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Properties

Label 3.5.3.20a
Base 3.1.1.0a1.1
Degree \(15\)
e \(3\)
f \(5\)
c \(20\)

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Defining polynomial over unramified subextension

$x^{3} + 3 a_{2} x^{2} + 9 c_{3} + 3$

Invariants

Residue field characteristic: $3$
Degree: $15$
Base field: $\Q_{3}$
Ramification index $e$: $3$
Residue field degree $f$: $5$
Discriminant exponent $c$: $20$
Artin slopes: $[2]$
Swan slopes: $[1]$
Means: $\langle\frac{2}{3}\rangle$
Rams: $(1)$
Field count: $100$ (complete)
Ambiguity: $15$
Mass: $242$
Absolute Mass: $242/5$

Diagrams

Varying

Indices of inseparability: $[2,0]$
Associated inertia: $[1]$ (show 75), $[2]$ (show 25)
Jump Set: undefined

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 100

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
3.5.3.20a1.1 1 $( x^{5} + 2 x + 1 )^{3} + 3 ( x^{5} + 2 x + 1 )^{2} + 3$ $S_3 \times C_5$ (as 15T4) $30$ $5$ $[2]^{10}$ $[1]^{10}$ $[\ ]^{2}$ $[\ ]^{2}$ $[2, 0]$ $[2]$ $z^2 + (2 t^3 + 1)$ undefined
3.5.3.20a2.1 3 $( x^{5} + 2 x + 1 )^{3} + 6 ( x^{5} + 2 x + 1 )^{2} + 3$ $C_{15}$ (as 15T1) $15$ $15$ $[2]^{5}$ $[1]^{5}$ $[\ ]$ $[\ ]$ $[2, 0]$ $[1]$ $z^2 + (t^3 + 2)$ undefined
3.5.3.20a2.2 3 $( x^{5} + 2 x + 1 )^{3} + 6 ( x^{5} + 2 x + 1 )^{2} + 12$ $C_{15}$ (as 15T1) $15$ $15$ $[2]^{5}$ $[1]^{5}$ $[\ ]$ $[\ ]$ $[2, 0]$ $[1]$ $z^2 + (t^3 + 2)$ undefined
3.5.3.20a2.3 3 $( x^{5} + 2 x + 1 )^{3} + 6 ( x^{5} + 2 x + 1 )^{2} + 21$ $C_{15}$ (as 15T1) $15$ $15$ $[2]^{5}$ $[1]^{5}$ $[\ ]$ $[\ ]$ $[2, 0]$ $[1]$ $z^2 + (t^3 + 2)$ undefined
3.5.3.20a3.1 2 $( x^{5} + 2 x + 1 )^{3} + 3 x ( x^{5} + 2 x + 1 )^{2} + 3$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2]^{15}$ $[1,1,1,1]^{15}$ $[2,2,2]^{3}$ $[1,1,1]^{3}$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t)$ undefined
3.5.3.20a3.2 2 $( x^{5} + 2 x + 1 )^{3} + 3 x ( x^{5} + 2 x + 1 )^{2} + 9 x^{2} + 3$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2]^{15}$ $[1,1,1,1]^{15}$ $[2,2,2]^{3}$ $[1,1,1]^{3}$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t)$ undefined
3.5.3.20a3.3 1 $( x^{5} + 2 x + 1 )^{3} + 3 x ( x^{5} + 2 x + 1 )^{2} + 18 x^{2} + 3$ $C_3^4:C_5$ (as 15T26) $405$ $3$ $[2, 2, 2, 2]^{5}$ $[1,1,1,1]^{5}$ $[2,2,2]$ $[1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t)$ undefined
3.5.3.20a4.1 2 $( x^{5} + 2 x + 1 )^{3} + \left(3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2]^{15}$ $[1,1,1,1]^{15}$ $[2,2,2]^{3}$ $[1,1,1]^{3}$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^3 + t + 2)$ undefined
3.5.3.20a4.2 1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 9 x^{4} + 3$ $C_3^4:C_5$ (as 15T26) $405$ $3$ $[2, 2, 2, 2]^{5}$ $[1,1,1,1]^{5}$ $[2,2,2]$ $[1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^3 + t + 2)$ undefined
3.5.3.20a4.3 2 $( x^{5} + 2 x + 1 )^{3} + \left(3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 18 x^{4} + 3$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2]^{15}$ $[1,1,1,1]^{15}$ $[2,2,2]^{3}$ $[1,1,1]^{3}$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^3 + t + 2)$ undefined
3.5.3.20a5.1 1 $( x^{5} + 2 x + 1 )^{3} + 6 x ( x^{5} + 2 x + 1 )^{2} + 3$ $C_3^4:C_{10}$ (as 15T33) $810$ $1$ $[2, 2, 2, 2]^{10}$ $[1,1,1,1]^{10}$ $[2,2,2]^{2}$ $[1,1,1]^{2}$ $[2, 0]$ $[2]$ $z^2 + (t^4 + 2 t)$ undefined
3.5.3.20a6.1 1 $( x^{5} + 2 x + 1 )^{3} + 3 x^{2} ( x^{5} + 2 x + 1 )^{2} + 3$ $C_3^5:C_{10}$ (as 15T44) $2430$ $1$ $[2, 2, 2, 2, 2]^{10}$ $[1,1,1,1,1]^{10}$ $[2,2,2,2]^{2}$ $[1,1,1,1]^{2}$ $[2, 0]$ $[2]$ $z^2 + (t^2 + 2 t + 1)$ undefined
3.5.3.20a7.1 1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{2} + 3 x\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $C_3^5:C_{10}$ (as 15T44) $2430$ $1$ $[2, 2, 2, 2, 2]^{10}$ $[1,1,1,1,1]^{10}$ $[2,2,2,2]^{2}$ $[1,1,1,1]^{2}$ $[2, 0]$ $[2]$ $z^2 + (2 t^4 + t^2 + 1)$ undefined
3.5.3.20a8.1 1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{2} + 3 x + 3\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $C_3^5:C_{10}$ (as 15T44) $2430$ $1$ $[2, 2, 2, 2, 2]^{10}$ $[1,1,1,1,1]^{10}$ $[2,2,2,2]^{2}$ $[1,1,1,1]^{2}$ $[2, 0]$ $[2]$ $z^2 + (2 t^4 + 2 t^3 + t^2 + 2)$ undefined
3.5.3.20a9.1 3 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{2} + 3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^3 + 2 t^2 + 2 t + 1)$ undefined
3.5.3.20a9.2 3 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{2} + 3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 12$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^3 + 2 t^2 + 2 t + 1)$ undefined
3.5.3.20a9.3 3 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{2} + 3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 21$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^3 + 2 t^2 + 2 t + 1)$ undefined
3.5.3.20a10.1 3 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{2} + 6 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (t^4 + t^3 + 2 t^2 + 1)$ undefined
3.5.3.20a10.2 3 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{2} + 6 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 12$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (t^4 + t^3 + 2 t^2 + 1)$ undefined
3.5.3.20a10.3 3 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{2} + 6 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 21$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (t^4 + t^3 + 2 t^2 + 1)$ undefined
3.5.3.20a11.1 3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 3 x\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^3 + 2 t^2 + 2 t)$ undefined
3.5.3.20a11.2 3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 3 x\right) ( x^{5} + 2 x + 1 )^{2} + 12$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^3 + 2 t^2 + 2 t)$ undefined
3.5.3.20a11.3 3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 3 x\right) ( x^{5} + 2 x + 1 )^{2} + 21$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^3 + 2 t^2 + 2 t)$ undefined
3.5.3.20a12.1 3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + 2 t^3 + 2 t^2 + 2 t + 2)$ undefined
3.5.3.20a12.2 3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 12$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + 2 t^3 + 2 t^2 + 2 t + 2)$ undefined
3.5.3.20a12.3 3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 21$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + 2 t^3 + 2 t^2 + 2 t + 2)$ undefined
3.5.3.20a13.1 2 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 3 x^{2}\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2]^{15}$ $[1,1,1,1]^{15}$ $[2,2,2]^{3}$ $[1,1,1]^{3}$ $[2, 0]$ $[1]$ $z^2 + (t^3 + 1)$ undefined
3.5.3.20a13.2 2 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 3 x^{2}\right) ( x^{5} + 2 x + 1 )^{2} + 9 x + 3$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2]^{15}$ $[1,1,1,1]^{15}$ $[2,2,2]^{3}$ $[1,1,1]^{3}$ $[2, 0]$ $[1]$ $z^2 + (t^3 + 1)$ undefined
3.5.3.20a13.3 1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 3 x^{2}\right) ( x^{5} + 2 x + 1 )^{2} + 18 x + 3$ $C_3^4:C_5$ (as 15T26) $405$ $3$ $[2, 2, 2, 2]^{5}$ $[1,1,1,1]^{5}$ $[2,2,2]$ $[1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (t^3 + 1)$ undefined
3.5.3.20a14.1 1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 3 x^{2} + 3 x\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $C_3^4:C_5$ (as 15T26) $405$ $3$ $[2, 2, 2, 2]^{5}$ $[1,1,1,1]^{5}$ $[2,2,2]$ $[1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^3 + t + 1)$ undefined
3.5.3.20a14.2 2 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 3 x^{2} + 3 x\right) ( x^{5} + 2 x + 1 )^{2} + 9 x + 3$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2]^{15}$ $[1,1,1,1]^{15}$ $[2,2,2]^{3}$ $[1,1,1]^{3}$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^3 + t + 1)$ undefined
3.5.3.20a14.3 2 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 3 x^{2} + 3 x\right) ( x^{5} + 2 x + 1 )^{2} + 18 x + 3$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2]^{15}$ $[1,1,1,1]^{15}$ $[2,2,2]^{3}$ $[1,1,1]^{3}$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^3 + t + 1)$ undefined
3.5.3.20a15.1 3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 6 x^{2}\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (t^3 + t^2 + 2 t + 2)$ undefined
3.5.3.20a15.2 3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 6 x^{2}\right) ( x^{5} + 2 x + 1 )^{2} + 12$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (t^3 + t^2 + 2 t + 2)$ undefined
3.5.3.20a15.3 3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 6 x^{2}\right) ( x^{5} + 2 x + 1 )^{2} + 21$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (t^3 + t^2 + 2 t + 2)$ undefined
3.5.3.20a16.1 3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 6 x^{2} + 3 x + 3\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^2)$ undefined
3.5.3.20a16.2 3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 6 x^{2} + 3 x + 3\right) ( x^{5} + 2 x + 1 )^{2} + 12$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^2)$ undefined
3.5.3.20a16.3 3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 6 x^{2} + 3 x + 3\right) ( x^{5} + 2 x + 1 )^{2} + 21$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^2)$ undefined
3.5.3.20a17.1 2 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 6 x^{2} + 6 x + 3\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2]^{15}$ $[1,1,1,1]^{15}$ $[2,2,2]^{3}$ $[1,1,1]^{3}$ $[2, 0]$ $[1]$ $z^2 + (t^4 + t^2 + t)$ undefined
3.5.3.20a17.2 1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 6 x^{2} + 6 x + 3\right) ( x^{5} + 2 x + 1 )^{2} + 9 x^{2} + 3$ $C_3^4:C_5$ (as 15T26) $405$ $3$ $[2, 2, 2, 2]^{5}$ $[1,1,1,1]^{5}$ $[2,2,2]$ $[1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (t^4 + t^2 + t)$ undefined
3.5.3.20a17.3 2 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 6 x^{2} + 6 x + 3\right) ( x^{5} + 2 x + 1 )^{2} + 18 x^{2} + 3$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2]^{15}$ $[1,1,1,1]^{15}$ $[2,2,2]^{3}$ $[1,1,1]^{3}$ $[2, 0]$ $[1]$ $z^2 + (t^4 + t^2 + t)$ undefined
3.5.3.20a18.1 3 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{3} + 3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^2 + 2)$ undefined
3.5.3.20a18.2 3 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{3} + 3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 12$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^2 + 2)$ undefined
3.5.3.20a18.3 3 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{3} + 3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 21$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^2 + 2)$ undefined
3.5.3.20a19.1 1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{3} + 6 x^{2} + 3 x + 3\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $C_3^5:C_{10}$ (as 15T44) $2430$ $1$ $[2, 2, 2, 2, 2]^{10}$ $[1,1,1,1,1]^{10}$ $[2,2,2,2]^{2}$ $[1,1,1,1]^{2}$ $[2, 0]$ $[2]$ $z^2 + (2 t^4 + t^3 + t)$ undefined
3.5.3.20a20.1 1 $( x^{5} + 2 x + 1 )^{3} + 3 x^{4} ( x^{5} + 2 x + 1 )^{2} + 3$ $C_3^5:C_{10}$ (as 15T44) $2430$ $1$ $[2, 2, 2, 2, 2]^{10}$ $[1,1,1,1,1]^{10}$ $[2,2,2,2]^{2}$ $[1,1,1,1]^{2}$ $[2, 0]$ $[2]$ $z^2 + (t^4 + 2 t^3 + t^2)$ undefined
3.5.3.20a21.1 1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 6 x\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $C_3^5:C_{10}$ (as 15T44) $2430$ $1$ $[2, 2, 2, 2, 2]^{10}$ $[1,1,1,1,1]^{10}$ $[2,2,2,2]^{2}$ $[1,1,1,1]^{2}$ $[2, 0]$ $[2]$ $z^2 + (2 t^4 + 2 t^3 + t^2 + 2 t)$ undefined
3.5.3.20a22.1 1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 3 x^{2} + 6\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $C_3^4:C_{10}$ (as 15T33) $810$ $1$ $[2, 2, 2, 2]^{10}$ $[1,1,1,1]^{10}$ $[2,2,2]^{2}$ $[1,1,1]^{2}$ $[2, 0]$ $[2]$ $z^2 + (t^4 + 2 t^2 + 2 t)$ undefined
3.5.3.20a23.1 1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 3 x^{2} + 6 x\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $C_3^5:C_{10}$ (as 15T44) $2430$ $1$ $[2, 2, 2, 2, 2]^{10}$ $[1,1,1,1,1]^{10}$ $[2,2,2,2]^{2}$ $[1,1,1,1]^{2}$ $[2, 0]$ $[2]$ $z^2 + (2 t^4 + 2 t^3 + 2 t^2 + t + 1)$ undefined
3.5.3.20a24.1 3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 3 x^{2} + 6 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $C_3\wr C_5$ (as 15T36) $1215$ $3$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + 2 t^2 + t)$ undefined
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