↑

Properties

Label 2.1.8.28a1.7-1.2.14a
Base 2.1.8.28a1.7
Degree \(2\)
e \(2\)
f \(1\)
c \(14\)

Related objects

Downloads

Learn more

Defining polynomial

$x^{2} + \left(b_{25} \pi^{13} + b_{23} \pi^{12} + b_{21} \pi^{11} + b_{19} \pi^{10} + b_{17} \pi^{9} + b_{15} \pi^{8} + a_{13} \pi^{7}\right) x + c_{26} \pi^{14} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $2$
Base field: 2.1.8.28a1.7
Ramification index $e$: $2$
Residue field degree $f$: $1$
Discriminant exponent $c$: $14$
Absolute Artin slopes: $[3,\frac{7}{2},\frac{9}{2},\frac{21}{4}]$
Swan slopes: $[13]$
Means: $\langle\frac{13}{2}\rangle$
Rams: $(13)$
Field count: $64$ (complete)
Ambiguity: $2$
Mass: $64$
Absolute Mass: $32$

Diagrams

Varying

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

Galois group: $C_2^5.C_2\wr C_4$ (show 32), $C_2^5.C_2\wr C_2^2$ (show 32) (incomplete)
Hidden Artin slopes: $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ (show 48), not computed (show 16) (incomplete)
Indices of inseparability: $[55,42,28,16,0]$
Associated inertia: $[1,1,1,1]$
Jump Set: $[1,3,7,15,31]$

Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set
Sort order Select

Showing 1-50 of 64

Next   displayed columns for results
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
2.1.16.70c1.357 $x^{16} + 4 x^{12} + 8 x^{10} + 24 x^{8} + 16 x^{7} + 2$ $C_2^5.C_2\wr C_2^2$ (as 16T1455) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.358 $x^{16} + 4 x^{12} + 8 x^{10} + 24 x^{8} + 16 x^{7} + 32 x^{3} + 2$ $C_2^5.C_2\wr C_2^2$ (as 16T1455) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.359 $x^{16} + 16 x^{15} + 4 x^{12} + 8 x^{10} + 24 x^{8} + 16 x^{7} + 2$ $C_2^5.C_2\wr C_2^2$ (as 16T1455) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.360 $x^{16} + 16 x^{15} + 4 x^{12} + 8 x^{10} + 24 x^{8} + 16 x^{7} + 32 x^{3} + 2$ $C_2^5.C_2\wr C_2^2$ (as 16T1455) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.361 $x^{16} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 24 x^{8} + 16 x^{7} + 2$ $C_2^5.C_2\wr C_2^2$ (as 16T1455) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.362 $x^{16} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 24 x^{8} + 16 x^{7} + 32 x^{3} + 2$ $C_2^5.C_2\wr C_2^2$ (as 16T1455) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.363 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 24 x^{8} + 16 x^{7} + 2$ $C_2^5.C_2\wr C_2^2$ (as 16T1455) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.364 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 24 x^{8} + 16 x^{7} + 32 x^{3} + 2$ $C_2^5.C_2\wr C_2^2$ (as 16T1455) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.365 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 24 x^{8} + 16 x^{7} + 2$ $C_2^5.C_2\wr C_2^2$ (as 16T1455) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.366 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 24 x^{8} + 16 x^{7} + 32 x^{3} + 2$ $C_2^5.C_2\wr C_2^2$ (as 16T1455) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.367 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 24 x^{8} + 16 x^{7} + 2$ $C_2^5.C_2\wr C_2^2$ (as 16T1455) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.368 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 24 x^{8} + 16 x^{7} + 32 x^{4} + 2$ $C_2^5.C_2\wr C_2^2$ (as 16T1455) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.369 $x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 16 x^{7} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.370 $x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 16 x^{7} + 32 x^{4} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.371 $x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 16 x^{7} + 32 x^{3} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.372 $x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 16 x^{7} + 32 x^{4} + 32 x^{3} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.373 $x^{16} + 16 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 16 x^{7} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.374 $x^{16} + 16 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 16 x^{7} + 32 x^{3} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.375 $x^{16} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 16 x^{7} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ not computed not computed not computed not computed $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.376 $x^{16} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 16 x^{7} + 32 x^{4} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ not computed not computed not computed not computed $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.377 $x^{16} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 16 x^{7} + 32 x^{3} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ not computed not computed not computed not computed $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.378 $x^{16} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 16 x^{7} + 32 x^{4} + 32 x^{3} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ not computed not computed not computed not computed $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.379 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 16 x^{7} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ not computed not computed not computed not computed $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.380 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 16 x^{7} + 32 x^{3} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ not computed not computed not computed not computed $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.381 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 16 x^{7} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ not computed not computed not computed not computed $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.382 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 16 x^{7} + 32 x^{3} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ not computed not computed not computed not computed $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.383 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 16 x^{7} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ not computed not computed not computed not computed $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.384 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 16 x^{7} + 32 x^{4} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ not computed not computed not computed not computed $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.385 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 16 x^{7} + 32 x^{3} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ not computed not computed not computed not computed $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.386 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 16 x^{7} + 32 x^{4} + 32 x^{3} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ not computed not computed not computed not computed $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.387 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 16 x^{7} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.388 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 16 x^{7} + 32 x^{3} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.389 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 16 x^{7} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.390 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 16 x^{7} + 32 x^{4} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.391 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 16 x^{7} + 32 x^{3} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.392 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 16 x^{7} + 32 x^{4} + 32 x^{3} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.393 $x^{16} + 4 x^{12} + 8 x^{10} + 8 x^{8} + 16 x^{7} + 16 x^{6} + 2$ $C_2^5.C_2\wr C_2^2$ (as 16T1455) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.394 $x^{16} + 4 x^{12} + 8 x^{10} + 8 x^{8} + 16 x^{7} + 16 x^{6} + 32 x^{4} + 2$ $C_2^5.C_2\wr C_2^2$ (as 16T1455) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.395 $x^{16} + 4 x^{12} + 8 x^{10} + 8 x^{8} + 16 x^{7} + 16 x^{6} + 32 x^{3} + 2$ $C_2^5.C_2\wr C_2^2$ (as 16T1455) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.396 $x^{16} + 4 x^{12} + 8 x^{10} + 8 x^{8} + 16 x^{7} + 16 x^{6} + 32 x^{4} + 32 x^{3} + 2$ $C_2^5.C_2\wr C_2^2$ (as 16T1455) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.397 $x^{16} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 8 x^{8} + 16 x^{7} + 16 x^{6} + 2$ $C_2^5.C_2\wr C_2^2$ (as 16T1455) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.398 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 8 x^{8} + 16 x^{7} + 16 x^{6} + 2$ $C_2^5.C_2\wr C_2^2$ (as 16T1455) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.399 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 8 x^{8} + 16 x^{7} + 16 x^{6} + 2$ $C_2^5.C_2\wr C_2^2$ (as 16T1455) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.400 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 8 x^{8} + 16 x^{7} + 16 x^{6} + 32 x^{4} + 2$ $C_2^5.C_2\wr C_2^2$ (as 16T1455) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.401 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 8 x^{8} + 16 x^{7} + 16 x^{6} + 32 x^{3} + 2$ $C_2^5.C_2\wr C_2^2$ (as 16T1455) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.402 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 8 x^{8} + 16 x^{7} + 16 x^{6} + 32 x^{4} + 32 x^{3} + 2$ $C_2^5.C_2\wr C_2^2$ (as 16T1455) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.403 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 8 x^{8} + 16 x^{7} + 16 x^{6} + 2$ $C_2^5.C_2\wr C_2^2$ (as 16T1455) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.404 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 8 x^{8} + 16 x^{7} + 16 x^{6} + 32 x^{3} + 2$ $C_2^5.C_2\wr C_2^2$ (as 16T1455) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.405 $x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 8 x^{8} + 16 x^{7} + 16 x^{6} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.70c1.406 $x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 8 x^{8} + 16 x^{7} + 16 x^{6} + 32 x^{3} + 2$ $C_2^5.C_2\wr C_4$ (as 16T1423) $2048$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{9}{2}, \frac{19}{4}, \frac{39}{8}, \frac{21}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4},\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{17}{4}]^{2}$ $[2,2,4,\frac{17}{4},\frac{19}{4},\frac{39}{8}]^{2}$ $[1,1,3,\frac{13}{4},\frac{15}{4},\frac{31}{8}]^{2}$ $[55, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
Next   displayed columns for results