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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.6.0.1 $x^{6} + x^{4} + x^{3} + x + 1$ $2$ $1$ $6$ $0$ $C_6$ (as 6T1) $[\ ]$ $[\ ]^{6}$ $t^{6} + t^{4} + t^{3} + t + 1$ $x - 2$
2.6.4.1 $x^{6} + 3 x^{5} + 10 x^{4} + 19 x^{3} + 22 x^{2} + 11 x + 7$ $2$ $3$ $2$ $4$ $S_3$ (as 6T2) $[\ ]$ $[\ ]_{3}^{2}$ $t^{2} + t + 1$ $x^{3} + 2 x + 2$
2.6.4.2 $x^{6} - 2 x^{3} + 4$ $2$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + t + 1$ $x^{3} + 2 t$
2.6.6.1 $x^{6} + 6 x^{5} + 34 x^{4} + 80 x^{3} + 204 x^{2} + 216 x + 216$ $2$ $2$ $3$ $6$ $A_4$ (as 6T4) $[2]$ $[2, 2]^{3}$ $t^{3} + t + 1$ $x^{2} + \left(2 t + 2\right) x + 6$
2.6.6.2 $x^{6} + 6 x^{5} + 14 x^{4} + 24 x^{3} + 44 x^{2} + 8 x + 72$ $2$ $2$ $3$ $6$ $A_4\times C_2$ (as 6T6) $[2]$ $[2, 2]^{6}$ $t^{3} + t + 1$ $x^{2} + \left(2 t + 2\right) x + 4 t^{2} + 2$
2.6.6.3 $x^{6} + 6 x^{5} + 20 x^{4} + 42 x^{3} + 55 x^{2} + 36 x + 9$ $2$ $2$ $3$ $6$ $C_6$ (as 6T1) $[2]$ $[2]^{3}$ $t^{3} + t + 1$ $x^{2} + 2 x + 2$
2.6.6.4 $x^{6} - 4 x^{5} + 14 x^{4} - 24 x^{3} + 100 x^{2} + 48 x + 88$ $2$ $2$ $3$ $6$ $A_4\times C_2$ (as 6T6) $[2]$ $[2, 2, 2]^{3}$ $t^{3} + t + 1$ $x^{2} + 2 t^{2} x + 4 t^{2} + 6$
2.6.6.5 $x^{6} + 6 x^{5} + 32 x^{4} + 90 x^{3} + 199 x^{2} + 204 x + 149$ $2$ $2$ $3$ $6$ $C_6$ (as 6T1) $[2]$ $[2]^{3}$ $t^{3} + t + 1$ $x^{2} + 2 x + 6$
2.6.6.6 $x^{6} - 4 x^{5} + 30 x^{4} - 16 x^{3} + 164 x^{2} + 160 x + 88$ $2$ $2$ $3$ $6$ $A_4\times C_2$ (as 6T6) $[2]$ $[2, 2, 2]^{3}$ $t^{3} + t + 1$ $x^{2} + \left(2 t^{2} + 2 t\right) x + 4 t^{2} + 6$
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) $[2]$ $[4/3, 4/3, 2]_{3}^{2}$ $t + 1$ $x^{6} + 2 x^{4} + 2 x^{3} + 6$
2.6.9.1 $x^{6} + 44 x^{4} + 2 x^{3} + 589 x^{2} - 82 x + 2367$ $2$ $2$ $3$ $9$ $C_6$ (as 6T1) $[3]$ $[3]^{3}$ $t^{3} + t + 1$ $x^{2} + 14$
2.6.9.2 $x^{6} + 4 x^{5} - 10 x^{4} + 160 x^{3} + 1212 x^{2} + 2160 x - 1048$ $2$ $2$ $3$ $9$ $A_4\times C_2$ (as 6T6) $[3]$ $[2, 2, 3]^{3}$ $t^{3} + t + 1$ $x^{2} + \left(4 t^{2} + 4\right) x + 8 t^{2} + 12 t + 2$
2.6.9.3 $x^{6} + 12 x^{5} + 86 x^{4} + 352 x^{3} + 892 x^{2} + 1552 x + 1384$ $2$ $2$ $3$ $9$ $C_6$ (as 6T1) $[3]$ $[3]^{3}$ $t^{3} + t + 1$ $x^{2} + \left(4 t + 4\right) x + 4 t^{2} + 8 t + 10$
2.6.9.4 $x^{6} + 4 x^{5} + 14 x^{4} + 224 x^{3} + 1244 x^{2} + 3184 x + 2376$ $2$ $2$ $3$ $9$ $A_4\times C_2$ (as 6T6) $[3]$ $[2, 2, 3]^{3}$ $t^{3} + t + 1$ $x^{2} + \left(4 t^{2} + 4\right) x + 8 t^{2} + 12 t + 10$
2.6.9.5 $x^{6} + 12 x^{5} + 68 x^{4} + 226 x^{3} + 457 x^{2} + 514 x + 243$ $2$ $2$ $3$ $9$ $C_6$ (as 6T1) $[3]$ $[3]^{3}$ $t^{3} + t + 1$ $x^{2} + 4 x + 6$
2.6.9.6 $x^{6} - 8 x^{5} + 86 x^{4} + 96 x^{3} + 860 x^{2} + 2976 x + 2728$ $2$ $2$ $3$ $9$ $A_4\times C_2$ (as 6T6) $[3]$ $[2, 2, 3]^{3}$ $t^{3} + t + 1$ $x^{2} + \left(4 t^{2} + 4 t\right) x + 12 t^{2} + 4 t + 10$
2.6.9.7 $x^{6} + 32 x^{4} + 2 x^{3} + 301 x^{2} - 58 x + 811$ $2$ $2$ $3$ $9$ $C_6$ (as 6T1) $[3]$ $[3]^{3}$ $t^{3} + t + 1$ $x^{2} + 10$
2.6.9.8 $x^{6} - 8 x^{5} + 62 x^{4} + 224 x^{3} + 316 x^{2} + 1184 x + 1608$ $2$ $2$ $3$ $9$ $A_4\times C_2$ (as 6T6) $[3]$ $[2, 2, 3]^{3}$ $t^{3} + t + 1$ $x^{2} + \left(4 t^{2} + 4 t\right) x + 12 t^{2} + 4 t + 2$
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) $[3]$ $[3]_{3}^{2}$ $t + 1$ $x^{6} + 4 x^{3} + 2$
2.6.11.2 $x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$ $2$ $6$ $1$ $11$ $S_4\times C_2$ (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) $[3]$ $[3]_{3}^{2}$ $t + 1$ $x^{6} + 4 x^{5} + 4 x^{2} + 2$
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) $[3]$ $[8/3, 8/3, 3]_{3}^{2}$ $t + 1$ $x^{6} + 4 x^{4} + 4 x^{3} + 4 x + 2$
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