| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.8.12.13 |
$8$ |
$x^{8} + 8 x^{7} + 28 x^{6} + 58 x^{5} + 87 x^{4} + 98 x^{3} + 58 x^{2} - 2 x + 1$ |
$2$ |
$4$ |
$2$ |
$12$ |
$D_4$ (as 8T4) |
$2$ |
$1$ |
$[2, 2]$ |
$[2, 2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 2 x^{3} + 2$ |
$[3, 3, 0]$ |
$[1]$ |
| 2.8.12.14 |
$8$ |
$x^{8} + 8 x^{7} + 28 x^{6} + 58 x^{5} + 95 x^{4} + 130 x^{3} + 58 x^{2} - 58 x + 13$ |
$2$ |
$4$ |
$2$ |
$12$ |
$D_4$ (as 8T4) |
$2$ |
$1$ |
$[2, 2]$ |
$[2, 2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 2 x^{3} + 6$ |
$[3, 3, 0]$ |
$[1]$ |
| 2.8.16.4 |
$8$ |
$x^{8} + 12 x^{7} + 58 x^{6} + 160 x^{5} + 329 x^{4} + 500 x^{3} + 408 x^{2} + 68 x + 61$ |
$2$ |
$4$ |
$2$ |
$16$ |
$D_4$ (as 8T4) |
$2$ |
$1$ |
$[2, 3]$ |
$[2, 3]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.8.16.5 |
$8$ |
$x^{8} + 4 x^{7} + 14 x^{6} + 36 x^{5} + 73 x^{4} + 88 x^{3} + 48 x^{2} + 56 x + 61$ |
$2$ |
$4$ |
$2$ |
$16$ |
$D_4$ (as 8T4) |
$2$ |
$1$ |
$[2, 3]$ |
$[2, 3]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 2 x^{2} + 4 x + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.8.22.1 |
$8$ |
$x^{8} + 16 x^{7} + 68 x^{6} + 24 x^{5} + 48 x^{4} + 128 x^{3} + 280 x^{2} + 144 x + 108$ |
$2$ |
$4$ |
$2$ |
$22$ |
$D_4$ (as 8T4) |
$2$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + \left(12 t + 8\right) x^{2} + 8 t x + 12 t + 6$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.8 |
$8$ |
$x^{8} + 20 x^{7} + 146 x^{6} + 520 x^{5} + 1239 x^{4} + 2240 x^{3} + 2470 x^{2} + 900 x + 475$ |
$2$ |
$4$ |
$2$ |
$22$ |
$D_4$ (as 8T4) |
$2$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 26$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.83 |
$8$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 4 x^{2} + 14$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4$ (as 8T4) |
$1$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 4 x^{2} + 14$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.84 |
$8$ |
$x^{8} + 4 x^{7} + 10 x^{4} + 4 x^{2} + 14$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4$ (as 8T4) |
$1$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 10 x^{4} + 4 x^{2} + 14$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.85 |
$8$ |
$x^{8} + 4 x^{7} + 10 x^{4} + 4 x^{2} + 6$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4$ (as 8T4) |
$1$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 10 x^{4} + 4 x^{2} + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.86 |
$8$ |
$x^{8} + 4 x^{7} + 14 x^{4} + 12 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4$ (as 8T4) |
$1$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 14 x^{4} + 12 x^{2} + 10$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.87 |
$8$ |
$x^{8} + 4 x^{7} + 6 x^{4} + 12 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4$ (as 8T4) |
$1$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 6 x^{4} + 12 x^{2} + 2$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.88 |
$8$ |
$x^{8} + 4 x^{7} + 6 x^{4} + 12 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4$ (as 8T4) |
$1$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 6 x^{4} + 12 x^{2} + 10$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.89 |
$8$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 4 x^{2} + 6$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4$ (as 8T4) |
$1$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 4 x^{2} + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.90 |
$8$ |
$x^{8} + 4 x^{7} + 14 x^{4} + 12 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4$ (as 8T4) |
$1$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 14 x^{4} + 12 x^{2} + 2$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.14 |
$8$ |
$x^{8} + 12 x^{6} + 6 x^{4} + 4 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$24$ |
$D_4$ (as 8T4) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 12 x^{6} + 6 x^{4} + 4 x^{2} + 8 x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.15 |
$8$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 6 x^{4} + 4 x^{2} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$24$ |
$D_4$ (as 8T4) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 6 x^{4} + 4 x^{2} + 8 x + 10$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.3 |
$8$ |
$x^{8} + 12 x^{6} + 6 x^{4} + 4 x^{2} + 8 x + 18$ |
$2$ |
$8$ |
$1$ |
$24$ |
$D_4$ (as 8T4) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 12 x^{6} + 6 x^{4} + 4 x^{2} + 8 x + 18$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.24.6 |
$8$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 6 x^{4} + 4 x^{2} + 8 x + 26$ |
$2$ |
$8$ |
$1$ |
$24$ |
$D_4$ (as 8T4) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 6 x^{4} + 4 x^{2} + 8 x + 26$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 3.8.6.2 |
$8$ |
$x^{8} + 6 x^{5} + 6 x^{4} + 18 x^{2} + 18 x + 9$ |
$3$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{4} + \left(3 t + 6\right) x + 3$ |
$[0]$ |
$[1]$ |
| 7.8.6.2 |
$8$ |
$x^{8} + 24 x^{7} + 228 x^{6} + 1080 x^{5} + 2660 x^{4} + 3408 x^{3} + 3312 x^{2} + 5184 x + 6304$ |
$7$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 6 t + 3$ |
$x^{4} + 7$ |
$[0]$ |
$[1]$ |
| 11.8.6.2 |
$8$ |
$x^{8} + 28 x^{7} + 302 x^{6} + 1540 x^{5} + 3623 x^{4} + 3388 x^{3} + 4178 x^{2} + 13468 x + 22324$ |
$11$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 7 t + 2$ |
$x^{4} + 11$ |
$[0]$ |
$[1]$ |
| 19.8.6.2 |
$8$ |
$x^{8} + 72 x^{7} + 1952 x^{6} + 23760 x^{5} + 112814 x^{4} + 48888 x^{3} + 44288 x^{2} + 435600 x + 1945825$ |
$19$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 18 t + 2$ |
$x^{4} + 19$ |
$[0]$ |
$[1]$ |
| 23.8.6.2 |
$8$ |
$x^{8} + 84 x^{7} + 2666 x^{6} + 38304 x^{5} + 221137 x^{4} + 193452 x^{3} + 126128 x^{2} + 833532 x + 4272507$ |
$23$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 21 t + 5$ |
$x^{4} + 23$ |
$[0]$ |
$[1]$ |
| 31.8.6.1 |
$8$ |
$x^{8} + 116 x^{7} + 5058 x^{6} + 98600 x^{5} + 737673 x^{4} + 299396 x^{3} + 200832 x^{2} + 2995004 x + 21614459$ |
$31$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 29 t + 3$ |
$x^{4} + 31$ |
$[0]$ |
$[1]$ |
| 43.8.6.1 |
$8$ |
$x^{8} + 168 x^{7} + 10596 x^{6} + 297864 x^{5} + 3175340 x^{4} + 900816 x^{3} + 548928 x^{2} + 12682656 x + 132895408$ |
$43$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 42 t + 3$ |
$x^{4} + 43$ |
$[0]$ |
$[1]$ |
| 47.8.6.1 |
$8$ |
$x^{8} + 180 x^{7} + 12170 x^{6} + 367200 x^{5} + 4222369 x^{4} + 1844460 x^{3} + 872480 x^{2} + 17027100 x + 190831059$ |
$47$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 45 t + 5$ |
$x^{4} + 47$ |
$[0]$ |
$[1]$ |
| 59.8.6.1 |
$8$ |
$x^{8} + 232 x^{7} + 20192 x^{6} + 781840 x^{5} + 11397374 x^{4} + 1577368 x^{3} + 1270208 x^{2} + 45966160 x + 666089425$ |
$59$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 58 t + 2$ |
$x^{4} + 59$ |
$[0]$ |
$[1]$ |
| 67.8.6.1 |
$8$ |
$x^{8} + 252 x^{7} + 23822 x^{6} + 1001700 x^{5} + 15848375 x^{4} + 2020284 x^{3} + 1689218 x^{2} + 66913308 x + 1053326044$ |
$67$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 63 t + 2$ |
$x^{4} + 67$ |
$[0]$ |
$[1]$ |
| 71.8.6.1 |
$8$ |
$x^{8} + 276 x^{7} + 28594 x^{6} + 1319832 x^{5} + 23067481 x^{4} + 9258420 x^{3} + 3423328 x^{2} + 92979708 x + 1599915123$ |
$71$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 69 t + 7$ |
$x^{4} + 71$ |
$[0]$ |
$[1]$ |
| 79.8.6.1 |
$8$ |
$x^{8} + 312 x^{7} + 36516 x^{6} + 1901016 x^{5} + 37234292 x^{4} + 5727696 x^{3} + 3209616 x^{2} + 149745024 x + 2918429536$ |
$79$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 78 t + 3$ |
$x^{4} + 79$ |
$[0]$ |
$[1]$ |
| 83.8.6.1 |
$8$ |
$x^{8} + 328 x^{7} + 40352 x^{6} + 2207440 x^{5} + 45373742 x^{4} + 4442104 x^{3} + 3507968 x^{2} + 182893456 x + 3748153441$ |
$83$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 82 t + 2$ |
$x^{4} + 83$ |
$[0]$ |
$[1]$ |
| 103.8.6.1 |
$8$ |
$x^{8} + 408 x^{7} + 62444 x^{6} + 4250952 x^{5} + 108867812 x^{4} + 21296784 x^{3} + 7984592 x^{2} + 436638336 x + 11127635392$ |
$103$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 102 t + 5$ |
$x^{4} + 103$ |
$[0]$ |
$[1]$ |
| 107.8.6.1 |
$8$ |
$x^{8} + 412 x^{7} + 63662 x^{6} + 4373380 x^{5} + 112805735 x^{4} + 8790844 x^{3} + 7063058 x^{2} + 467425948 x + 12033875284$ |
$107$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 103 t + 2$ |
$x^{4} + 107$ |
$[0]$ |
$[1]$ |
| 127.8.6.1 |
$8$ |
$x^{8} + 504 x^{7} + 95268 x^{6} + 8006040 x^{5} + 252619220 x^{4} + 24082128 x^{3} + 12950352 x^{2} + 1015628544 x + 31985840224$ |
$127$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 126 t + 3$ |
$x^{4} + 127$ |
$[0]$ |
$[1]$ |
| 131.8.6.1 |
$8$ |
$x^{8} + 508 x^{7} + 96782 x^{6} + 8196580 x^{5} + 260532023 x^{4} + 16459708 x^{3} + 13061378 x^{2} + 1072957468 x + 34062063004$ |
$131$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 127 t + 2$ |
$x^{4} + 131$ |
$[0]$ |
$[1]$ |
| 139.8.6.1 |
$8$ |
$x^{8} + 552 x^{7} + 114272 x^{6} + 10515600 x^{5} + 363131294 x^{4} + 21107928 x^{3} + 16336448 x^{2} + 1460752080 x + 50390520625$ |
$139$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 138 t + 2$ |
$x^{4} + 139$ |
$[0]$ |
$[1]$ |
| 151.8.6.1 |
$8$ |
$x^{8} + 596 x^{7} + 133230 x^{6} + 13242524 x^{5} + 494483391 x^{4} + 79545140 x^{3} + 24899514 x^{2} + 1996510004 x + 74345123096$ |
$151$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 149 t + 6$ |
$x^{4} + 151$ |
$[0]$ |
$[1]$ |
| 163.8.6.1 |
$8$ |
$x^{8} + 636 x^{7} + 151694 x^{6} + 16082532 x^{5} + 639736055 x^{4} + 32268732 x^{3} + 25327682 x^{2} + 2620213788 x + 104145082108$ |
$163$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 159 t + 2$ |
$x^{4} + 163$ |
$[0]$ |
$[1]$ |
| 167.8.6.1 |
$8$ |
$x^{8} + 664 x^{7} + 165356 x^{6} + 18307144 x^{5} + 760986980 x^{4} + 91646608 x^{3} + 31734992 x^{2} + 3054049408 x + 126716633536$ |
$167$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 166 t + 5$ |
$x^{4} + 167$ |
$[0]$ |
$[1]$ |
| 179.8.6.1 |
$8$ |
$x^{8} + 688 x^{7} + 177512 x^{6} + 20357920 x^{5} + 875923454 x^{4} + 40838992 x^{3} + 32478968 x^{2} + 3642595360 x + 156620806225$ |
$179$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 172 t + 2$ |
$x^{4} + 179$ |
$[0]$ |
$[1]$ |
| 191.8.6.1 |
$8$ |
$x^{8} + 760 x^{7} + 216676 x^{6} + 27479320 x^{5} + 1311443348 x^{4} + 522252240 x^{3} + 119547088 x^{2} + 5237214720 x + 248389387104$ |
$191$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 190 t + 19$ |
$x^{4} + 191$ |
$[0]$ |
$[1]$ |
| 199.8.6.1 |
$8$ |
$x^{8} + 772 x^{7} + 223506 x^{6} + 28763176 x^{5} + 1388829417 x^{4} + 86443156 x^{3} + 46479696 x^{2} + 5721127564 x + 276021204851$ |
$199$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 193 t + 3$ |
$x^{4} + 199$ |
$[0]$ |
$[1]$ |
