Properties

Label 5.2.10.32a
Base 5.1.1.0a1.1
Degree \(20\)
e \(10\)
f \(2\)
c \(32\)

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Defining polynomial over unramified subextension

$x^{10} + 5 b_{8} x^{8} + 5 a_{7} x^{7} + 5 d_{0}$

Invariants

Residue field characteristic: $5$
Degree: $20$
Base field: $\Q_{5}$
Ramification index $e$: $10$
Residue field degree $f$: $2$
Discriminant exponent $c$: $32$
Artin slopes: $[\frac{15}{8}]$
Swan slopes: $[\frac{7}{8}]$
Means: $\langle\frac{7}{10}\rangle$
Rams: $(\frac{7}{4})$
Field count: $310$ (complete)
Ambiguity: $4$
Mass: $600$
Absolute Mass: $300$

Diagrams

Varying

Indices of inseparability: $[7,0]$
Associated inertia: $[1,1]$
Jump Set: undefined

Fields


Showing 1-50 of 310

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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
5.2.10.32a1.1 $( x^{2} + 4 x + 2 )^{10} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.2 $( x^{2} + 4 x + 2 )^{10} + 5 x ( x^{2} + 4 x + 2 )^{8} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ $C_5^4.\OD_{32}$ (as 20T504) $20000$ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.3 $( x^{2} + 4 x + 2 )^{10} + 10 x ( x^{2} + 4 x + 2 )^{8} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.4 $( x^{2} + 4 x + 2 )^{10} + 15 x ( x^{2} + 4 x + 2 )^{8} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.5 $( x^{2} + 4 x + 2 )^{10} + 20 x ( x^{2} + 4 x + 2 )^{8} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ $C_5^4.\OD_{32}$ (as 20T504) $20000$ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.6 $( x^{2} + 4 x + 2 )^{10} + 5 ( x^{2} + 4 x + 2 )^{8} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ $C_5^4.\OD_{32}$ (as 20T504) $20000$ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.7 $( x^{2} + 4 x + 2 )^{10} + \left(5 x + 5\right) ( x^{2} + 4 x + 2 )^{8} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.8 $( x^{2} + 4 x + 2 )^{10} + \left(10 x + 5\right) ( x^{2} + 4 x + 2 )^{8} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.9 $( x^{2} + 4 x + 2 )^{10} + \left(15 x + 5\right) ( x^{2} + 4 x + 2 )^{8} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.10 $( x^{2} + 4 x + 2 )^{10} + \left(20 x + 5\right) ( x^{2} + 4 x + 2 )^{8} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.11 $( x^{2} + 4 x + 2 )^{10} + 10 ( x^{2} + 4 x + 2 )^{8} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ $C_5^4.\OD_{32}$ (as 20T504) $20000$ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.12 $( x^{2} + 4 x + 2 )^{10} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 )^{8} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.13 $( x^{2} + 4 x + 2 )^{10} + \left(10 x + 10\right) ( x^{2} + 4 x + 2 )^{8} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ $C_5^4.\OD_{32}$ (as 20T504) $20000$ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.14 $( x^{2} + 4 x + 2 )^{10} + \left(15 x + 10\right) ( x^{2} + 4 x + 2 )^{8} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ $C_5^4.\OD_{32}$ (as 20T504) $20000$ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.15 $( x^{2} + 4 x + 2 )^{10} + \left(20 x + 10\right) ( x^{2} + 4 x + 2 )^{8} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ $C_5^4.\OD_{32}$ (as 20T504) $20000$ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.16 $( x^{2} + 4 x + 2 )^{10} + 15 ( x^{2} + 4 x + 2 )^{8} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ $C_5^4.\OD_{32}$ (as 20T504) $20000$ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.17 $( x^{2} + 4 x + 2 )^{10} + \left(5 x + 15\right) ( x^{2} + 4 x + 2 )^{8} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.18 $( x^{2} + 4 x + 2 )^{10} + \left(10 x + 15\right) ( x^{2} + 4 x + 2 )^{8} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ $C_5^4.\OD_{32}$ (as 20T504) $20000$ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.19 $( x^{2} + 4 x + 2 )^{10} + \left(15 x + 15\right) ( x^{2} + 4 x + 2 )^{8} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ $C_5^4.\OD_{32}$ (as 20T504) $20000$ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.20 $( x^{2} + 4 x + 2 )^{10} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{8} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.21 $( x^{2} + 4 x + 2 )^{10} + 20 ( x^{2} + 4 x + 2 )^{8} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.22 $( x^{2} + 4 x + 2 )^{10} + \left(5 x + 20\right) ( x^{2} + 4 x + 2 )^{8} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.23 $( x^{2} + 4 x + 2 )^{10} + \left(10 x + 20\right) ( x^{2} + 4 x + 2 )^{8} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.24 $( x^{2} + 4 x + 2 )^{10} + \left(15 x + 20\right) ( x^{2} + 4 x + 2 )^{8} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.25 $( x^{2} + 4 x + 2 )^{10} + \left(20 x + 20\right) ( x^{2} + 4 x + 2 )^{8} + 10 x ( x^{2} + 4 x + 2 )^{7} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ $C_5^4.\OD_{32}$ (as 20T504) $20000$ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.26 $( x^{2} + 4 x + 2 )^{10} + 10 ( x^{2} + 4 x + 2 )^{7} + 5$ $C_5^2:\OD_{16}$ (as 20T115) $400$ $2$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.27 $( x^{2} + 4 x + 2 )^{10} + 5 x ( x^{2} + 4 x + 2 )^{8} + 10 ( x^{2} + 4 x + 2 )^{7} + 5$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.28 $( x^{2} + 4 x + 2 )^{10} + 10 x ( x^{2} + 4 x + 2 )^{8} + 10 ( x^{2} + 4 x + 2 )^{7} + 5$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.29 $( x^{2} + 4 x + 2 )^{10} + 5 ( x^{2} + 4 x + 2 )^{8} + 10 ( x^{2} + 4 x + 2 )^{7} + 5$ $C_5^2:\OD_{16}$ (as 20T115) $400$ $2$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.30 $( x^{2} + 4 x + 2 )^{10} + \left(5 x + 5\right) ( x^{2} + 4 x + 2 )^{8} + 10 ( x^{2} + 4 x + 2 )^{7} + 5$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.31 $( x^{2} + 4 x + 2 )^{10} + \left(10 x + 5\right) ( x^{2} + 4 x + 2 )^{8} + 10 ( x^{2} + 4 x + 2 )^{7} + 5$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.32 $( x^{2} + 4 x + 2 )^{10} + 10 ( x^{2} + 4 x + 2 )^{8} + 10 ( x^{2} + 4 x + 2 )^{7} + 5$ not computed $ $not computed$ $ $2$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.33 $( x^{2} + 4 x + 2 )^{10} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 )^{8} + 10 ( x^{2} + 4 x + 2 )^{7} + 5$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.34 $( x^{2} + 4 x + 2 )^{10} + \left(10 x + 10\right) ( x^{2} + 4 x + 2 )^{8} + 10 ( x^{2} + 4 x + 2 )^{7} + 5$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.35 $( x^{2} + 4 x + 2 )^{10} + 15 ( x^{2} + 4 x + 2 )^{8} + 10 ( x^{2} + 4 x + 2 )^{7} + 5$ not computed $ $not computed$ $ $2$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.36 $( x^{2} + 4 x + 2 )^{10} + \left(5 x + 15\right) ( x^{2} + 4 x + 2 )^{8} + 10 ( x^{2} + 4 x + 2 )^{7} + 5$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.37 $( x^{2} + 4 x + 2 )^{10} + \left(10 x + 15\right) ( x^{2} + 4 x + 2 )^{8} + 10 ( x^{2} + 4 x + 2 )^{7} + 5$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.38 $( x^{2} + 4 x + 2 )^{10} + 20 ( x^{2} + 4 x + 2 )^{8} + 10 ( x^{2} + 4 x + 2 )^{7} + 5$ $C_5^2:\OD_{16}$ (as 20T115) $400$ $2$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.39 $( x^{2} + 4 x + 2 )^{10} + \left(5 x + 20\right) ( x^{2} + 4 x + 2 )^{8} + 10 ( x^{2} + 4 x + 2 )^{7} + 5$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a1.40 $( x^{2} + 4 x + 2 )^{10} + \left(10 x + 20\right) ( x^{2} + 4 x + 2 )^{8} + 10 ( x^{2} + 4 x + 2 )^{7} + 5$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (t + 2)$ undefined
5.2.10.32a2.1 $( x^{2} + 4 x + 2 )^{10} + 5 ( x^{2} + 4 x + 2 )^{7} + 5$ $C_5^2:\OD_{16}$ (as 20T115) $400$ $2$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (3 t + 1)$ undefined
5.2.10.32a2.2 $( x^{2} + 4 x + 2 )^{10} + 5 x ( x^{2} + 4 x + 2 )^{8} + 5 ( x^{2} + 4 x + 2 )^{7} + 5$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (3 t + 1)$ undefined
5.2.10.32a2.3 $( x^{2} + 4 x + 2 )^{10} + 10 x ( x^{2} + 4 x + 2 )^{8} + 5 ( x^{2} + 4 x + 2 )^{7} + 5$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (3 t + 1)$ undefined
5.2.10.32a2.4 $( x^{2} + 4 x + 2 )^{10} + 5 ( x^{2} + 4 x + 2 )^{8} + 5 ( x^{2} + 4 x + 2 )^{7} + 5$ $C_5^2:\OD_{16}$ (as 20T115) $400$ $2$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (3 t + 1)$ undefined
5.2.10.32a2.5 $( x^{2} + 4 x + 2 )^{10} + \left(5 x + 5\right) ( x^{2} + 4 x + 2 )^{8} + 5 ( x^{2} + 4 x + 2 )^{7} + 5$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (3 t + 1)$ undefined
5.2.10.32a2.6 $( x^{2} + 4 x + 2 )^{10} + \left(10 x + 5\right) ( x^{2} + 4 x + 2 )^{8} + 5 ( x^{2} + 4 x + 2 )^{7} + 5$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (3 t + 1)$ undefined
5.2.10.32a2.7 $( x^{2} + 4 x + 2 )^{10} + 10 ( x^{2} + 4 x + 2 )^{8} + 5 ( x^{2} + 4 x + 2 )^{7} + 5$ not computed $ $not computed$ $ $2$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (3 t + 1)$ undefined
5.2.10.32a2.8 $( x^{2} + 4 x + 2 )^{10} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 )^{8} + 5 ( x^{2} + 4 x + 2 )^{7} + 5$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (3 t + 1)$ undefined
5.2.10.32a2.9 $( x^{2} + 4 x + 2 )^{10} + \left(10 x + 10\right) ( x^{2} + 4 x + 2 )^{8} + 5 ( x^{2} + 4 x + 2 )^{7} + 5$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (3 t + 1)$ undefined
5.2.10.32a2.10 $( x^{2} + 4 x + 2 )^{10} + 15 ( x^{2} + 4 x + 2 )^{8} + 5 ( x^{2} + 4 x + 2 )^{7} + 5$ $C_5^2:\OD_{16}$ (as 20T115) $400$ $2$ not computed not computed not computed not computed $[7, 0]$ $[1, 1]$ $z^5 + 2,2 z + (3 t + 1)$ undefined
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