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Properties

Label 2.1.10.19a
Base 2.1.1.0a1.1
Degree \(10\)
e \(10\)
f \(1\)
c \(19\)

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Defining polynomial

$x^{10} + 4 b_{19} x^{9} + 4 b_{17} x^{7} + 4 b_{15} x^{5} + 4 b_{13} x^{3} + 4 b_{11} x + 8 c_{20} + 2$

Invariants

Residue field characteristic: $2$
Degree: $10$
Base field: $\Q_{2}$
Ramification index $e$: $10$
Residue field degree $f$: $1$
Discriminant exponent $c$: $19$
Artin slopes: $[3]$
Swan slopes: $[2]$
Means: $\langle1\rangle$
Rams: $(10)$
Field count: $64$ (complete)
Ambiguity: $2$
Mass: $32$
Absolute Mass: $32$

Diagrams

Varying

Indices of inseparability: $[10,0]$
Associated inertia: $[4,1]$
Jump Set: $[5,15]$

Galois groups and Hidden Artin slopes

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Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set Fields per packet
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Showing 1-50 of 64

Next   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
2.1.10.19a1.1 4 $x^{10} + 2$ $F_{5}\times C_2$ (as 10T5) $40$ $2$ $[3]_{5}^{4}$ $[2]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.2 4 $x^{10} + 10$ $F_{5}\times C_2$ (as 10T5) $40$ $2$ $[3]_{5}^{4}$ $[2]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.3 4 $x^{10} + 4 x^{9} + 2$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{6}{5}, \frac{6}{5}, \frac{6}{5}, \frac{6}{5}, 3]_{5}^{4}$ $[\frac{1}{5},\frac{1}{5},\frac{1}{5},\frac{1}{5},2]_{5}^{4}$ $[\frac{6}{5},\frac{6}{5},\frac{6}{5},\frac{6}{5}]^{4}$ $[\frac{1}{5},\frac{1}{5},\frac{1}{5},\frac{1}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.4 4 $x^{10} + 4 x^{9} + 10$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{6}{5}, \frac{6}{5}, \frac{6}{5}, \frac{6}{5}, 3]_{5}^{4}$ $[\frac{1}{5},\frac{1}{5},\frac{1}{5},\frac{1}{5},2]_{5}^{4}$ $[\frac{6}{5},\frac{6}{5},\frac{6}{5},\frac{6}{5}]^{4}$ $[\frac{1}{5},\frac{1}{5},\frac{1}{5},\frac{1}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.5 8 $x^{10} + 4 x^{7} + 2$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{8}{5}, \frac{8}{5}, \frac{8}{5}, \frac{8}{5}, 3]_{5}^{4}$ $[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5},2]_{5}^{4}$ $[\frac{8}{5},\frac{8}{5},\frac{8}{5},\frac{8}{5}]^{4}$ $[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.6 8 $x^{10} + 4 x^{7} + 10$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{8}{5}, \frac{8}{5}, \frac{8}{5}, \frac{8}{5}, 3]_{5}^{4}$ $[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5},2]_{5}^{4}$ $[\frac{8}{5},\frac{8}{5},\frac{8}{5},\frac{8}{5}]^{4}$ $[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.7 8 $x^{10} + 4 x^{9} + 4 x^{7} + 2$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{8}{5}, \frac{8}{5}, \frac{8}{5}, \frac{8}{5}, 3]_{5}^{4}$ $[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5},2]_{5}^{4}$ $[\frac{8}{5},\frac{8}{5},\frac{8}{5},\frac{8}{5}]^{4}$ $[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.8 8 $x^{10} + 4 x^{9} + 4 x^{7} + 10$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{8}{5}, \frac{8}{5}, \frac{8}{5}, \frac{8}{5}, 3]_{5}^{4}$ $[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5},2]_{5}^{4}$ $[\frac{8}{5},\frac{8}{5},\frac{8}{5},\frac{8}{5}]^{4}$ $[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.9 4 $x^{10} + 4 x^{5} + 2$ $F_{5}\times C_2$ (as 10T5) $40$ $2$ $[3]_{5}^{4}$ $[2]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.10 4 $x^{10} + 4 x^{5} + 10$ $F_{5}\times C_2$ (as 10T5) $40$ $2$ $[3]_{5}^{4}$ $[2]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.11 4 $x^{10} + 4 x^{9} + 4 x^{5} + 2$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{6}{5}, \frac{6}{5}, \frac{6}{5}, \frac{6}{5}, 3]_{5}^{4}$ $[\frac{1}{5},\frac{1}{5},\frac{1}{5},\frac{1}{5},2]_{5}^{4}$ $[\frac{6}{5},\frac{6}{5},\frac{6}{5},\frac{6}{5}]^{4}$ $[\frac{1}{5},\frac{1}{5},\frac{1}{5},\frac{1}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.12 4 $x^{10} + 4 x^{9} + 4 x^{5} + 10$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{6}{5}, \frac{6}{5}, \frac{6}{5}, \frac{6}{5}, 3]_{5}^{4}$ $[\frac{1}{5},\frac{1}{5},\frac{1}{5},\frac{1}{5},2]_{5}^{4}$ $[\frac{6}{5},\frac{6}{5},\frac{6}{5},\frac{6}{5}]^{4}$ $[\frac{1}{5},\frac{1}{5},\frac{1}{5},\frac{1}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.13 8 $x^{10} + 4 x^{7} + 4 x^{5} + 2$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{8}{5}, \frac{8}{5}, \frac{8}{5}, \frac{8}{5}, 3]_{5}^{4}$ $[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5},2]_{5}^{4}$ $[\frac{8}{5},\frac{8}{5},\frac{8}{5},\frac{8}{5}]^{4}$ $[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.14 8 $x^{10} + 4 x^{7} + 4 x^{5} + 10$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{8}{5}, \frac{8}{5}, \frac{8}{5}, \frac{8}{5}, 3]_{5}^{4}$ $[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5},2]_{5}^{4}$ $[\frac{8}{5},\frac{8}{5},\frac{8}{5},\frac{8}{5}]^{4}$ $[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.15 8 $x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{5} + 2$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{8}{5}, \frac{8}{5}, \frac{8}{5}, \frac{8}{5}, 3]_{5}^{4}$ $[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5},2]_{5}^{4}$ $[\frac{8}{5},\frac{8}{5},\frac{8}{5},\frac{8}{5}]^{4}$ $[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.16 8 $x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{5} + 10$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{8}{5}, \frac{8}{5}, \frac{8}{5}, \frac{8}{5}, 3]_{5}^{4}$ $[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5},2]_{5}^{4}$ $[\frac{8}{5},\frac{8}{5},\frac{8}{5},\frac{8}{5}]^{4}$ $[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.17 16 $x^{10} + 4 x^{3} + 2$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}, 3]_{5}^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5},2]_{5}^{4}$ $[\frac{12}{5},\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.18 16 $x^{10} + 4 x^{3} + 10$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}, 3]_{5}^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5},2]_{5}^{4}$ $[\frac{12}{5},\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.19 16 $x^{10} + 4 x^{9} + 4 x^{3} + 2$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}, 3]_{5}^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5},2]_{5}^{4}$ $[\frac{12}{5},\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.20 16 $x^{10} + 4 x^{9} + 4 x^{3} + 10$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}, 3]_{5}^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5},2]_{5}^{4}$ $[\frac{12}{5},\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.21 16 $x^{10} + 4 x^{7} + 4 x^{3} + 2$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}, 3]_{5}^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5},2]_{5}^{4}$ $[\frac{12}{5},\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.22 16 $x^{10} + 4 x^{7} + 4 x^{3} + 10$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}, 3]_{5}^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5},2]_{5}^{4}$ $[\frac{12}{5},\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.23 16 $x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{3} + 2$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}, 3]_{5}^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5},2]_{5}^{4}$ $[\frac{12}{5},\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.24 16 $x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{3} + 10$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}, 3]_{5}^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5},2]_{5}^{4}$ $[\frac{12}{5},\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.25 16 $x^{10} + 4 x^{5} + 4 x^{3} + 2$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}, 3]_{5}^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5},2]_{5}^{4}$ $[\frac{12}{5},\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.26 16 $x^{10} + 4 x^{5} + 4 x^{3} + 10$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}, 3]_{5}^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5},2]_{5}^{4}$ $[\frac{12}{5},\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.27 16 $x^{10} + 4 x^{9} + 4 x^{5} + 4 x^{3} + 2$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}, 3]_{5}^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5},2]_{5}^{4}$ $[\frac{12}{5},\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.28 16 $x^{10} + 4 x^{9} + 4 x^{5} + 4 x^{3} + 10$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}, 3]_{5}^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5},2]_{5}^{4}$ $[\frac{12}{5},\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.29 16 $x^{10} + 4 x^{7} + 4 x^{5} + 4 x^{3} + 2$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}, 3]_{5}^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5},2]_{5}^{4}$ $[\frac{12}{5},\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.30 16 $x^{10} + 4 x^{7} + 4 x^{5} + 4 x^{3} + 10$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}, 3]_{5}^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5},2]_{5}^{4}$ $[\frac{12}{5},\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.31 16 $x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{5} + 4 x^{3} + 2$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}, 3]_{5}^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5},2]_{5}^{4}$ $[\frac{12}{5},\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.32 16 $x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{5} + 4 x^{3} + 10$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}, 3]_{5}^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5},2]_{5}^{4}$ $[\frac{12}{5},\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.33 32 $x^{10} + 4 x + 2$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}, 3]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5},2]_{5}^{4}$ $[\frac{14}{5},\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.34 32 $x^{10} + 4 x + 10$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}, 3]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5},2]_{5}^{4}$ $[\frac{14}{5},\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.35 32 $x^{10} + 4 x^{9} + 4 x + 2$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}, 3]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5},2]_{5}^{4}$ $[\frac{14}{5},\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.36 32 $x^{10} + 4 x^{9} + 4 x + 10$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}, 3]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5},2]_{5}^{4}$ $[\frac{14}{5},\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.37 32 $x^{10} + 4 x^{7} + 4 x + 2$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}, 3]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5},2]_{5}^{4}$ $[\frac{14}{5},\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.38 32 $x^{10} + 4 x^{7} + 4 x + 10$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}, 3]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5},2]_{5}^{4}$ $[\frac{14}{5},\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.39 32 $x^{10} + 4 x^{9} + 4 x^{7} + 4 x + 2$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}, 3]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5},2]_{5}^{4}$ $[\frac{14}{5},\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.40 32 $x^{10} + 4 x^{9} + 4 x^{7} + 4 x + 10$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}, 3]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5},2]_{5}^{4}$ $[\frac{14}{5},\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.41 32 $x^{10} + 4 x^{5} + 4 x + 2$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}, 3]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5},2]_{5}^{4}$ $[\frac{14}{5},\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.42 32 $x^{10} + 4 x^{5} + 4 x + 10$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}, 3]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5},2]_{5}^{4}$ $[\frac{14}{5},\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.43 32 $x^{10} + 4 x^{9} + 4 x^{5} + 4 x + 2$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}, 3]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5},2]_{5}^{4}$ $[\frac{14}{5},\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.44 32 $x^{10} + 4 x^{9} + 4 x^{5} + 4 x + 10$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}, 3]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5},2]_{5}^{4}$ $[\frac{14}{5},\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.45 32 $x^{10} + 4 x^{7} + 4 x^{5} + 4 x + 2$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}, 3]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5},2]_{5}^{4}$ $[\frac{14}{5},\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.46 32 $x^{10} + 4 x^{7} + 4 x^{5} + 4 x + 10$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}, 3]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5},2]_{5}^{4}$ $[\frac{14}{5},\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.47 32 $x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{5} + 4 x + 2$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}, 3]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5},2]_{5}^{4}$ $[\frac{14}{5},\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.48 32 $x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{5} + 4 x + 10$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}, 3]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5},2]_{5}^{4}$ $[\frac{14}{5},\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.49 32 $x^{10} + 4 x^{3} + 4 x + 2$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}, 3]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5},2]_{5}^{4}$ $[\frac{14}{5},\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.19a1.50 32 $x^{10} + 4 x^{3} + 4 x + 10$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $640$ $2$ $[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}, 3]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5},2]_{5}^{4}$ $[\frac{14}{5},\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[10, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
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