Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Slope content |
5.10.0.1 |
$10$ |
x10 + x2 - x + 3 |
$5$ |
$1$ |
$10$ |
$0$ |
$C_{10}$ (as 10T1) |
$10$ |
$1$ |
$[\ ]^{10}$ |
5.10.5.1 |
$10$ |
x10 - 50x6 + 625x2 - 12500 |
$5$ |
$2$ |
$5$ |
$5$ |
$C_{10}$ (as 10T1) |
$5$ |
$2$ |
$[\ ]_{2}^{5}$ |
5.10.5.2 |
$10$ |
x10 - 625x2 + 6250 |
$5$ |
$2$ |
$5$ |
$5$ |
$C_{10}$ (as 10T1) |
$5$ |
$2$ |
$[\ ]_{2}^{5}$ |
5.10.10.1 |
$10$ |
x10 + 10x5 + 75x2 + 25 |
$5$ |
$5$ |
$2$ |
$10$ |
$C_5^2 : C_8$ (as 10T18) |
$2$ |
$4$ |
$[5/4, 5/4]_{4}^{2}$ |
5.10.10.10 |
$10$ |
x10 + 10x8 + 5x6 + 10x5 - 20x4 - 20x2 + 2 |
$5$ |
$5$ |
$2$ |
$10$ |
$F_{5}\times C_2$ (as 10T5) |
$2$ |
$4$ |
$[5/4]_{4}^{2}$ |
5.10.10.11 |
$10$ |
x10 + 5x6 + 10x5 + 25x2 + 25x + 25 |
$5$ |
$5$ |
$2$ |
$10$ |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
$2$ |
$4$ |
$[5/4, 5/4]_{4}^{2}$ |
5.10.10.12 |
$10$ |
x10 + 20x6 + 10x5 + 25x2 + 100x + 25 |
$5$ |
$5$ |
$2$ |
$10$ |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
$2$ |
$4$ |
$[5/4, 5/4]_{4}^{2}$ |
5.10.10.13 |
$10$ |
x10 + 15x6 + 10x5 + 100x2 + 75x + 25 |
$5$ |
$5$ |
$2$ |
$10$ |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
$2$ |
$4$ |
$[5/4, 5/4]_{4}^{2}$ |
5.10.10.14 |
$10$ |
x10 + 10x6 + 10x5 + 100x2 + 50x + 25 |
$5$ |
$5$ |
$2$ |
$10$ |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
$2$ |
$4$ |
$[5/4, 5/4]_{4}^{2}$ |
5.10.10.15 |
$10$ |
x10 + 20x + 5 |
$5$ |
$10$ |
$1$ |
$10$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[9/8, 9/8]_{8}^{2}$ |
5.10.10.16 |
$10$ |
x10 + 10x + 5 |
$5$ |
$10$ |
$1$ |
$10$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[9/8, 9/8]_{8}^{2}$ |
5.10.10.17 |
$10$ |
x10 + 20x + 10 |
$5$ |
$10$ |
$1$ |
$10$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[9/8, 9/8]_{8}^{2}$ |
5.10.10.18 |
$10$ |
x10 + 15x + 10 |
$5$ |
$10$ |
$1$ |
$10$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[9/8, 9/8]_{8}^{2}$ |
5.10.10.2 |
$10$ |
x10 + 5x6 + 10x5 + 50x2 + 25x + 25 |
$5$ |
$5$ |
$2$ |
$10$ |
$C_5^2 : C_8$ (as 10T18) |
$2$ |
$4$ |
$[5/4, 5/4]_{4}^{2}$ |
5.10.10.3 |
$10$ |
x10 + 10x5 + 50x2 + 25 |
$5$ |
$5$ |
$2$ |
$10$ |
$C_5^2 : C_8$ (as 10T18) |
$2$ |
$4$ |
$[5/4, 5/4]_{4}^{2}$ |
5.10.10.4 |
$10$ |
x10 + 20x6 + 10x5 + 50x2 + 100x + 25 |
$5$ |
$5$ |
$2$ |
$10$ |
$C_5^2 : C_8$ (as 10T18) |
$2$ |
$4$ |
$[5/4, 5/4]_{4}^{2}$ |
5.10.10.5 |
$10$ |
x10 + 15x6 + 10x5 + 75x2 + 75x + 25 |
$5$ |
$5$ |
$2$ |
$10$ |
$C_5^2 : C_8$ (as 10T18) |
$2$ |
$4$ |
$[5/4, 5/4]_{4}^{2}$ |
5.10.10.6 |
$10$ |
x10 + 10x6 + 10x5 + 75x2 + 50x + 25 |
$5$ |
$5$ |
$2$ |
$10$ |
$C_5^2 : C_8$ (as 10T18) |
$2$ |
$4$ |
$[5/4, 5/4]_{4}^{2}$ |
5.10.10.7 |
$10$ |
x10 + 10x8 + 10x5 - 20x4 - 20x2 + 12 |
$5$ |
$5$ |
$2$ |
$10$ |
$F_{5}\times C_2$ (as 10T5) |
$2$ |
$4$ |
$[5/4]_{4}^{2}$ |
5.10.10.8 |
$10$ |
x10 + 10x8 + 20x6 + 10x5 - 20x4 - 20x2 + 22 |
$5$ |
$5$ |
$2$ |
$10$ |
$F_{5}\times C_2$ (as 10T5) |
$2$ |
$4$ |
$[5/4]_{4}^{2}$ |
5.10.10.9 |
$10$ |
x10 + 10x8 + 10x6 + 10x5 - 20x4 - 20x2 + 17 |
$5$ |
$5$ |
$2$ |
$10$ |
$F_{5}\times C_2$ (as 10T5) |
$2$ |
$4$ |
$[5/4]_{4}^{2}$ |
5.10.11.1 |
$10$ |
x10 + 20x2 + 5 |
$5$ |
$10$ |
$1$ |
$11$ |
$F_5$ (as 10T4) |
$1$ |
$4$ |
$[5/4]_{4}$ |
5.10.11.2 |
$10$ |
x10 + 5x2 + 5 |
$5$ |
$10$ |
$1$ |
$11$ |
$F_5$ (as 10T4) |
$1$ |
$4$ |
$[5/4]_{4}$ |
5.10.11.3 |
$10$ |
x10 + 10x2 + 5 |
$5$ |
$10$ |
$1$ |
$11$ |
$F_{5}\times C_2$ (as 10T5) |
$2$ |
$4$ |
$[5/4]_{4}^{2}$ |
5.10.11.4 |
$10$ |
x10 + 15x2 + 5 |
$5$ |
$10$ |
$1$ |
$11$ |
$F_{5}\times C_2$ (as 10T5) |
$2$ |
$4$ |
$[5/4]_{4}^{2}$ |
5.10.11.5 |
$10$ |
x10 + 15x2 + 10 |
$5$ |
$10$ |
$1$ |
$11$ |
$F_5$ (as 10T4) |
$1$ |
$4$ |
$[5/4]_{4}$ |
5.10.11.6 |
$10$ |
x10 + 10x2 + 10 |
$5$ |
$10$ |
$1$ |
$11$ |
$F_5$ (as 10T4) |
$1$ |
$4$ |
$[5/4]_{4}$ |
5.10.11.7 |
$10$ |
x10 + 5x2 + 10 |
$5$ |
$10$ |
$1$ |
$11$ |
$F_{5}\times C_2$ (as 10T5) |
$2$ |
$4$ |
$[5/4]_{4}^{2}$ |
5.10.11.8 |
$10$ |
x10 + 20x2 + 10 |
$5$ |
$10$ |
$1$ |
$11$ |
$F_{5}\times C_2$ (as 10T5) |
$2$ |
$4$ |
$[5/4]_{4}^{2}$ |
5.10.12.1 |
$10$ |
x10 + 10x5 + 75x4 + 25 |
$5$ |
$5$ |
$2$ |
$12$ |
$C_5^2 : C_8$ (as 10T18) |
$4$ |
$2$ |
$[3/2, 3/2]_{2}^{4}$ |
5.10.12.10 |
$10$ |
x10 + 10x8 + 20x7 + 15x6 - 5x5 + 5x4 + 5x2 - 5x + 7 |
$5$ |
$5$ |
$2$ |
$12$ |
$D_{10}$ (as 10T3) |
$2$ |
$2$ |
$[3/2]_{2}^{2}$ |
5.10.12.11 |
$10$ |
x10 + 5x7 + 10x5 + 25x4 + 25x2 + 25 |
$5$ |
$5$ |
$2$ |
$12$ |
$C_5^2 : C_4$ (as 10T10) |
$2$ |
$2$ |
$[3/2, 3/2]_{2}^{2}$ |
5.10.12.12 |
$10$ |
x10 + 20x7 + 10x5 + 25x4 + 100x2 + 25 |
$5$ |
$5$ |
$2$ |
$12$ |
$C_5^2 : C_4$ (as 10T10) |
$2$ |
$2$ |
$[3/2, 3/2]_{2}^{2}$ |
5.10.12.13 |
$10$ |
x10 + 15x7 + 10x5 + 100x4 + 75x2 + 25 |
$5$ |
$5$ |
$2$ |
$12$ |
$D_5^2$ (as 10T9) |
$2$ |
$2$ |
$[3/2, 3/2]_{2}^{2}$ |
5.10.12.14 |
$10$ |
x10 + 10x7 + 10x5 + 100x4 + 50x2 + 25 |
$5$ |
$5$ |
$2$ |
$12$ |
$D_5^2$ (as 10T9) |
$2$ |
$2$ |
$[3/2, 3/2]_{2}^{2}$ |
5.10.12.15 |
$10$ |
x10 + 20x3 + 5 |
$5$ |
$10$ |
$1$ |
$12$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[11/8, 11/8]_{8}^{2}$ |
5.10.12.16 |
$10$ |
x10 + 15x3 + 10 |
$5$ |
$10$ |
$1$ |
$12$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[11/8, 11/8]_{8}^{2}$ |
5.10.12.17 |
$10$ |
x10 + 10x3 + 5 |
$5$ |
$10$ |
$1$ |
$12$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[11/8, 11/8]_{8}^{2}$ |
5.10.12.18 |
$10$ |
x10 + 20x3 + 10 |
$5$ |
$10$ |
$1$ |
$12$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[11/8, 11/8]_{8}^{2}$ |
5.10.12.2 |
$10$ |
x10 + 15x7 + 10x5 + 75x4 + 75x2 + 25 |
$5$ |
$5$ |
$2$ |
$12$ |
$C_5^2 : C_8$ (as 10T18) |
$4$ |
$2$ |
$[3/2, 3/2]_{2}^{4}$ |
5.10.12.3 |
$10$ |
x10 + 5x7 + 10x5 + 50x4 + 25x2 + 25 |
$5$ |
$5$ |
$2$ |
$12$ |
$C_5^2 : C_8$ (as 10T18) |
$4$ |
$2$ |
$[3/2, 3/2]_{2}^{4}$ |
5.10.12.4 |
$10$ |
x10 + 10x5 + 50x4 + 25 |
$5$ |
$5$ |
$2$ |
$12$ |
$C_5^2 : C_8$ (as 10T18) |
$4$ |
$2$ |
$[3/2, 3/2]_{2}^{4}$ |
5.10.12.5 |
$10$ |
x10 + 20x7 + 10x5 + 50x4 + 100x2 + 25 |
$5$ |
$5$ |
$2$ |
$12$ |
$C_5^2 : C_8$ (as 10T18) |
$4$ |
$2$ |
$[3/2, 3/2]_{2}^{4}$ |
5.10.12.6 |
$10$ |
x10 + 10x7 + 10x5 + 75x4 + 50x2 + 25 |
$5$ |
$5$ |
$2$ |
$12$ |
$C_5^2 : C_8$ (as 10T18) |
$4$ |
$2$ |
$[3/2, 3/2]_{2}^{4}$ |
5.10.12.7 |
$10$ |
x10 + 10x8 + 5x7 + 15x6 + 5x4 + 5x2 - 20x + 7 |
$5$ |
$5$ |
$2$ |
$12$ |
$D_{10}$ (as 10T3) |
$2$ |
$2$ |
$[3/2]_{2}^{2}$ |
5.10.12.8 |
$10$ |
x10 + 10x8 + 15x7 + 15x6 - 20x5 + 5x4 + 5x2 - 10x + 7 |
$5$ |
$5$ |
$2$ |
$12$ |
$F_5$ (as 10T4) |
$2$ |
$2$ |
$[3/2]_{2}^{2}$ |
5.10.12.9 |
$10$ |
x10 + 10x8 + 10x7 + 15x6 - 10x5 + 5x4 + 5x2 - 15x + 7 |
$5$ |
$5$ |
$2$ |
$12$ |
$F_5$ (as 10T4) |
$2$ |
$2$ |
$[3/2]_{2}^{2}$ |
5.10.13.1 |
$10$ |
x10 + 15x4 + 5 |
$5$ |
$10$ |
$1$ |
$13$ |
$D_5$ (as 10T2) |
$1$ |
$2$ |
$[3/2]_{2}$ |
5.10.13.10 |
$10$ |
x10 + 10x4 + 10 |
$5$ |
$10$ |
$1$ |
$13$ |
$F_{5}\times C_2$ (as 10T5) |
$4$ |
$2$ |
$[3/2]_{2}^{4}$ |
5.10.13.11 |
$10$ |
x10 - 15x5 + 5x4 + 10 |
$5$ |
$10$ |
$1$ |
$13$ |
$D_5\times C_5$ (as 10T6) |
$5$ |
$2$ |
$[3/2]_{2}^{5}$ |