Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Ind. of Insep. |
Assoc. Inertia |
2.10.0.1 |
$10$ |
x10 + x6 + x5 + x3 + x2 + x + 1 |
$2$ |
$1$ |
$10$ |
$0$ |
$C_{10}$ (as 10T1) |
$10$ |
$1$ |
$[\ ]$ |
$[\ ]^{10}$ |
$[0]$ |
$[]$ |
2.10.8.1 |
$10$ |
x10 + 5x9 + 15x8 + 30x7 + 45x6 + 55x5 + 55x4 + 10x3 - 25x2 - 5x + 7 |
$2$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$[0]$ |
$[2]$ |
2.10.10.1 |
$10$ |
x10 + 4x9 + 6x8 + 80x7 + 616x6 + 2352x5 + 6000x4 + 11136x3 + 13776x2 + 9472x + 2784 |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2^4 : C_5$ (as 10T8) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{5}$ |
$[1, 0]$ |
$[1]$ |
2.10.10.10 |
$10$ |
x10 + 10x9 + 22x8 + 160x6 + 1200x5 + 3168x4 + 4480x3 + 3760x2 + 1824x + 416 |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2]^{5}$ |
$[1, 0]$ |
$[1]$ |
2.10.10.11 |
$10$ |
x10 + 10x9 + 38x8 + 64x7 + 152x6 + 688x5 + 912x4 - 1024x3 - 1968x2 + 32x - 32 |
$2$ |
$2$ |
$5$ |
$10$ |
$C_{10}$ (as 10T1) |
$5$ |
$1$ |
$[2]$ |
$[2]^{5}$ |
$[1, 0]$ |
$[1]$ |
2.10.10.12 |
$10$ |
x10 + 10x9 + 34x8 + 112x7 + 328x6 + 640x5 + 1360x4 + 2176x3 + 1168x2 + 1888x - 1248 |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2]^{5}$ |
$[1, 0]$ |
$[1]$ |
2.10.10.13 |
$10$ |
x10 + 10x9 + 10x8 + 56x7 + 192x6 + 800x5 + 1536x4 + 2208x3 + 2224x2 + 96x - 1056 |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2]^{5}$ |
$[1, 0]$ |
$[1]$ |
2.10.10.14 |
$10$ |
x10 + 4x9 - 6x8 + 176x7 + 848x6 + 2256x5 + 1216x4 - 1088x3 - 5392x2 - 5120x - 3616 |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2]^{5}$ |
$[1, 0]$ |
$[1]$ |
2.10.10.15 |
$10$ |
x10 + 2x + 2 |
$2$ |
$10$ |
$1$ |
$10$ |
$(C_2^4 : C_5):C_4$ (as 10T24) |
$4$ |
$5$ |
$[6/5]$ |
$[6/5, 6/5, 6/5, 6/5]_{5}^{4}$ |
$[1, 0]$ |
$[1, 4]$ |
2.10.10.16 |
$10$ |
x10 + 2x2 + 2x + 2 |
$2$ |
$10$ |
$1$ |
$10$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[6/5]$ |
$[6/5, 6/5, 6/5, 6/5]_{5}^{4}$ |
$[1, 0]$ |
$[1, 4]$ |
2.10.10.2 |
$10$ |
x10 + 4x9 + 46x8 + 328x7 + 1232x6 + 4048x5 + 5824x4 + 6496x3 - 8272x2 - 14336x - 17632 |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2^4 : C_5$ (as 10T8) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{5}$ |
$[1, 0]$ |
$[1]$ |
2.10.10.3 |
$10$ |
x10 + 10x9 + 74x8 + 320x7 + 1104x6 + 2752x5 + 6176x4 + 12096x3 + 17712x2 + 15968x + 8416 |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2^4 : C_5$ (as 10T8) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{5}$ |
$[1, 0]$ |
$[1]$ |
2.10.10.4 |
$10$ |
x10 - 2x8 + 16x7 - 8x6 - 432x5 - 176x4 - 960x3 - 1776x2 - 448x - 32 |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$10$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{10}$ |
$[1, 0]$ |
$[1]$ |
2.10.10.5 |
$10$ |
x10 + 34x8 - 24x7 + 368x6 - 496x5 + 1568x4 - 1760x3 + 2992x2 - 1856x + 352 |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$10$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{10}$ |
$[1, 0]$ |
$[1]$ |
2.10.10.6 |
$10$ |
x10 - 6x9 + 42x8 - 104x7 - 256x6 - 112x5 - 1568x4 - 2016x3 - 2832x2 - 4960x - 3616 |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$10$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{10}$ |
$[1, 0]$ |
$[1]$ |
2.10.10.7 |
$10$ |
x10 + 10x9 + 50x8 + 160x7 + 360x6 + 592x5 + 656x4 + 384x3 - 112x2 - 352x - 1248 |
$2$ |
$2$ |
$5$ |
$10$ |
$C_{10}$ (as 10T1) |
$5$ |
$1$ |
$[2]$ |
$[2]^{5}$ |
$[1, 0]$ |
$[1]$ |
2.10.10.8 |
$10$ |
x10 + 4x9 + 14x8 + 240x7 + 928x6 + 4400x5 + 6368x4 + 13888x3 - 336x2 + 2432x - 17632 |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2]^{5}$ |
$[1, 0]$ |
$[1]$ |
2.10.10.9 |
$10$ |
x10 + 10x9 + 22x8 - 8x7 + 72x6 + 1328x5 + 4496x4 + 3680x3 - 3696x2 - 96x - 32 |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2]^{5}$ |
$[1, 0]$ |
$[1]$ |
2.10.12.1 |
$10$ |
x10 + 2x6 + 2x3 + 2 |
$2$ |
$10$ |
$1$ |
$12$ |
$(C_2^4 : C_5):C_4$ (as 10T24) |
$4$ |
$5$ |
$[8/5]$ |
$[8/5, 8/5, 8/5, 8/5]_{5}^{4}$ |
$[3, 0]$ |
$[1, 4]$ |
2.10.12.2 |
$10$ |
x10 + 2x6 + 2x5 + 2x3 + 2 |
$2$ |
$10$ |
$1$ |
$12$ |
$(C_2^4 : C_5):C_4$ (as 10T24) |
$4$ |
$5$ |
$[8/5]$ |
$[8/5, 8/5, 8/5, 8/5]_{5}^{4}$ |
$[3, 0]$ |
$[1, 4]$ |
2.10.12.3 |
$10$ |
x10 + 2x3 + 2 |
$2$ |
$10$ |
$1$ |
$12$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[8/5]$ |
$[8/5, 8/5, 8/5, 8/5]_{5}^{4}$ |
$[3, 0]$ |
$[1, 4]$ |
2.10.12.4 |
$10$ |
x10 + 2x5 + 2x3 + 2 |
$2$ |
$10$ |
$1$ |
$12$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[8/5]$ |
$[8/5, 8/5, 8/5, 8/5]_{5}^{4}$ |
$[3, 0]$ |
$[1, 4]$ |
2.10.14.1 |
$10$ |
x10 + 2x8 + 2x7 + 2x6 + 2x5 + 2x4 + 2 |
$2$ |
$10$ |
$1$ |
$14$ |
$F_{5}\times C_2$ (as 10T5) |
$4$ |
$5$ |
$[2]$ |
$[2]_{5}^{4}$ |
$[5, 0]$ |
$[1, 4]$ |
2.10.14.2 |
$10$ |
x10 + 2x9 + 2x5 + 2 |
$2$ |
$10$ |
$1$ |
$14$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[2]$ |
$[6/5, 6/5, 6/5, 6/5, 2]_{5}^{4}$ |
$[5, 0]$ |
$[1, 4]$ |
2.10.14.3 |
$10$ |
x10 + 2x9 + 2x8 + 2x7 + 2x5 + 2 |
$2$ |
$10$ |
$1$ |
$14$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[2]$ |
$[8/5, 8/5, 8/5, 8/5, 2]_{5}^{4}$ |
$[5, 0]$ |
$[1, 4]$ |
2.10.14.4 |
$10$ |
x10 + 2x8 + 2x7 + 2x5 + 2 |
$2$ |
$10$ |
$1$ |
$14$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[2]$ |
$[8/5, 8/5, 8/5, 8/5, 2]_{5}^{4}$ |
$[5, 0]$ |
$[1, 4]$ |
2.10.14.5 |
$10$ |
x10 + 2x5 + 6 |
$2$ |
$10$ |
$1$ |
$14$ |
$F_{5}\times C_2$ (as 10T5) |
$4$ |
$5$ |
$[2]$ |
$[2]_{5}^{4}$ |
$[5, 0]$ |
$[1, 4]$ |
2.10.14.6 |
$10$ |
x10 + 2x9 + 2x7 + 2x5 + 2x4 + 6 |
$2$ |
$10$ |
$1$ |
$14$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[2]$ |
$[6/5, 6/5, 6/5, 6/5, 2]_{5}^{4}$ |
$[5, 0]$ |
$[1, 4]$ |
2.10.14.7 |
$10$ |
x10 + 2x9 + 2x8 + 2x6 + 2x5 + 2x4 + 2 |
$2$ |
$10$ |
$1$ |
$14$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[2]$ |
$[8/5, 8/5, 8/5, 8/5, 2]_{5}^{4}$ |
$[5, 0]$ |
$[1, 4]$ |
2.10.14.8 |
$10$ |
x10 + 2x5 + 2x4 + 6 |
$2$ |
$10$ |
$1$ |
$14$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[2]$ |
$[8/5, 8/5, 8/5, 8/5, 2]_{5}^{4}$ |
$[5, 0]$ |
$[1, 4]$ |
2.10.15.1 |
$10$ |
x10 + 70x8 + 2x7 + 1960x6 - 26x5 + 27441x4 - 2240x3 + 192110x2 - 14504x + 537993 |
$2$ |
$2$ |
$5$ |
$15$ |
$C_{10}$ (as 10T1) |
$5$ |
$1$ |
$[3]$ |
$[3]^{5}$ |
$[2, 0]$ |
$[1]$ |
2.10.15.10 |
$10$ |
x10 - 12x9 + 110x8 - 416x7 + 4264x6 - 11936x5 + 27504x4 - 98432x3 + 20560x2 - 83648x + 9568 |
$2$ |
$2$ |
$5$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$[2, 0]$ |
$[1]$ |
2.10.15.11 |
$10$ |
x10 + 20x9 + 222x8 + 1632x7 + 8392x6 + 35680x5 + 129840x4 + 366464x3 + 703952x2 + 802624x + 377696 |
$2$ |
$2$ |
$5$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$[2, 0]$ |
$[1]$ |
2.10.15.12 |
$10$ |
x10 - 12x9 + 30x8 - 96x7 + 2440x6 + 5728x5 + 31664x4 + 22656x3 + 16080x2 + 26944x + 9568 |
$2$ |
$2$ |
$5$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$[2, 0]$ |
$[1]$ |
2.10.15.13 |
$10$ |
x10 - 12x9 + 174x8 - 640x7 - 40x6 + 11424x5 - 7984x4 - 79360x3 + 84112x2 + 955968x + 1404384 |
$2$ |
$2$ |
$5$ |
$15$ |
$C_{10}$ (as 10T1) |
$5$ |
$1$ |
$[3]$ |
$[3]^{5}$ |
$[2, 0]$ |
$[1]$ |
2.10.15.14 |
$10$ |
x10 - 12x9 + 54x8 - 320x7 + 3784x6 + 6816x5 + 104176x4 + 90624x3 + 798672x2 + 117824x + 1510112 |
$2$ |
$2$ |
$5$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$[2, 0]$ |
$[1]$ |
2.10.15.15 |
$10$ |
x10 - 12x9 + 70x8 + 32x7 + 1832x6 + 2528x5 - 9424x4 - 73600x3 - 157616x2 - 129216x - 23328 |
$2$ |
$2$ |
$5$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$[2, 0]$ |
$[1]$ |
2.10.15.16 |
$10$ |
x10 + 20x9 + 182x8 + 992x7 + 3336x6 + 10848x5 + 51312x4 + 168320x3 + 262864x2 + 156480x - 23328 |
$2$ |
$2$ |
$5$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$[2, 0]$ |
$[1]$ |
2.10.15.2 |
$10$ |
x10 + 8x9 + 102x8 + 832x7 + 6440x6 + 35904x5 + 191792x4 + 594688x3 + 1067088x2 + 999040x + 445152 |
$2$ |
$2$ |
$5$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$[2, 0]$ |
$[1]$ |
2.10.15.3 |
$10$ |
x10 - 12x9 + 82x8 - 32x7 + 1976x6 + 8544x5 + 38064x4 + 155008x3 + 517392x2 + 885056x + 574496 |
$2$ |
$2$ |
$5$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$[2, 0]$ |
$[1]$ |
2.10.15.4 |
$10$ |
x10 + 14x8 + 952x6 + 15696x4 + 92432x2 + 183776 |
$2$ |
$2$ |
$5$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$[2, 0]$ |
$[1]$ |
2.10.15.5 |
$10$ |
x10 + 46x8 + 808x6 + 6768x4 + 27216x2 + 9568 |
$2$ |
$2$ |
$5$ |
$15$ |
$C_{10}$ (as 10T1) |
$5$ |
$1$ |
$[3]$ |
$[3]^{5}$ |
$[2, 0]$ |
$[1]$ |
2.10.15.6 |
$10$ |
x10 - 12x9 + 34x8 + 1040x7 - 168x6 + 19712x5 - 16464x4 + 66752x3 - 45424x2 + 23232x - 17632 |
$2$ |
$2$ |
$5$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$[2, 0]$ |
$[1]$ |
2.10.15.7 |
$10$ |
x10 + 62x8 - 96x7 + 840x6 + 64x5 + 22832x4 + 70528x3 + 199632x2 + 445184x + 361824 |
$2$ |
$2$ |
$5$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$[2, 0]$ |
$[1]$ |
2.10.15.8 |
$10$ |
x10 + 20x9 + 234x8 + 2512x7 + 17000x6 + 100480x5 + 430224x4 + 1312448x3 + 2519632x2 + 2593984x + 1080096 |
$2$ |
$2$ |
$5$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$[2, 0]$ |
$[1]$ |
2.10.15.9 |
$10$ |
x10 + 20x9 + 206x8 + 1376x7 + 6504x6 + 22496x5 + 57328x4 + 105856x3 + 135504x2 + 108864x + 9568 |
$2$ |
$2$ |
$5$ |
$15$ |
$C_{10}$ (as 10T1) |
$5$ |
$1$ |
$[3]$ |
$[3]^{5}$ |
$[2, 0]$ |
$[1]$ |
2.10.16.1 |
$10$ |
x10 + 2x7 + 4x4 + 4x2 + 2 |
$2$ |
$10$ |
$1$ |
$16$ |
$(C_2^4 : C_5):C_4$ (as 10T24) |
$4$ |
$5$ |
$[12/5]$ |
$[12/5, 12/5, 12/5, 12/5]_{5}^{4}$ |
$[7, 0]$ |
$[1, 4]$ |
2.10.16.10 |
$10$ |
x10 + 2x8 + 2x7 + 2x6 + 2x4 + 4x3 + 4x2 + 4x + 2 |
$2$ |
$10$ |
$1$ |
$16$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[12/5]$ |
$[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$ |
$[7, 0]$ |
$[1, 4]$ |
2.10.16.11 |
$10$ |
x10 + 2x9 + 2x7 + 4x3 + 6 |
$2$ |
$10$ |
$1$ |
$16$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[12/5]$ |
$[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$ |
$[7, 0]$ |
$[1, 4]$ |
2.10.16.12 |
$10$ |
x10 + 2x8 + 2x7 + 2x4 + 4x3 + 4x2 + 2 |
$2$ |
$10$ |
$1$ |
$16$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[12/5]$ |
$[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$ |
$[7, 0]$ |
$[1, 4]$ |