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Degree $n$ Residue characteristic $p$ Discriminant exponent $c$ Galois group
Ramification index $e$ Residue field degree $f$ Galois tame degree $t$ Galois unram. degree $u$
Num. automorphisms Inertia subgroup Indices Assoc. Inertia Jump Set
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Label Polynomial $p$ $f$ $e$ $c$ Galois group $u$ $t$ Visible Artin slopes Visible Swan slopes Artin slope content Swan slope content Hidden Artin slopes Hidden Swan slopes Unram. Ext. Eisen. Poly. Ind. of Insep. Assoc. Inertia Resid. Poly Jump Set
3.5.3.20a3.1 $( x^{5} + 2 x + 1 )^{3} + 3 x ( x^{5} + 2 x + 1 )^{2} + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $15$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2]^{15}$ $[1,1,1,1]^{15}$ $[2,2,2]^{3}$ $[1,1,1]^{3}$ $t^{5} + 2 t + 1$ $x^{3} + 3 t x^{2} + 9 t^{2} + 3$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t)$ undefined
3.5.3.20a3.2 $( x^{5} + 2 x + 1 )^{3} + 3 x ( x^{5} + 2 x + 1 )^{2} + 9 x^{2} + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $15$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2]^{15}$ $[1,1,1,1]^{15}$ $[2,2,2]^{3}$ $[1,1,1]^{3}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t + 6\right) x^{2} + 9 t + 3$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t)$ undefined
3.5.3.20a4.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $15$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2]^{15}$ $[1,1,1,1]^{15}$ $[2,2,2]^{3}$ $[1,1,1]^{3}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{2} + 3\right) x^{2} + 9 t + 3$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^3 + t + 2)$ undefined
3.5.3.20a4.3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 18 x^{4} + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $15$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2]^{15}$ $[1,1,1,1]^{15}$ $[2,2,2]^{3}$ $[1,1,1]^{3}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t + 6\right) x^{2} + 9 t^{4} + 3$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^3 + t + 2)$ undefined
3.5.3.20a9.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{2} + 3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 3 t + 6\right) x^{2} + 12$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^3 + 2 t^2 + 2 t + 1)$ undefined
3.5.3.20a9.2 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{2} + 3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 12$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{3} + 6 t^{2} + 3 t + 6\right) x^{2} + 21$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^3 + 2 t^2 + 2 t + 1)$ undefined
3.5.3.20a9.3 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{2} + 3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 21$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t^{3} + 3 t^{2} + 6 t\right) x^{2} + 3$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^3 + 2 t^2 + 2 t + 1)$ undefined
3.5.3.20a10.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{2} + 6 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 6 t + 6\right) x^{2} + 12$ $[2, 0]$ $[1]$ $z^2 + (t^4 + t^3 + 2 t^2 + 1)$ undefined
3.5.3.20a10.2 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{2} + 6 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 12$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{3} + 3 t + 3\right) x^{2} + 21$ $[2, 0]$ $[1]$ $z^2 + (t^4 + t^3 + 2 t^2 + 1)$ undefined
3.5.3.20a10.3 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{2} + 6 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 21$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t^{3} + 6 t^{2}\right) x^{2} + 3$ $[2, 0]$ $[1]$ $z^2 + (t^4 + t^3 + 2 t^2 + 1)$ undefined
3.5.3.20a11.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 3 x\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{2} + 3 t + 3\right) x^{2} + 12$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^3 + 2 t^2 + 2 t)$ undefined
3.5.3.20a11.2 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 3 x\right) ( x^{5} + 2 x + 1 )^{2} + 12$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{3} + 3 t\right) x^{2} + 21$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^3 + 2 t^2 + 2 t)$ undefined
3.5.3.20a11.3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 3 x\right) ( x^{5} + 2 x + 1 )^{2} + 21$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{3} + 3 t^{2} + 6 t + 6\right) x^{2} + 3$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^3 + 2 t^2 + 2 t)$ undefined
3.5.3.20a12.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{2} + 3 t\right) x^{2} + 12$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + 2 t^3 + 2 t^2 + 2 t + 2)$ undefined
3.5.3.20a12.2 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 12$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{3} + 3 t\right) x^{2} + 21$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + 2 t^3 + 2 t^2 + 2 t + 2)$ undefined
3.5.3.20a12.3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 21$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{3} + 3 t^{2} + 6 t + 3\right) x^{2} + 3$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + 2 t^3 + 2 t^2 + 2 t + 2)$ undefined
3.5.3.20a13.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 3 x^{2}\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $15$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2]^{15}$ $[1,1,1,1]^{15}$ $[2,2,2]^{3}$ $[1,1,1]^{3}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{3} + 6 t^{2} + 6 t\right) x^{2} + 18 t + 3$ $[2, 0]$ $[1]$ $z^2 + (t^3 + 1)$ undefined
3.5.3.20a13.2 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 3 x^{2}\right) ( x^{5} + 2 x + 1 )^{2} + 9 x + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $15$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2]^{15}$ $[1,1,1,1]^{15}$ $[2,2,2]^{3}$ $[1,1,1]^{3}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{3} + 6 t^{2} + 6 t\right) x^{2} + 9 t + 3$ $[2, 0]$ $[1]$ $z^2 + (t^3 + 1)$ undefined
3.5.3.20a14.2 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 3 x^{2} + 3 x\right) ( x^{5} + 2 x + 1 )^{2} + 9 x + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $15$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2]^{15}$ $[1,1,1,1]^{15}$ $[2,2,2]^{3}$ $[1,1,1]^{3}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t^{3} + 3 t^{2} + 6 t + 6\right) x^{2} + 9 t^{2} + 3$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^3 + t + 1)$ undefined
3.5.3.20a14.3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 3 x^{2} + 3 x\right) ( x^{5} + 2 x + 1 )^{2} + 18 x + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $15$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2]^{15}$ $[1,1,1,1]^{15}$ $[2,2,2]^{3}$ $[1,1,1]^{3}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t^{3} + 3 t^{2} + 6\right) x^{2} + 9 t + 3$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^3 + t + 1)$ undefined
3.5.3.20a15.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 6 x^{2}\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{2} + 6 t + 6\right) x^{2} + 3$ $[2, 0]$ $[1]$ $z^2 + (t^3 + t^2 + 2 t + 2)$ undefined
3.5.3.20a15.2 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 6 x^{2}\right) ( x^{5} + 2 x + 1 )^{2} + 12$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3\right) x^{2} + 12$ $[2, 0]$ $[1]$ $z^2 + (t^3 + t^2 + 2 t + 2)$ undefined
3.5.3.20a15.3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 6 x^{2}\right) ( x^{5} + 2 x + 1 )^{2} + 21$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{2} + 6 t + 6\right) x^{2} + 21$ $[2, 0]$ $[1]$ $z^2 + (t^3 + t^2 + 2 t + 2)$ undefined
3.5.3.20a16.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 6 x^{2} + 3 x + 3\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 3\right) x^{2} + 12$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^2)$ undefined
3.5.3.20a16.2 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 6 x^{2} + 3 x + 3\right) ( x^{5} + 2 x + 1 )^{2} + 12$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 3\right) x^{2} + 21$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^2)$ undefined
3.5.3.20a16.3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 6 x^{2} + 3 x + 3\right) ( x^{5} + 2 x + 1 )^{2} + 21$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t^{3} + 3 t^{2} + 6 t + 6\right) x^{2} + 3$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^2)$ undefined
3.5.3.20a17.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 6 x^{2} + 6 x + 3\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $15$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2]^{15}$ $[1,1,1,1]^{15}$ $[2,2,2]^{3}$ $[1,1,1]^{3}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{3} + 6 t^{2} + 6 t\right) x^{2} + 9 t + 3$ $[2, 0]$ $[1]$ $z^2 + (t^4 + t^2 + t)$ undefined
3.5.3.20a17.3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 6 x^{2} + 6 x + 3\right) ( x^{5} + 2 x + 1 )^{2} + 18 x^{2} + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $15$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2]^{15}$ $[1,1,1,1]^{15}$ $[2,2,2]^{3}$ $[1,1,1]^{3}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{3} + 6 t\right) x^{2} + 9 t + 3$ $[2, 0]$ $[1]$ $z^2 + (t^4 + t^2 + t)$ undefined
3.5.3.20a18.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{3} + 3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{3} + 3 t^{2} + 3\right) x^{2} + 12$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^2 + 2)$ undefined
3.5.3.20a18.2 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{3} + 3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 12$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{3} + 3 t^{2} + 3\right) x^{2} + 21$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^2 + 2)$ undefined
3.5.3.20a18.3 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{3} + 3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 21$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{2} + 3 t + 6\right) x^{2} + 3$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + t^2 + 2)$ undefined
3.5.3.20a24.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 3 x^{2} + 6 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t + 6\right) x^{2} + 3$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + 2 t^2 + t)$ undefined
3.5.3.20a24.2 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 3 x^{2} + 6 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 12$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{2} + 6 t + 6\right) x^{2} + 12$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + 2 t^2 + t)$ undefined
3.5.3.20a24.3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 3 x^{2} + 6 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 21$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{2} + 6 t + 6\right) x^{2} + 21$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + 2 t^2 + t)$ undefined
3.5.3.20a27.2 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 3 x^{3} + 3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 9 x + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $15$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2]^{15}$ $[1,1,1,1]^{15}$ $[2,2,2]^{3}$ $[1,1,1]^{3}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{2} + 6\right) x^{2} + 18 t^{3} + 3$ $[2, 0]$ $[1]$ $z^2 + (t^3 + 2 t + 2)$ undefined
3.5.3.20a27.3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 3 x^{3} + 3 x + 6\right) ( x^{5} + 2 x + 1 )^{2} + 18 x + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $15$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2]^{15}$ $[1,1,1,1]^{15}$ $[2,2,2]^{3}$ $[1,1,1]^{3}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{3} + 3 t^{2} + 3 t + 3\right) x^{2} + 18 t^{2} + 3$ $[2, 0]$ $[1]$ $z^2 + (t^3 + 2 t + 2)$ undefined
3.5.3.20a28.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 3 x^{3} + 3 x^{2} + 6 x + 3\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 3 t\right) x^{2} + 21$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + 2 t^3 + t^2 + 2 t + 2)$ undefined
3.5.3.20a28.2 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 3 x^{3} + 3 x^{2} + 6 x + 3\right) ( x^{5} + 2 x + 1 )^{2} + 12$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t^{3} + 6 t^{2} + 6 t + 6\right) x^{2} + 3$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + 2 t^3 + t^2 + 2 t + 2)$ undefined
3.5.3.20a28.3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 3 x^{3} + 3 x^{2} + 6 x + 3\right) ( x^{5} + 2 x + 1 )^{2} + 21$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t^{3} + 6 t^{2} + 6 t + 6\right) x^{2} + 12$ $[2, 0]$ $[1]$ $z^2 + (2 t^4 + 2 t^3 + t^2 + 2 t + 2)$ undefined
3.5.3.20a29.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 3 x^{3} + 6 x^{2} + 3\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{3} + 3 t + 6\right) x^{2} + 3$ $[2, 0]$ $[1]$ $z^2 + (t^4 + 2 t^3 + 2 t^2 + 2 t)$ undefined
3.5.3.20a29.2 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 3 x^{3} + 6 x^{2} + 3\right) ( x^{5} + 2 x + 1 )^{2} + 12$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{3} + 3 t + 6\right) x^{2} + 12$ $[2, 0]$ $[1]$ $z^2 + (t^4 + 2 t^3 + 2 t^2 + 2 t)$ undefined
3.5.3.20a29.3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 3 x^{3} + 6 x^{2} + 3\right) ( x^{5} + 2 x + 1 )^{2} + 21$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{3} + 6 t^{2} + 3 t\right) x^{2} + 21$ $[2, 0]$ $[1]$ $z^2 + (t^4 + 2 t^3 + 2 t^2 + 2 t)$ undefined
3.5.3.20a30.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 3 x^{3} + 6 x^{2} + 3 x\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t^{3} + 6 t + 3\right) x^{2} + 12$ $[2, 0]$ $[1]$ $z^2 + (2 t^2 + 2)$ undefined
3.5.3.20a30.2 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 3 x^{3} + 6 x^{2} + 3 x\right) ( x^{5} + 2 x + 1 )^{2} + 12$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{3} + 6 t\right) x^{2} + 21$ $[2, 0]$ $[1]$ $z^2 + (2 t^2 + 2)$ undefined
3.5.3.20a30.3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 3 x^{3} + 6 x^{2} + 3 x\right) ( x^{5} + 2 x + 1 )^{2} + 21$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t^{3} + 6 t^{2} + 3 t\right) x^{2} + 3$ $[2, 0]$ $[1]$ $z^2 + (2 t^2 + 2)$ undefined
3.5.3.20a32.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 6 x^{3} + 6\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $15$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2]^{15}$ $[1,1,1,1]^{15}$ $[2,2,2]^{3}$ $[1,1,1]^{3}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{3} + 3 t^{2} + 3 t + 3\right) x^{2} + 9 t + 3$ $[2, 0]$ $[1]$ $z^2 + (t^4 + 2 t^3 + 2 t^2 + 2 t + 2)$ undefined
3.5.3.20a32.3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 6 x^{3} + 6\right) ( x^{5} + 2 x + 1 )^{2} + 18 x + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $15$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2]^{15}$ $[1,1,1,1]^{15}$ $[2,2,2]^{3}$ $[1,1,1]^{3}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t^{3} + 3 t^{2}\right) x^{2} + 18 t + 3$ $[2, 0]$ $[1]$ $z^2 + (t^4 + 2 t^3 + 2 t^2 + 2 t + 2)$ undefined
3.5.3.20a38.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 6 x^{3} + 6 x^{2} + 6\right) ( x^{5} + 2 x + 1 )^{2} + 3$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{3} + 6 t^{2} + 6\right) x^{2} + 21$ $[2, 0]$ $[1]$ $z^2 + (t^4 + 2 t^3 + t^2 + 1)$ undefined
3.5.3.20a38.2 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 6 x^{3} + 6 x^{2} + 6\right) ( x^{5} + 2 x + 1 )^{2} + 12$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{3} + 6 t^{2} + 3 t + 6\right) x^{2} + 3$ $[2, 0]$ $[1]$ $z^2 + (t^4 + 2 t^3 + t^2 + 1)$ undefined
3.5.3.20a38.3 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 6 x^{3} + 6 x^{2} + 6\right) ( x^{5} + 2 x + 1 )^{2} + 21$ $3$ $5$ $3$ $20$ $C_3\wr C_5$ (as 15T36) $5$ $1$ $[2]$ $[1]$ $[2, 2, 2, 2, 2]^{5}$ $[1,1,1,1,1]^{5}$ $[2,2,2,2]$ $[1,1,1,1]$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{3} + 6 t^{2} + 6 t + 3\right) x^{2} + 12$ $[2, 0]$ $[1]$ $z^2 + (t^4 + 2 t^3 + t^2 + 1)$ undefined
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