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Results (20 matches)

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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
19.12.0.1 $x^{12} + 3 x^{7} + 2 x^{6} + 18 x^{5} + 2 x^{4} + 9 x^{3} + 16 x^{2} + 7 x + 2$ $19$ $1$ $12$ $0$ $C_{12}$ (as 12T1) $[\ ]$ $[\ ]^{12}$ $t^{12} + 3 t^{7} + 2 t^{6} + 18 t^{5} + 2 t^{4} + 9 t^{3} + 16 t^{2} + 7 t + 2$ $x - 19$
19.12.6.1 $x^{12} + 114 x^{10} + 34 x^{9} + 5449 x^{8} + 12 x^{7} + 134889 x^{6} - 75118 x^{5} + 1847901 x^{4} - 1865072 x^{3} + 14269503 x^{2} - 12672520 x + 53461691$ $19$ $2$ $6$ $6$ $C_6\times C_2$ (as 12T2) $[\ ]$ $[\ ]_{2}^{6}$ $t^{6} + 17 t^{3} + 17 t^{2} + 6 t + 2$ $x^{2} + 19$
19.12.6.2 $x^{12} - 116603 x^{6} + 2215457 x^{4} - 14856594 x^{2} + 94091762$ $19$ $2$ $6$ $6$ $C_{12}$ (as 12T1) $[\ ]$ $[\ ]_{2}^{6}$ $t^{6} + 17 t^{3} + 17 t^{2} + 6 t + 2$ $x^{2} + 19 t$
19.12.8.1 $x^{12} + 386 x^{10} + 109 x^{9} + 55308 x^{8} + 21792 x^{7} + 3500499 x^{6} + 2034936 x^{5} + 84821873 x^{4} + 99877907 x^{3} + 174885148 x^{2} + 920938017 x + 335157671$ $19$ $3$ $4$ $8$ $C_{12}$ (as 12T1) $[\ ]$ $[\ ]_{3}^{4}$ $t^{4} + 2 t^{2} + 11 t + 2$ $x^{3} + 95 x + 19$
19.12.8.2 $x^{12} - 76 x^{9} + 2888 x^{6} + 775067 x^{3} + 521284$ $19$ $3$ $4$ $8$ $C_{12}$ (as 12T1) $[\ ]$ $[\ ]_{3}^{4}$ $t^{4} + 2 t^{2} + 11 t + 2$ $x^{3} + 19 t^{2}$
19.12.8.3 $x^{12} + 722 x^{6} - 75449 x^{3} + 260642$ $19$ $3$ $4$ $8$ $C_{12}$ (as 12T1) $[\ ]$ $[\ ]_{3}^{4}$ $t^{4} + 2 t^{2} + 11 t + 2$ $x^{3} + 19 t$
19.12.9.1 $x^{12} + 16 x^{10} + 68 x^{9} + 153 x^{8} + 816 x^{7} + 1382 x^{6} - 12240 x^{5} + 17643 x^{4} + 18836 x^{3} + 180010 x^{2} + 131580 x + 194652$ $19$ $4$ $3$ $9$ $D_4 \times C_3$ (as 12T14) $[\ ]$ $[\ ]_{4}^{6}$ $t^{3} + 4 t + 17$ $x^{4} + 19$
19.12.9.2 $x^{12} + 1444 x^{4} - 116603$ $19$ $4$ $3$ $9$ $D_4 \times C_3$ (as 12T14) $[\ ]$ $[\ ]_{4}^{6}$ $t^{3} + 4 t + 17$ $x^{4} + 19 t$
19.12.10.1 $x^{12} + 108 x^{11} + 4872 x^{10} + 117720 x^{9} + 1613580 x^{8} + 12041568 x^{7} + 40427622 x^{6} + 24085188 x^{5} + 6545520 x^{4} + 3116880 x^{3} + 29259672 x^{2} + 208806768 x + 622519465$ $19$ $6$ $2$ $10$ $C_6\times C_2$ (as 12T2) $[\ ]$ $[\ ]_{6}^{2}$ $t^{2} + 18 t + 2$ $x^{6} + 19$
19.12.10.2 $x^{12} + 304 x^{6} - 5415$ $19$ $6$ $2$ $10$ $C_6\times C_2$ (as 12T2) $[\ ]$ $[\ ]_{6}^{2}$ $t^{2} + 18 t + 2$ $x^{6} + 19 t + 323$
19.12.10.3 $x^{12} - 5396 x^{6} - 21660$ $19$ $6$ $2$ $10$ $C_6\times C_2$ (as 12T2) $[\ ]$ $[\ ]_{6}^{2}$ $t^{2} + 18 t + 2$ $x^{6} + 304 t + 38$
19.12.10.4 $x^{12} - 342 x^{6} + 722$ $19$ $6$ $2$ $10$ $C_{12}$ (as 12T1) $[\ ]$ $[\ ]_{6}^{2}$ $t^{2} + 18 t + 2$ $x^{6} + 19 t$
19.12.10.5 $x^{12} - 5510 x^{6} - 1650131$ $19$ $6$ $2$ $10$ $C_{12}$ (as 12T1) $[\ ]$ $[\ ]_{6}^{2}$ $t^{2} + 18 t + 2$ $x^{6} + 342 t + 323$
19.12.10.6 $x^{12} - 5928 x^{6} - 454860$ $19$ $6$ $2$ $10$ $C_{12}$ (as 12T1) $[\ ]$ $[\ ]_{6}^{2}$ $t^{2} + 18 t + 2$ $x^{6} + 342 t + 114$
19.12.11.1 $x^{12} + 76$ $19$ $12$ $1$ $11$ $D_4 \times C_3$ (as 12T14) $[\ ]$ $[\ ]_{12}^{2}$ $t + 17$ $x^{12} + 76$
19.12.11.2 $x^{12} + 19$ $19$ $12$ $1$ $11$ $D_4 \times C_3$ (as 12T14) $[\ ]$ $[\ ]_{12}^{2}$ $t + 17$ $x^{12} + 19$
19.12.11.3 $x^{12} + 95$ $19$ $12$ $1$ $11$ $D_4 \times C_3$ (as 12T14) $[\ ]$ $[\ ]_{12}^{2}$ $t + 17$ $x^{12} + 95$
19.12.11.4 $x^{12} + 152$ $19$ $12$ $1$ $11$ $D_4 \times C_3$ (as 12T14) $[\ ]$ $[\ ]_{12}^{2}$ $t + 17$ $x^{12} + 152$
19.12.11.5 $x^{12} + 38$ $19$ $12$ $1$ $11$ $D_4 \times C_3$ (as 12T14) $[\ ]$ $[\ ]_{12}^{2}$ $t + 17$ $x^{12} + 38$
19.12.11.6 $x^{12} + 190$ $19$ $12$ $1$ $11$ $D_4 \times C_3$ (as 12T14) $[\ ]$ $[\ ]_{12}^{2}$ $t + 17$ $x^{12} + 190$
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