| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.8.8.1 |
$8$ |
$x^{8} + 8 x^{7} + 32 x^{6} + 82 x^{5} + 148 x^{4} + 184 x^{3} + 137 x^{2} + 44 x + 5$ |
$2$ |
$2$ |
$4$ |
$8$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$1$ |
$[2]$ |
$[2]^{4}$ |
$t^{4} + t + 1$ |
$x^{2} + 2 x + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.8.12.1 |
$8$ |
$x^{8} - 12 x^{7} + 52 x^{6} + 840 x^{5} + 3808 x^{4} + 10224 x^{3} + 17968 x^{2} + 20576 x + 15216$ |
$2$ |
$2$ |
$4$ |
$12$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$1$ |
$[3]$ |
$[3]^{4}$ |
$t^{4} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2}\right) x + 12 t^{3} + 12 t^{2} + 4 t + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.8.12.2 |
$8$ |
$x^{8} + 16 x^{7} + 120 x^{6} + 546 x^{5} + 1646 x^{4} + 3352 x^{3} + 4457 x^{2} + 3470 x + 1203$ |
$2$ |
$2$ |
$4$ |
$12$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$1$ |
$[3]$ |
$[3]^{4}$ |
$t^{4} + t + 1$ |
$x^{2} + 4 x + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.8.16.1 |
$8$ |
$x^{8} + 8 x^{7} + 24 x^{6} + 40 x^{5} + 60 x^{4} + 32 x^{3} + 88 x^{2} + 108$ |
$2$ |
$4$ |
$2$ |
$16$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$1$ |
$[2, 3]$ |
$[2, 3]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t + 6\right) x^{2} + 4 x + 12 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.8.16.2 |
$8$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 16 x^{4} + 16 x^{3} + 40 x^{2} + 48 x + 84$ |
$2$ |
$4$ |
$2$ |
$16$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$1$ |
$[2, 3]$ |
$[2, 3]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 2 x^{2} + 4 x + 8 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.8.16.3 |
$8$ |
$x^{8} + 8 x^{7} + 16 x^{6} + 8 x^{5} + 36 x^{4} - 32 x^{3} + 88 x^{2} - 32 x + 124$ |
$2$ |
$4$ |
$2$ |
$16$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$1$ |
$[2, 3]$ |
$[2, 3]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t + 2\right) x^{2} + 4 x + 12 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.8.22.2 |
$8$ |
$x^{8} + 16 x^{7} + 88 x^{6} + 192 x^{5} + 180 x^{4} + 288 x^{3} + 432 x^{2} + 516$ |
$2$ |
$4$ |
$2$ |
$22$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + 12 x^{2} + 16 t + 26$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.5 |
$8$ |
$x^{8} + 20 x^{7} + 154 x^{6} + 592 x^{5} + 1315 x^{4} + 1968 x^{3} + 2050 x^{2} + 828 x + 111$ |
$2$ |
$4$ |
$2$ |
$22$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + 12 x^{2} + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.6 |
$8$ |
$x^{8} + 16 x^{7} + 76 x^{6} + 88 x^{5} + 8 x^{4} + 192 x^{3} + 280 x^{2} + 48 x + 252$ |
$2$ |
$4$ |
$2$ |
$22$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + \left(4 t + 8\right) x^{2} + 8 t x + 12 t + 18$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.7 |
$8$ |
$x^{8} + 20 x^{7} + 154 x^{6} + 592 x^{5} + 1331 x^{4} + 2128 x^{3} + 2386 x^{2} + 764 x + 103$ |
$2$ |
$4$ |
$2$ |
$22$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + 12 x^{2} + 18$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.24.1 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 14 x^{4} + 4 x^{2} + 8 x + 22$ |
$2$ |
$8$ |
$1$ |
$24$ |
$C_4\times C_2$ (as 8T2) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 14 x^{4} + 4 x^{2} + 8 x + 22$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.2 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 14 x^{4} + 4 x^{2} + 8 x + 6$ |
$2$ |
$8$ |
$1$ |
$24$ |
$C_4\times C_2$ (as 8T2) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 14 x^{4} + 4 x^{2} + 8 x + 6$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.5 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 18$ |
$2$ |
$8$ |
$1$ |
$24$ |
$C_4\times C_2$ (as 8T2) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 18$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.7 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 6 x^{4} + 4 x^{2} + 8 x + 14$ |
$2$ |
$8$ |
$1$ |
$24$ |
$C_4\times C_2$ (as 8T2) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 6 x^{4} + 4 x^{2} + 8 x + 14$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.9 |
$8$ |
$x^{8} + 8 x^{6} + 14 x^{4} + 4 x^{2} + 8 x + 30$ |
$2$ |
$8$ |
$1$ |
$24$ |
$C_4\times C_2$ (as 8T2) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 14 x^{4} + 4 x^{2} + 8 x + 30$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.10 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$24$ |
$C_4\times C_2$ (as 8T2) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.11 |
$8$ |
$x^{8} + 8 x^{7} + 2 x^{4} + 4 x^{2} + 8 x + 26$ |
$2$ |
$8$ |
$1$ |
$24$ |
$C_4\times C_2$ (as 8T2) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 2 x^{4} + 4 x^{2} + 8 x + 26$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.13 |
$8$ |
$x^{8} + 8 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$24$ |
$C_4\times C_2$ (as 8T2) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 10$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 3.8.4.1 |
$8$ |
$x^{8} + 4 x^{7} + 16 x^{6} + 36 x^{5} + 94 x^{4} + 116 x^{3} + 144 x^{2} + 36 x + 229$ |
$3$ |
$2$ |
$4$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{2} + 3$ |
$[0]$ |
$[1]$ |
| 5.8.4.1 |
$8$ |
$x^{8} + 80 x^{7} + 2428 x^{6} + 33688 x^{5} + 195810 x^{4} + 305952 x^{3} + 870132 x^{2} + 1037416 x + 503089$ |
$5$ |
$2$ |
$4$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 4 t^{2} + 4 t + 2$ |
$x^{2} + 20 x + 5$ |
$[0]$ |
$[1]$ |
| 5.8.6.1 |
$8$ |
$x^{8} + 16 x^{7} + 104 x^{6} + 352 x^{5} + 674 x^{4} + 784 x^{3} + 776 x^{2} + 928 x + 721$ |
$5$ |
$4$ |
$2$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 4 t + 2$ |
$x^{4} + 5$ |
$[0]$ |
$[1]$ |
| 5.8.6.2 |
$8$ |
$x^{8} + 10 x^{4} - 25$ |
$5$ |
$4$ |
$2$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 4 t + 2$ |
$x^{4} + 5 t + 15$ |
$[0]$ |
$[1]$ |
| 7.8.4.1 |
$8$ |
$x^{8} + 38 x^{6} + 8 x^{5} + 395 x^{4} - 72 x^{3} + 1026 x^{2} - 872 x + 401$ |
$7$ |
$2$ |
$4$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 5 t^{2} + 4 t + 3$ |
$x^{2} + 7$ |
$[0]$ |
$[1]$ |
| 11.8.4.1 |
$8$ |
$x^{8} + 60 x^{6} + 20 x^{5} + 970 x^{4} - 280 x^{3} + 4664 x^{2} - 5460 x + 2325$ |
$11$ |
$2$ |
$4$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 8 t^{2} + 10 t + 2$ |
$x^{2} + 11$ |
$[0]$ |
$[1]$ |
| 13.8.4.1 |
$8$ |
$x^{8} + 520 x^{7} + 101458 x^{6} + 8810644 x^{5} + 288610205 x^{4} + 142111548 x^{3} + 982314112 x^{2} + 3617879976 x + 920156436$ |
$13$ |
$2$ |
$4$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 3 t^{2} + 12 t + 2$ |
$x^{2} + 130 x + 13$ |
$[0]$ |
$[1]$ |
| 13.8.6.1 |
$8$ |
$x^{8} + 48 x^{7} + 872 x^{6} + 7200 x^{5} + 24242 x^{4} + 15024 x^{3} + 14408 x^{2} + 86496 x + 254881$ |
$13$ |
$4$ |
$2$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 12 t + 2$ |
$x^{4} + 13$ |
$[0]$ |
$[1]$ |
| 13.8.6.2 |
$8$ |
$x^{8} + 130 x^{4} - 1521$ |
$13$ |
$4$ |
$2$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 12 t + 2$ |
$x^{4} + 13 t + 143$ |
$[0]$ |
$[1]$ |
| 17.8.4.1 |
$8$ |
$x^{8} + 612 x^{7} + 140536 x^{6} + 14363966 x^{5} + 553913435 x^{4} + 345855654 x^{3} + 4032327212 x^{2} + 6379401496 x + 2294776272$ |
$17$ |
$2$ |
$4$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 7 t^{2} + 10 t + 3$ |
$x^{2} + 153 x + 17$ |
$[0]$ |
$[1]$ |
| 17.8.6.1 |
$8$ |
$x^{8} + 64 x^{7} + 1548 x^{6} + 16960 x^{5} + 74840 x^{4} + 51968 x^{3} + 39432 x^{2} + 270464 x + 1062564$ |
$17$ |
$4$ |
$2$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 16 t + 3$ |
$x^{4} + 17$ |
$[0]$ |
$[1]$ |
| 17.8.6.2 |
$8$ |
$x^{8} + 204 x^{4} - 7225$ |
$17$ |
$4$ |
$2$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 16 t + 3$ |
$x^{4} + 17 t + 238$ |
$[0]$ |
$[1]$ |
| 19.8.4.1 |
$8$ |
$x^{8} + 80 x^{6} + 22 x^{5} + 2250 x^{4} - 792 x^{3} + 25817 x^{2} - 22946 x + 107924$ |
$19$ |
$2$ |
$4$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 2 t^{2} + 11 t + 2$ |
$x^{2} + 19$ |
$[0]$ |
$[1]$ |
| 23.8.4.1 |
$8$ |
$x^{8} + 98 x^{6} + 38 x^{5} + 3331 x^{4} - 1634 x^{3} + 44919 x^{2} - 57494 x + 224528$ |
$23$ |
$2$ |
$4$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 3 t^{2} + 19 t + 5$ |
$x^{2} + 23$ |
$[0]$ |
$[1]$ |
| 29.8.4.1 |
$8$ |
$x^{8} + 2784 x^{7} + 2906616 x^{6} + 1348864734 x^{5} + 234834277018 x^{4} + 41857830864 x^{3} + 492109772617 x^{2} + 3561769809750 x + 616658760166$ |
$29$ |
$2$ |
$4$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 2 t^{2} + 15 t + 2$ |
$x^{2} + 696 x + 29$ |
$[0]$ |
$[1]$ |
| 29.8.6.1 |
$8$ |
$x^{8} + 96 x^{7} + 3464 x^{6} + 55872 x^{5} + 345682 x^{4} + 114528 x^{3} + 113384 x^{2} + 1587648 x + 9488961$ |
$29$ |
$4$ |
$2$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 24 t + 2$ |
$x^{4} + 29$ |
$[0]$ |
$[1]$ |
| 29.8.6.2 |
$8$ |
$x^{8} - 1914 x^{4} - 2069701$ |
$29$ |
$4$ |
$2$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 24 t + 2$ |
$x^{4} + 145 t + 783$ |
$[0]$ |
$[1]$ |
| 31.8.4.1 |
$8$ |
$x^{8} + 130 x^{6} + 32 x^{5} + 5967 x^{4} - 1888 x^{3} + 113114 x^{2} - 89184 x + 766577$ |
$31$ |
$2$ |
$4$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 3 t^{2} + 16 t + 3$ |
$x^{2} + 31$ |
$[0]$ |
$[1]$ |
| 37.8.4.1 |
$8$ |
$x^{8} + 3700 x^{7} + 5133910 x^{6} + 3166256548 x^{5} + 732510094073 x^{4} + 136269235536 x^{3} + 4476368972260 x^{2} + 17928293629116 x + 2173698901413$ |
$37$ |
$2$ |
$4$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 6 t^{2} + 24 t + 2$ |
$x^{2} + 925 x + 37$ |
$[0]$ |
$[1]$ |
| 37.8.6.1 |
$8$ |
$x^{8} + 132 x^{7} + 6542 x^{6} + 144540 x^{5} + 1212155 x^{4} + 293964 x^{3} + 267038 x^{2} + 5290428 x + 43558414$ |
$37$ |
$4$ |
$2$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 33 t + 2$ |
$x^{4} + 37$ |
$[0]$ |
$[1]$ |
| 37.8.6.2 |
$8$ |
$x^{8} - 2294 x^{4} - 4603947$ |
$37$ |
$4$ |
$2$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 33 t + 2$ |
$x^{4} + 148 t + 1295$ |
$[0]$ |
$[1]$ |
| 41.8.4.1 |
$8$ |
$x^{8} + 3772 x^{7} + 5335658 x^{6} + 3354711230 x^{5} + 791201413052 x^{4} + 137665893766 x^{3} + 86143602389 x^{2} + 18207949968812 x + 5534365087156$ |
$41$ |
$2$ |
$4$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 23 t + 6$ |
$x^{2} + 943 x + 41$ |
$[0]$ |
$[1]$ |
| 41.8.6.1 |
$8$ |
$x^{8} + 152 x^{7} + 8688 x^{6} + 222224 x^{5} + 2189402 x^{4} + 1339576 x^{3} + 665040 x^{2} + 8919664 x + 84075609$ |
$41$ |
$4$ |
$2$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 38 t + 6$ |
$x^{4} + 41$ |
$[0]$ |
$[1]$ |
| 41.8.6.2 |
$8$ |
$x^{8} - 1804 x^{4} - 4557191$ |
$41$ |
$4$ |
$2$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 38 t + 6$ |
$x^{4} + 123 t + 1435$ |
$[0]$ |
$[1]$ |
| 43.8.4.1 |
$8$ |
$x^{8} + 182 x^{6} + 84 x^{5} + 11555 x^{4} - 6804 x^{3} + 301934 x^{2} - 447636 x + 2755621$ |
$43$ |
$2$ |
$4$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 5 t^{2} + 42 t + 3$ |
$x^{2} + 43$ |
$[0]$ |
$[1]$ |
| 47.8.4.1 |
$8$ |
$x^{8} + 204 x^{6} + 80 x^{5} + 14080 x^{4} - 6880 x^{3} + 384824 x^{2} - 499680 x + 3453444$ |
$47$ |
$2$ |
$4$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 8 t^{2} + 40 t + 5$ |
$x^{2} + 47$ |
$[0]$ |
$[1]$ |
| 53.8.4.1 |
$8$ |
$x^{8} + 9752 x^{7} + 35663294 x^{6} + 57966048984 x^{5} + 35333436724405 x^{4} + 3595233169984 x^{3} + 320278224174124 x^{2} + 1356456509257952 x + 99990743929156$ |
$53$ |
$2$ |
$4$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 9 t^{2} + 38 t + 2$ |
$x^{2} + 2438 x + 53$ |
$[0]$ |
$[1]$ |
| 53.8.6.1 |
$8$ |
$x^{8} + 196 x^{7} + 14414 x^{6} + 471772 x^{5} + 5822555 x^{4} + 953932 x^{3} + 819902 x^{2} + 24880828 x + 304519678$ |
$53$ |
$4$ |
$2$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 49 t + 2$ |
$x^{4} + 53$ |
$[0]$ |
$[1]$ |
| 53.8.6.2 |
$8$ |
$x^{8} - 4982 x^{4} - 20682667$ |
$53$ |
$4$ |
$2$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 49 t + 2$ |
$x^{4} + 212 t + 2703$ |
$[0]$ |
$[1]$ |
| 59.8.4.1 |
$8$ |
$x^{8} + 240 x^{6} + 80 x^{5} + 21130 x^{4} - 9280 x^{3} + 808256 x^{2} - 825840 x + 11417625$ |
$59$ |
$2$ |
$4$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 2 t^{2} + 40 t + 2$ |
$x^{2} + 59$ |
$[0]$ |
$[1]$ |
| 61.8.4.1 |
$8$ |
$x^{8} + 9516 x^{7} + 33958096 x^{6} + 53858928086 x^{5} + 32035798457059 x^{4} + 3448323535094 x^{3} + 98379480266246 x^{2} + 1286299880976982 x + 96975348777163$ |
$61$ |
$2$ |
$4$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 3 t^{2} + 40 t + 2$ |
$x^{2} + 2379 x + 61$ |
$[0]$ |
$[1]$ |
| 61.8.6.1 |
$8$ |
$x^{8} + 240 x^{7} + 21608 x^{6} + 865440 x^{5} + 13046546 x^{4} + 1745520 x^{3} + 1402568 x^{2} + 52618080 x + 788807425$ |
$61$ |
$4$ |
$2$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 60 t + 2$ |
$x^{4} + 61$ |
$[0]$ |
$[1]$ |
