3]$ $z^8 + 1,z^4 + 1,z^3 + z + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l2.25 $x^{16} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 10$ $C_2^8:(C_2\times C_6)$ (as 16T1516) $3072$ $1$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, 4]^{3}$ $[1,1,1,2,2,2,\frac{5}{2},\frac{5}{2},3,3]^{3}$ $[2,2,3,3,\frac{7}{2},\frac{7}{2}]^{3}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2}]^{3}$ $[41, 34, 20, 8, 0]$ $[1, 1, 3]$ $z^8 + 1,z^4 + 1,z^3 + z + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l2.26 $x^{16} + 8 x^{15} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 10$ $C_2^8:(C_2\times C_6)$ (as 16T1516) $3072$ $1$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, 4]^{3}$ $[1,1,1,2,2,2,\frac{5}{2},\frac{5}{2},3,3]^{3}$ $[2,2,3,3,\frac{7}{2},\frac{7}{2}]^{3}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2}]^{3}$ $[41, 34, 20, 8, 0]$ $[1, 1, 3]$ $z^8 + 1,z^4 + 1,z^3 + z + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l2.27 $x^{16} + 8 x^{14} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 10$ $C_2^8:(C_2\times C_6)$ (as 16T1516) $3072$ $1$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, 4]^{3}$ $[1,1,1,2,2,2,\frac{5}{2},\frac{5}{2},3,3]^{3}$ $[2,2,3,3,\frac{7}{2},\frac{7}{2}]^{3}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2}]^{3}$ $[41, 34, 20, 8, 0]$ $[1, 1, 3]$ $z^8 + 1,z^4 + 1,z^3 + z + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l2.28 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 10$ $C_2^8:(C_2\times C_6)$ (as 16T1516) $3072$ $1$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, 4]^{3}$ $[1,1,1,2,2,2,\frac{5}{2},\frac{5}{2},3,3]^{3}$ $[2,2,3,3,\frac{7}{2},\frac{7}{2}]^{3}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2}]^{3}$ $[41, 34, 20, 8, 0]$ $[1, 1, 3]$ $z^8 + 1,z^4 + 1,z^3 + z + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l2.29 $x^{16} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 10$ $C_2^8:(C_2\times C_6)$ (as 16T1516) $3072$ $1$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, 4]^{3}$ $[1,1,1,2,2,2,\frac{5}{2},\frac{5}{2},3,3]^{3}$ $[2,2,3,3,\frac{7}{2},\frac{7}{2}]^{3}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2}]^{3}$ $[41, 34, 20, 8, 0]$ $[1, 1, 3]$ $z^8 + 1,z^4 + 1,z^3 + z + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l2.30 $x^{16} + 8 x^{15} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 10$ $C_2^8:(C_2\times C_6)$ (as 16T1516) $3072$ $1$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, 4]^{3}$ $[1,1,1,2,2,2,\frac{5}{2},\frac{5}{2},3,3]^{3}$ $[2,2,3,3,\frac{7}{2},\frac{7}{2}]^{3}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2}]^{3}$ $[41, 34, 20, 8, 0]$ $[1, 1, 3]$ $z^8 + 1,z^4 + 1,z^3 + z + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l2.31 $x^{16} + 8 x^{14} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 10$ $C_2^8:(C_2\times C_6)$ (as 16T1516) $3072$ $1$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, 4]^{3}$ $[1,1,1,2,2,2,\frac{5}{2},\frac{5}{2},3,3]^{3}$ $[2,2,3,3,\frac{7}{2},\frac{7}{2}]^{3}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2}]^{3}$ $[41, 34, 20, 8, 0]$ $[1, 1, 3]$ $z^8 + 1,z^4 + 1,z^3 + z + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l2.32 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 10$ $C_2^8:(C_2\times C_6)$ (as 16T1516) $3072$ $1$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, 4]^{3}$ $[1,1,1,2,2,2,\frac{5}{2},\frac{5}{2},3,3]^{3}$ $[2,2,3,3,\frac{7}{2},\frac{7}{2}]^{3}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2}]^{3}$ $[41, 34, 20, 8, 0]$ $[1, 1, 3]$ $z^8 + 1,z^4 + 1,z^3 + z + 1$ $[1, 2, 4, 32, 48]$
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