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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.6.6.7 $x^{6} + 2 x^{2} + 2 x + 2$ $2$ $6$ $1$ $6$ $S_4$ (as 6T7) $[4/3]$ $[4/3, 4/3]_{3}^{2}$ $t + 1$ $x^{6} + 2 x^{2} + 2 x + 2$
2.6.6.8 $x^{6} + 2 x + 2$ $2$ $6$ $1$ $6$ $S_4$ (as 6T8) $[4/3]$ $[4/3, 4/3]_{3}^{2}$ $t + 1$ $x^{6} + 2 x + 2$
2.6.8.1 $x^{6} + 2 x^{3} + 2$ $2$ $6$ $1$ $8$ $D_{6}$ (as 6T3) $[2]$ $[2]_{3}^{2}$ $t + 1$ $x^{6} + 2 x^{3} + 2$
2.6.8.2 $x^{6} + 2 x^{4} + 2 x^{3} + 2$ $2$ $6$ $1$ $8$ $S_4\times C_2$ (as 6T11) $[2]$ $[4/3, 4/3, 2]_{3}^{2}$ $t + 1$ $x^{6} + 2 x^{4} + 2 x^{3} + 2$
2.6.8.3 $x^{6} + 2 x^{3} + 6$ $2$ $6$ $1$ $8$ $D_{6}$ (as 6T3) $[2]$ $[2]_{3}^{2}$ $t + 1$ $x^{6} + 2 x^{3} + 6$
2.6.8.4 $x^{6} + 2 x^{4} + 2 x^{3} + 6$ $2$ $6$ $1$ $8$ $S_4\times C_2$ (as 6T11) $[2]$ $[4/3, 4/3, 2]_{3}^{2}$ $t + 1$ $x^{6} + 2 x^{4} + 2 x^{3} + 6$
2.6.10.1 $x^{6} + 2 x^{5} + 4 x^{2} + 4 x + 2$ $2$ $6$ $1$ $10$ $S_4$ (as 6T7) $[8/3]$ $[8/3, 8/3]_{3}^{2}$ $t + 1$ $x^{6} + 2 x^{5} + 4 x^{2} + 4 x + 2$
2.6.10.2 $x^{6} + 2 x^{5} + 4 x^{4} + 4 x + 2$ $2$ $6$ $1$ $10$ $S_4$ (as 6T7) $[8/3]$ $[8/3, 8/3]_{3}^{2}$ $t + 1$ $x^{6} + 2 x^{5} + 4 x^{4} + 4 x + 2$
2.6.10.3 $x^{6} + 2 x^{5} + 4 x + 2$ $2$ $6$ $1$ $10$ $S_4$ (as 6T8) $[8/3]$ $[8/3, 8/3]_{3}^{2}$ $t + 1$ $x^{6} + 2 x^{5} + 4 x + 2$
2.6.10.4 $x^{6} + 2 x^{5} + 4 x^{3} + 4 x + 2$ $2$ $6$ $1$ $10$ $S_4$ (as 6T8) $[8/3]$ $[8/3, 8/3]_{3}^{2}$ $t + 1$ $x^{6} + 2 x^{5} + 4 x^{3} + 4 x + 2$
2.6.10.5 $x^{6} + 2 x^{5} + 4 x^{3} + 4 x^{2} + 2$ $2$ $6$ $1$ $10$ $S_4\times C_2$ (as 6T11) $[8/3]$ $[2, 8/3, 8/3]_{3}^{2}$ $t + 1$ $x^{6} + 2 x^{5} + 4 x^{3} + 4 x^{2} + 2$
2.6.10.6 $x^{6} + 2 x^{5} + 4 x^{2} + 2$ $2$ $6$ $1$ $10$ $S_4\times C_2$ (as 6T11) $[8/3]$ $[2, 8/3, 8/3]_{3}^{2}$ $t + 1$ $x^{6} + 2 x^{5} + 4 x^{2} + 2$
2.6.10.7 $x^{6} + 2 x^{5} + 4 x^{3} + 2$ $2$ $6$ $1$ $10$ $S_4\times C_2$ (as 6T11) $[8/3]$ $[2, 8/3, 8/3]_{3}^{2}$ $t + 1$ $x^{6} + 2 x^{5} + 4 x^{3} + 2$
2.6.10.8 $x^{6} + 2 x^{5} + 2$ $2$ $6$ $1$ $10$ $S_4\times C_2$ (as 6T11) $[8/3]$ $[2, 8/3, 8/3]_{3}^{2}$ $t + 1$ $x^{6} + 2 x^{5} + 2$
2.6.11.1 $x^{6} + 4 x^{3} + 2$ $2$ $6$ $1$ $11$ $D_{6}$ (as 6T3) $[3]$ $[3]_{3}^{2}$ $t + 1$ $x^{6} + 4 x^{3} + 2$
2.6.11.10 $x^{6} + 4 x^{2} + 2$ $2$ $6$ $1$ $11$ $S_4\times C_2$ (as 6T11) $[3]$ $[4/3, 4/3, 3]_{3}^{2}$ $t + 1$ $x^{6} + 4 x^{2} + 2$
2.6.11.11 $x^{6} + 4 x^{4} + 4 x + 14$ $2$ $6$ $1$ $11$ $S_4\times C_2$ (as 6T11) $[3]$ $[8/3, 8/3, 3]_{3}^{2}$ $t + 1$ $x^{6} + 4 x^{4} + 4 x + 14$
2.6.11.12 $x^{6} + 4 x^{4} + 4 x^{3} + 4 x + 10$ $2$ $6$ $1$ $11$ $S_4\times C_2$ (as 6T11) $[3]$ $[8/3, 8/3, 3]_{3}^{2}$ $t + 1$ $x^{6} + 4 x^{4} + 4 x^{3} + 4 x + 10$
2.6.11.13 $x^{6} + 10$ $2$ $6$ $1$ $11$ $D_{6}$ (as 6T3) $[3]$ $[3]_{3}^{2}$ $t + 1$ $x^{6} + 10$
2.6.11.14 $x^{6} + 4 x^{2} + 10$ $2$ $6$ $1$ $11$ $S_4\times C_2$ (as 6T11) $[3]$ $[4/3, 4/3, 3]_{3}^{2}$ $t + 1$ $x^{6} + 4 x^{2} + 10$
2.6.11.15 $x^{6} + 4 x^{4} + 4 x + 6$ $2$ $6$ $1$ $11$ $S_4\times C_2$ (as 6T11) $[3]$ $[8/3, 8/3, 3]_{3}^{2}$ $t + 1$ $x^{6} + 4 x^{4} + 4 x + 6$
2.6.11.16 $x^{6} + 4 x^{4} + 4 x^{3} + 4 x + 2$ $2$ $6$ $1$ $11$ $S_4\times C_2$ (as 6T11) $[3]$ $[8/3, 8/3, 3]_{3}^{2}$ $t + 1$ $x^{6} + 4 x^{4} + 4 x^{3} + 4 x + 2$
2.6.11.2 $x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$ $2$ $6$ $1$ $11$ $S_4\times C_2$ (as 6T11) $[3]$ $[4/3, 4/3, 3]_{3}^{2}$ $t + 1$ $x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$
2.6.11.3 $x^{6} + 4 x^{2} + 4 x + 10$ $2$ $6$ $1$ $11$ $S_4\times C_2$ (as 6T11) $[3]$ $[8/3, 8/3, 3]_{3}^{2}$ $t + 1$ $x^{6} + 4 x^{2} + 4 x + 10$
2.6.11.4 $x^{6} + 4 x^{4} + 4 x^{2} + 4 x + 2$ $2$ $6$ $1$ $11$ $S_4\times C_2$ (as 6T11) $[3]$ $[8/3, 8/3, 3]_{3}^{2}$ $t + 1$ $x^{6} + 4 x^{4} + 4 x^{2} + 4 x + 2$
2.6.11.5 $x^{6} + 4 x^{3} + 10$ $2$ $6$ $1$ $11$ $D_{6}$ (as 6T3) $[3]$ $[3]_{3}^{2}$ $t + 1$ $x^{6} + 4 x^{3} + 10$
2.6.11.6 $x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 10$ $2$ $6$ $1$ $11$ $S_4\times C_2$ (as 6T11) $[3]$ $[4/3, 4/3, 3]_{3}^{2}$ $t + 1$ $x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 10$
2.6.11.7 $x^{6} + 4 x^{2} + 4 x + 2$ $2$ $6$ $1$ $11$ $S_4\times C_2$ (as 6T11) $[3]$ $[8/3, 8/3, 3]_{3}^{2}$ $t + 1$ $x^{6} + 4 x^{2} + 4 x + 2$
2.6.11.8 $x^{6} + 4 x^{5} + 4 x^{2} + 4 x + 2$ $2$ $6$ $1$ $11$ $S_4\times C_2$ (as 6T11) $[3]$ $[8/3, 8/3, 3]_{3}^{2}$ $t + 1$ $x^{6} + 4 x^{5} + 4 x^{2} + 4 x + 2$
2.6.11.9 $x^{6} + 4 x^{5} + 4 x^{2} + 2$ $2$ $6$ $1$ $11$ $D_{6}$ (as 6T3) $[3]$ $[3]_{3}^{2}$ $t + 1$ $x^{6} + 4 x^{5} + 4 x^{2} + 2$
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