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Results (17 matches)

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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
5.12.0.1 $x^{12} + x^{7} + x^{6} + 4 x^{4} + 4 x^{3} + 3 x^{2} + 2 x + 2$ $5$ $1$ $12$ $0$ $C_{12}$ (as 12T1) $[\ ]$ $[\ ]^{12}$ $t^{12} + t^{7} + t^{6} + 4 t^{4} + 4 t^{3} + 3 t^{2} + 2 t + 2$ $x - 5$
5.12.6.1 $x^{12} + 120 x^{11} + 6032 x^{10} + 163208 x^{9} + 2529528 x^{8} + 21853448 x^{7} + 92223962 x^{6} + 138649448 x^{5} + 223472880 x^{4} + 401794296 x^{3} + 295909124 x^{2} + 118616440 x + 126881009$ $5$ $2$ $6$ $6$ $C_6\times C_2$ (as 12T2) $[\ ]$ $[\ ]_{2}^{6}$ $t^{6} + t^{4} + 4 t^{3} + t^{2} + 2$ $x^{2} + 20 x + 5$
5.12.6.2 $x^{12} + 25 x^{8} - 500 x^{6} + 625 x^{4} + 31250$ $5$ $2$ $6$ $6$ $C_{12}$ (as 12T1) $[\ ]$ $[\ ]_{2}^{6}$ $t^{6} + t^{4} + 4 t^{3} + t^{2} + 2$ $x^{2} + 5 t$
5.12.8.1 $x^{12} + 12 x^{10} + 32 x^{9} + 54 x^{8} + 96 x^{7} - 50 x^{6} + 240 x^{5} - 360 x^{4} - 884 x^{3} + 4044 x^{2} - 3912 x + 4173$ $5$ $3$ $4$ $8$ $C_3 : C_4$ (as 12T5) $[\ ]$ $[\ ]_{3}^{4}$ $t^{4} + 4 t^{2} + 4 t + 2$ $x^{3} + 5$
5.12.8.2 $x^{12} + 100 x^{6} - 500 x^{3} + 1250$ $5$ $3$ $4$ $8$ $C_3\times (C_3 : C_4)$ (as 12T19) $[\ ]$ $[\ ]_{3}^{12}$ $t^{4} + 4 t^{2} + 4 t + 2$ $x^{3} + 5 t$
5.12.9.1 $x^{12} - 30 x^{8} + 225 x^{4} + 1125$ $5$ $4$ $3$ $9$ $C_{12}$ (as 12T1) $[\ ]$ $[\ ]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{4} + 5 t^{2}$
5.12.9.2 $x^{12} + 12 x^{10} + 12 x^{9} + 69 x^{8} + 108 x^{7} + 42 x^{6} - 396 x^{5} + 840 x^{4} + 252 x^{3} + 1476 x^{2} + 684 x + 1601$ $5$ $4$ $3$ $9$ $C_{12}$ (as 12T1) $[\ ]$ $[\ ]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{4} + 5$
5.12.9.3 $x^{12} + 75 x^{4} - 375$ $5$ $4$ $3$ $9$ $C_{12}$ (as 12T1) $[\ ]$ $[\ ]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{4} + 5 t$
5.12.9.4 $x^{12} + 30 x^{8} + 600 x^{4} + 1000$ $5$ $4$ $3$ $9$ $C_{12}$ (as 12T1) $[\ ]$ $[\ ]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{4} + 10 t + 10$
5.12.10.1 $x^{12} + 20 x^{7} + 10 x^{6} + 50 x^{2} + 100 x + 25$ $5$ $6$ $2$ $10$ $D_6$ (as 12T3) $[\ ]$ $[\ ]_{6}^{2}$ $t^{2} + 4 t + 2$ $x^{6} + \left(5 t + 20\right) x + 5$
5.12.10.2 $x^{12} - 20 x^{6} - 100$ $5$ $6$ $2$ $10$ $C_6\times S_3$ (as 12T18) $[\ ]$ $[\ ]_{6}^{6}$ $t^{2} + 4 t + 2$ $x^{6} + 10 t + 10$
5.12.10.3 $x^{12} - 50 x^{6} - 175$ $5$ $6$ $2$ $10$ $C_3 : C_4$ (as 12T5) $[\ ]$ $[\ ]_{6}^{2}$ $t^{2} + 4 t + 2$ $x^{6} + 20 t + 15$
5.12.10.4 $x^{12} - 70 x^{6} + 425$ $5$ $6$ $2$ $10$ $C_3\times (C_3 : C_4)$ (as 12T19) $[\ ]$ $[\ ]_{6}^{6}$ $t^{2} + 4 t + 2$ $x^{6} + 20 t + 5$
5.12.11.1 $x^{12} + 20$ $5$ $12$ $1$ $11$ $S_3 \times C_4$ (as 12T11) $[\ ]$ $[\ ]_{12}^{2}$ $t + 3$ $x^{12} + 20$
5.12.11.2 $x^{12} + 5$ $5$ $12$ $1$ $11$ $S_3 \times C_4$ (as 12T11) $[\ ]$ $[\ ]_{12}^{2}$ $t + 3$ $x^{12} + 5$
5.12.11.3 $x^{12} + 10$ $5$ $12$ $1$ $11$ $S_3 \times C_4$ (as 12T11) $[\ ]$ $[\ ]_{12}^{2}$ $t + 3$ $x^{12} + 10$
5.12.11.4 $x^{12} + 15$ $5$ $12$ $1$ $11$ $S_3 \times C_4$ (as 12T11) $[\ ]$ $[\ ]_{12}^{2}$ $t + 3$ $x^{12} + 15$
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