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Degree $n$ Residue characteristic $p$ Discriminant exponent $c$ Galois group Num. automorphisms
Ramification index $e$ Residue field degree $f$ Galois tame degree $t$ Galois unram. degree $u$ Intermediate field
Inertia subgroup Indices Assoc. Inertia Jump Set
Top Artin slope Galois Artin Visible Artin Wild inertia subgroup
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Results (1-50 of 118 matches)

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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
2.6.2.12a1.1 $( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + 2 ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ $2$ $6$ $2$ $12$ $C_6\times C_2$ (as 12T2) $6$ $1$ $[2]$ $[1]$ $[2]^{6}$ $[1]^{6}$ $[\ ]$ $[\ ]$ $t^{6} + t^{4} + t^{3} + t + 1$ $x^{2} + 2 x + 2$ $[1, 0]$ $[1]$ $z + 1$ $[1, 2]$
2.6.2.18a1.1 $( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + 2$ $2$ $6$ $2$ $18$ $C_6\times C_2$ (as 12T2) $6$ $1$ $[3]$ $[2]$ $[3]^{6}$ $[2]^{6}$ $[\ ]$ $[\ ]$ $t^{6} + t^{4} + t^{3} + t + 1$ $x^{2} + 2$ $[2, 0]$ $[1]$ $z + 1$ $[1, 3]$
2.6.2.18a1.17 $( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + 4 ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ $2$ $6$ $2$ $18$ $C_6\times C_2$ (as 12T2) $6$ $1$ $[3]$ $[2]$ $[3]^{6}$ $[2]^{6}$ $[\ ]$ $[\ ]$ $t^{6} + t^{4} + t^{3} + t + 1$ $x^{2} + 4 x + 2$ $[2, 0]$ $[1]$ $z + 1$ $[1, 3]$
2.3.4.24b1.1 $( x^{3} + x + 1 )^{4} + 2 ( x^{3} + x + 1 )^{2} + 4 ( x^{3} + x + 1 ) + 2$ $2$ $3$ $4$ $24$ $C_6\times C_2$ (as 12T2) $3$ $1$ $[2, 3]$ $[1,2]$ $[2, 3]^{3}$ $[1,2]^{3}$ $[\ ]$ $[\ ]$ $t^{3} + t + 1$ $x^{4} + 2 x^{2} + 4 x + 2$ $[5, 2, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 2, 4]$
2.3.4.24b1.2 $( x^{3} + x + 1 )^{4} + 2 ( x^{3} + x + 1 )^{2} + 4 ( x^{3} + x + 1 ) + 10$ $2$ $3$ $4$ $24$ $C_6\times C_2$ (as 12T2) $3$ $1$ $[2, 3]$ $[1,2]$ $[2, 3]^{3}$ $[1,2]^{3}$ $[\ ]$ $[\ ]$ $t^{3} + t + 1$ $x^{4} + 2 x^{2} + 4 x + 10$ $[5, 2, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 8, 12]$
2.3.4.24b1.9 $( x^{3} + x + 1 )^{4} + 4 ( x^{3} + x + 1 )^{3} + 2 ( x^{3} + x + 1 )^{2} + 4 ( x^{3} + x + 1 ) + 6$ $2$ $3$ $4$ $24$ $C_6\times C_2$ (as 12T2) $3$ $1$ $[2, 3]$ $[1,2]$ $[2, 3]^{3}$ $[1,2]^{3}$ $[\ ]$ $[\ ]$ $t^{3} + t + 1$ $x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 6$ $[5, 2, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 2, 8]$
2.3.4.24b1.10 $( x^{3} + x + 1 )^{4} + 4 ( x^{3} + x + 1 )^{3} + 2 ( x^{3} + x + 1 )^{2} + 4 ( x^{3} + x + 1 ) + 14$ $2$ $3$ $4$ $24$ $C_6\times C_2$ (as 12T2) $3$ $1$ $[2, 3]$ $[1,2]$ $[2, 3]^{3}$ $[1,2]^{3}$ $[\ ]$ $[\ ]$ $t^{3} + t + 1$ $x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 14$ $[5, 2, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 2, 8]$
3.6.2.6a1.2 $( x^{6} + 2 x^{4} + x^{2} + 2 x + 2 )^{2} + 3$ $3$ $6$ $2$ $6$ $C_6\times C_2$ (as 12T2) $6$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{6}$ $[\ ]_{2}^{6}$ $[\ ]$ $[\ ]$ $t^{6} + 2 t^{4} + t^{2} + 2 t + 2$ $x^{2} + 3$ $[0]$ $[1]$ $z + 2$ $[1]$
3.2.6.18a1.16 $( x^{2} + 2 x + 2 )^{6} + 6 ( x^{2} + 2 x + 2 )^{4} + 3$ $3$ $2$ $6$ $18$ $C_6\times C_2$ (as 12T2) $2$ $2$ $[2]$ $[1]$ $[2]_{2}^{2}$ $[1]_{2}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 2 t + 2$ $x^{6} + 6 x^{4} + 3$ $[4, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 1$ $[1, 3]$
3.2.6.18a1.17 $( x^{2} + 2 x + 2 )^{6} + 6 ( x^{2} + 2 x + 2 )^{4} + 12$ $3$ $2$ $6$ $18$ $C_6\times C_2$ (as 12T2) $2$ $2$ $[2]$ $[1]$ $[2]_{2}^{2}$ $[1]_{2}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 2 t + 2$ $x^{6} + 6 x^{4} + 12$ $[4, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 1$ $[1, 9]$
3.2.6.18a1.18 $( x^{2} + 2 x + 2 )^{6} + 6 ( x^{2} + 2 x + 2 )^{4} + 21$ $3$ $2$ $6$ $18$ $C_6\times C_2$ (as 12T2) $2$ $2$ $[2]$ $[1]$ $[2]_{2}^{2}$ $[1]_{2}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 2 t + 2$ $x^{6} + 6 x^{4} + 21$ $[4, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 1$ $[1, 9]$
5.6.2.6a1.2 $( x^{6} + x^{4} + 4 x^{3} + x^{2} + 2 )^{2} + 5$ $5$ $6$ $2$ $6$ $C_6\times C_2$ (as 12T2) $6$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{6}$ $[\ ]_{2}^{6}$ $[\ ]$ $[\ ]$ $t^{6} + t^{4} + 4 t^{3} + t^{2} + 2$ $x^{2} + 5$ $[0]$ $[1]$ $z + 2$ undefined
7.6.2.6a1.2 $( x^{6} + x^{4} + 5 x^{3} + 4 x^{2} + 6 x + 3 )^{2} + 7$ $7$ $6$ $2$ $6$ $C_6\times C_2$ (as 12T2) $6$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{6}$ $[\ ]_{2}^{6}$ $[\ ]$ $[\ ]$ $t^{6} + t^{4} + 5 t^{3} + 4 t^{2} + 6 t + 3$ $x^{2} + 7$ $[0]$ $[1]$ $z + 2$ undefined
7.2.6.10a1.2 $( x^{2} + 6 x + 3 )^{6} + 7$ $7$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 6 t + 3$ $x^{6} + 7$ $[0]$ $[1]$ $z^5 + 6 z^4 + z^3 + 6 z^2 + z + 6$ $[1]$
7.2.6.10a1.4 $( x^{2} + 6 x + 3 )^{6} + 7 x + 28$ $7$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 6 t + 3$ $x^{6} + 7 t + 28$ $[0]$ $[1]$ $z^5 + 6 z^4 + z^3 + 6 z^2 + z + 6$ undefined
7.2.6.10a1.6 $( x^{2} + 6 x + 3 )^{6} + 14 x + 42$ $7$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 6 t + 3$ $x^{6} + 14 t + 42$ $[0]$ $[1]$ $z^5 + 6 z^4 + z^3 + 6 z^2 + z + 6$ undefined
11.6.2.6a1.2 $( x^{6} + 3 x^{4} + 4 x^{3} + 6 x^{2} + 7 x + 2 )^{2} + 11$ $11$ $6$ $2$ $6$ $C_6\times C_2$ (as 12T2) $6$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{6}$ $[\ ]_{2}^{6}$ $[\ ]$ $[\ ]$ $t^{6} + 3 t^{4} + 4 t^{3} + 6 t^{2} + 7 t + 2$ $x^{2} + 11$ $[0]$ $[1]$ $z + 2$ undefined
13.6.2.6a1.2 $( x^{6} + 10 x^{3} + 11 x^{2} + 11 x + 2 )^{2} + 13$ $13$ $6$ $2$ $6$ $C_6\times C_2$ (as 12T2) $6$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{6}$ $[\ ]_{2}^{6}$ $[\ ]$ $[\ ]$ $t^{6} + 10 t^{3} + 11 t^{2} + 11 t + 2$ $x^{2} + 13$ $[0]$ $[1]$ $z + 2$ undefined
13.2.6.10a1.2 $( x^{2} + 12 x + 2 )^{6} + 13$ $13$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 12 t + 2$ $x^{6} + 13$ $[0]$ $[1]$ $z^5 + 6 z^4 + 2 z^3 + 7 z^2 + 2 z + 6$ undefined
13.2.6.10a1.3 $( x^{2} + 12 x + 2 )^{6} + 130 x + 26$ $13$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 12 t + 2$ $x^{6} + 130 t + 26$ $[0]$ $[1]$ $z^5 + 6 z^4 + 2 z^3 + 7 z^2 + 2 z + 6$ undefined
13.2.6.10a1.5 $( x^{2} + 12 x + 2 )^{6} + 13 x + 143$ $13$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 12 t + 2$ $x^{6} + 13 t + 143$ $[0]$ $[1]$ $z^5 + 6 z^4 + 2 z^3 + 7 z^2 + 2 z + 6$ undefined
17.6.2.6a1.2 $( x^{6} + 2 x^{4} + 10 x^{2} + 3 x + 3 )^{2} + 17$ $17$ $6$ $2$ $6$ $C_6\times C_2$ (as 12T2) $6$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{6}$ $[\ ]_{2}^{6}$ $[\ ]$ $[\ ]$ $t^{6} + 2 t^{4} + 10 t^{2} + 3 t + 3$ $x^{2} + 17$ $[0]$ $[1]$ $z + 2$ undefined
19.6.2.6a1.2 $( x^{6} + 17 x^{3} + 17 x^{2} + 6 x + 2 )^{2} + 19$ $19$ $6$ $2$ $6$ $C_6\times C_2$ (as 12T2) $6$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{6}$ $[\ ]_{2}^{6}$ $[\ ]$ $[\ ]$ $t^{6} + 17 t^{3} + 17 t^{2} + 6 t + 2$ $x^{2} + 19$ $[0]$ $[1]$ $z + 2$ undefined
19.2.6.10a1.2 $( x^{2} + 18 x + 2 )^{6} + 19$ $19$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 18 t + 2$ $x^{6} + 19$ $[0]$ $[1]$ $z^5 + 6 z^4 + 15 z^3 + z^2 + 15 z + 6$ undefined
19.2.6.10a1.3 $( x^{2} + 18 x + 2 )^{6} + 304 x + 38$ $19$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 18 t + 2$ $x^{6} + 304 t + 38$ $[0]$ $[1]$ $z^5 + 6 z^4 + 15 z^3 + z^2 + 15 z + 6$ undefined
19.2.6.10a1.5 $( x^{2} + 18 x + 2 )^{6} + 19 x + 323$ $19$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 18 t + 2$ $x^{6} + 19 t + 323$ $[0]$ $[1]$ $z^5 + 6 z^4 + 15 z^3 + z^2 + 15 z + 6$ undefined
23.6.2.6a1.2 $( x^{6} + x^{4} + 9 x^{3} + 9 x^{2} + x + 5 )^{2} + 23$ $23$ $6$ $2$ $6$ $C_6\times C_2$ (as 12T2) $6$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{6}$ $[\ ]_{2}^{6}$ $[\ ]$ $[\ ]$ $t^{6} + t^{4} + 9 t^{3} + 9 t^{2} + t + 5$ $x^{2} + 23$ $[0]$ $[1]$ $z + 2$ undefined
29.6.2.6a1.2 $( x^{6} + x^{4} + 25 x^{3} + 17 x^{2} + 13 x + 2 )^{2} + 29$ $29$ $6$ $2$ $6$ $C_6\times C_2$ (as 12T2) $6$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{6}$ $[\ ]_{2}^{6}$ $[\ ]$ $[\ ]$ $t^{6} + t^{4} + 25 t^{3} + 17 t^{2} + 13 t + 2$ $x^{2} + 29$ $[0]$ $[1]$ $z + 2$ undefined
31.6.2.6a1.2 $( x^{6} + 19 x^{3} + 16 x^{2} + 8 x + 3 )^{2} + 31$ $31$ $6$ $2$ $6$ $C_6\times C_2$ (as 12T2) $6$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{6}$ $[\ ]_{2}^{6}$ $[\ ]$ $[\ ]$ $t^{6} + 19 t^{3} + 16 t^{2} + 8 t + 3$ $x^{2} + 31$ $[0]$ $[1]$ $z + 2$ undefined
31.2.6.10a1.2 $( x^{2} + 29 x + 3 )^{6} + 31$ $31$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 29 t + 3$ $x^{6} + 31$ $[0]$ $[1]$ $z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ undefined
31.2.6.10a1.5 $( x^{2} + 29 x + 3 )^{6} + 62 x + 868$ $31$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 29 t + 3$ $x^{6} + 62 t + 868$ $[0]$ $[1]$ $z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ undefined
31.2.6.10a1.6 $( x^{2} + 29 x + 3 )^{6} + 837 x + 868$ $31$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 29 t + 3$ $x^{6} + 837 t + 868$ $[0]$ $[1]$ $z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ undefined
37.6.2.6a1.2 $( x^{6} + 35 x^{3} + 4 x^{2} + 30 x + 2 )^{2} + 37$ $37$ $6$ $2$ $6$ $C_6\times C_2$ (as 12T2) $6$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{6}$ $[\ ]_{2}^{6}$ $[\ ]$ $[\ ]$ $t^{6} + 35 t^{3} + 4 t^{2} + 30 t + 2$ $x^{2} + 37$ $[0]$ $[1]$ $z + 2$ undefined
37.2.6.10a1.2 $( x^{2} + 33 x + 2 )^{6} + 37$ $37$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 33 t + 2$ $x^{6} + 37$ $[0]$ $[1]$ $z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ undefined
37.2.6.10a1.3 $( x^{2} + 33 x + 2 )^{6} + 407 x + 333$ $37$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 33 t + 2$ $x^{6} + 407 t + 333$ $[0]$ $[1]$ $z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ undefined
37.2.6.10a1.6 $( x^{2} + 33 x + 2 )^{6} + 148 x + 1295$ $37$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 33 t + 2$ $x^{6} + 148 t + 1295$ $[0]$ $[1]$ $z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ undefined
41.6.2.6a1.2 $( x^{6} + 4 x^{4} + 33 x^{3} + 39 x^{2} + 6 x + 6 )^{2} + 41$ $41$ $6$ $2$ $6$ $C_6\times C_2$ (as 12T2) $6$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{6}$ $[\ ]_{2}^{6}$ $[\ ]$ $[\ ]$ $t^{6} + 4 t^{4} + 33 t^{3} + 39 t^{2} + 6 t + 6$ $x^{2} + 41$ $[0]$ $[1]$ $z + 2$ undefined
43.6.2.6a1.2 $( x^{6} + 19 x^{3} + 28 x^{2} + 21 x + 3 )^{2} + 43$ $43$ $6$ $2$ $6$ $C_6\times C_2$ (as 12T2) $6$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{6}$ $[\ ]_{2}^{6}$ $[\ ]$ $[\ ]$ $t^{6} + 19 t^{3} + 28 t^{2} + 21 t + 3$ $x^{2} + 43$ $[0]$ $[1]$ $z + 2$ undefined
43.2.6.10a1.2 $( x^{2} + 42 x + 3 )^{6} + 43$ $43$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 42 t + 3$ $x^{6} + 43$ $[0]$ $[1]$ $z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ undefined
43.2.6.10a1.3 $( x^{2} + 42 x + 3 )^{6} + 1634 x + 258$ $43$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 42 t + 3$ $x^{6} + 1634 t + 258$ $[0]$ $[1]$ $z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ undefined
43.2.6.10a1.5 $( x^{2} + 42 x + 3 )^{6} + 43 x + 1720$ $43$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 42 t + 3$ $x^{6} + 43 t + 1720$ $[0]$ $[1]$ $z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ undefined
47.6.2.6a1.2 $( x^{6} + 2 x^{4} + 35 x^{3} + 9 x^{2} + 41 x + 5 )^{2} + 47$ $47$ $6$ $2$ $6$ $C_6\times C_2$ (as 12T2) $6$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{6}$ $[\ ]_{2}^{6}$ $[\ ]$ $[\ ]$ $t^{6} + 2 t^{4} + 35 t^{3} + 9 t^{2} + 41 t + 5$ $x^{2} + 47$ $[0]$ $[1]$ $z + 2$ undefined
53.6.2.6a1.2 $( x^{6} + x^{4} + 7 x^{3} + 4 x^{2} + 45 x + 2 )^{2} + 53$ $53$ $6$ $2$ $6$ $C_6\times C_2$ (as 12T2) $6$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{6}$ $[\ ]_{2}^{6}$ $[\ ]$ $[\ ]$ $t^{6} + t^{4} + 7 t^{3} + 4 t^{2} + 45 t + 2$ $x^{2} + 53$ $[0]$ $[1]$ $z + 2$ undefined
59.6.2.6a1.2 $( x^{6} + 2 x^{4} + 18 x^{3} + 38 x^{2} + 2 )^{2} + 59$ $59$ $6$ $2$ $6$ $C_6\times C_2$ (as 12T2) $6$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{6}$ $[\ ]_{2}^{6}$ $[\ ]$ $[\ ]$ $t^{6} + 2 t^{4} + 18 t^{3} + 38 t^{2} + 2$ $x^{2} + 59$ $[0]$ $[1]$ $z + 2$ undefined
61.6.2.6a1.2 $( x^{6} + 49 x^{3} + 3 x^{2} + 29 x + 2 )^{2} + 61$ $61$ $6$ $2$ $6$ $C_6\times C_2$ (as 12T2) $6$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{6}$ $[\ ]_{2}^{6}$ $[\ ]$ $[\ ]$ $t^{6} + 49 t^{3} + 3 t^{2} + 29 t + 2$ $x^{2} + 61$ $[0]$ $[1]$ $z + 2$ undefined
61.2.6.10a1.2 $( x^{2} + 60 x + 2 )^{6} + 61$ $61$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 60 t + 2$ $x^{6} + 61$ $[0]$ $[1]$ $z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ undefined
61.2.6.10a1.3 $( x^{2} + 60 x + 2 )^{6} + 3538 x + 122$ $61$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 60 t + 2$ $x^{6} + 3538 t + 122$ $[0]$ $[1]$ $z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ undefined
61.2.6.10a1.5 $( x^{2} + 60 x + 2 )^{6} + 61 x + 3599$ $61$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 60 t + 2$ $x^{6} + 61 t + 3599$ $[0]$ $[1]$ $z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ undefined
67.6.2.6a1.2 $( x^{6} + 63 x^{3} + 49 x^{2} + 55 x + 2 )^{2} + 67$ $67$ $6$ $2$ $6$ $C_6\times C_2$ (as 12T2) $6$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{6}$ $[\ ]_{2}^{6}$ $[\ ]$ $[\ ]$ $t^{6} + 63 t^{3} + 49 t^{2} + 55 t + 2$ $x^{2} + 67$ $[0]$ $[1]$ $z + 2$ undefined
67.2.6.10a1.2 $( x^{2} + 63 x + 2 )^{6} + 67$ $67$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 63 t + 2$ $x^{6} + 67$ $[0]$ $[1]$ $z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ undefined
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