Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Slope content |
5.15.0.1 |
$15$ |
x15 + x2 + 2 |
$5$ |
$1$ |
$15$ |
$0$ |
$C_{15}$ (as 15T1) |
$15$ |
$1$ |
$[\ ]^{15}$ |
5.15.10.1 |
$15$ |
x15 - 625x3 + 6250 |
$5$ |
$3$ |
$5$ |
$10$ |
$S_3 \times C_5$ (as 15T4) |
$10$ |
$3$ |
$[\ ]_{3}^{10}$ |
5.15.15.1 |
$15$ |
x15 + 15x14 + 15x13 + 10x12 + 10x11 + 2x10 + 20x9 + 15x8 + 15x7 + 7x5 + 15x4 + 15x3 + 5x + 17 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.10 |
$15$ |
x15 + 5x14 + 15x13 + 5x12 + 20x11 + 12x10 + 20x9 + 10x7 + 5x6 + 22x5 + 5x4 + 10x3 + 5x + 22 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.11 |
$15$ |
x15 + 10x14 + 20x13 + 15x12 + 10x11 + 22x10 + 10x9 + 20x8 + 5x7 + 5x6 + 17x5 + 5x4 + 20x3 + 10x2 + 7 |
$5$ |
$5$ |
$3$ |
$15$ |
$(C_5^2 : C_4):C_3$ (as 15T19) |
$3$ |
$4$ |
$[5/4, 5/4]_{4}^{3}$ |
5.15.15.12 |
$15$ |
x15 + 10x14 + 20x13 + 5x12 + 15x11 + 7x10 + 20x9 + 10x8 + 20x7 + 5x6 + 7x5 + 5x4 + 20x3 + 10x2 + 5x + 22 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.13 |
$15$ |
x15 + 20x12 + 7x10 + 5x9 + 15x8 + 20x7 + 20x6 + 7x5 + 10x4 + 20x3 + 20x2 + 20x + 22 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.14 |
$15$ |
x15 + 5x14 + 15x13 + 20x12 + 20x11 + 2x10 + 15x9 + 5x7 + 20x6 + 12x5 + 20x2 + 7 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.15 |
$15$ |
x15 + 10x14 + 20x12 + 20x11 + 7x10 + 5x9 + 15x8 + 10x7 + 10x6 + 7x5 + 10x4 + 20x3 + 15x2 + 5x + 17 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.16 |
$15$ |
x15 + 15x14 + 15x13 + 10x12 + 10x11 + 7x10 + 15x8 + 20x7 + 15x6 + 17x5 + 20x4 + 20x3 + 5x2 + 5x + 7 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.17 |
$15$ |
x15 + 5x14 + 20x13 + 15x11 + 2x10 + 5x9 + 5x6 + 2x5 + 15x2 + 5x + 17 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.18 |
$15$ |
x15 + 20x13 + 10x12 + 15x11 + 17x10 + 10x9 + 15x8 + 20x7 + 20x6 + 7x5 + 20x4 + 20x3 + 10x2 + 10x + 2 |
$5$ |
$5$ |
$3$ |
$15$ |
$F_5\times C_3$ (as 15T8) |
$3$ |
$4$ |
$[5/4]_{4}^{3}$ |
5.15.15.19 |
$15$ |
x15 + 5x14 + 20x12 + 12x10 + 5x9 + 10x8 + 15x7 + 12x5 + 20x + 22 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.2 |
$15$ |
x15 + 5x14 + 20x13 + 5x11 + 17x10 + 15x9 + 5x8 + 20x7 + 10x6 + 12x5 + 15x4 + 20x3 + 15x2 + 22 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.20 |
$15$ |
x15 + 20x13 + 20x12 + 17x10 + 20x9 + 20x8 + 10x7 + 5x6 + 7x5 + 5x4 + 15x3 + 20x2 + 20x + 12 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.21 |
$15$ |
x15 + 10x14 + 5x13 + 20x12 + 22x10 + 15x6 + 17x5 + 5x3 + 15x2 + 2 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.22 |
$15$ |
x15 + 15x13 + 5x12 + 15x11 + 12x10 + 20x9 + 15x8 + 15x6 + 22x5 + 20x4 + 10x3 + 2 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.23 |
$15$ |
x15 + 20x14 + 5x13 + 5x12 + 22x10 + 15x9 + 5x8 + 15x7 + 10x6 + 7x5 + 15x2 + 15x + 7 |
$5$ |
$5$ |
$3$ |
$15$ |
$(C_5^2 : C_4):C_3$ (as 15T19) |
$3$ |
$4$ |
$[5/4, 5/4]_{4}^{3}$ |
5.15.15.24 |
$15$ |
x15 + 10x14 + 20x12 + 15x11 + 7x10 + 10x9 + 20x8 + 5x7 + 5x6 + 2x5 + 10x4 + 5x2 + 10x + 22 |
$5$ |
$5$ |
$3$ |
$15$ |
$(C_5^2 : C_4):C_3$ (as 15T19) |
$3$ |
$4$ |
$[5/4, 5/4]_{4}^{3}$ |
5.15.15.25 |
$15$ |
x15 + 5x14 + 5x13 + 20x12 + 20x11 + 22x10 + 20x8 + 5x7 + 12x5 + 15x4 + 5x2 + 20x + 12 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.26 |
$15$ |
x15 + 10x14 + 10x12 + 15x11 + 22x10 + 5x9 + 20x8 + 5x7 + 22x5 + 5x4 + 15x3 + 5x + 17 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.27 |
$15$ |
x15 + 15x14 + 5x13 + 5x12 + 7x10 + 5x8 + 5x6 + 17x5 + 10x4 + 20x3 + 20x2 + 5x + 2 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.28 |
$15$ |
x15 + 15x14 + 15x13 + 10x11 + 7x10 + 5x8 + 15x7 + 15x6 + 7x5 + 15x4 + 15x2 + 2 |
$5$ |
$5$ |
$3$ |
$15$ |
$(C_5^2 : C_4):C_3$ (as 15T19) |
$3$ |
$4$ |
$[5/4, 5/4]_{4}^{3}$ |
5.15.15.29 |
$15$ |
x15 + 20x14 + 15x13 + 12x10 + 15x9 + 10x8 + 5x7 + 20x6 + 2x5 + 15x2 + 10x + 22 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.3 |
$15$ |
x15 + 10x14 + 20x13 + 2x10 + 20x9 + 20x8 + 15x7 + 2x5 + 10x4 + 15x3 + 10x + 7 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.30 |
$15$ |
x15 + 10x14 + 15x13 + 5x12 + 10x11 + 22x10 + 5x9 + 10x8 + 10x7 + 5x6 + 12x5 + 15x4 + 10x3 + 5x2 + 15x + 7 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.31 |
$15$ |
x15 + 10x14 + 5x13 + 15x12 + 15x11 + 2x10 + 15x9 + 10x7 + 20x6 + 17x5 + 15x4 + 5x3 + 12 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.32 |
$15$ |
x15 + 15x14 + 5x13 + 20x12 + 5x11 + 12x10 + 20x9 + 15x8 + 15x6 + 2x5 + 10x4 + 10x3 + 10x + 12 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.33 |
$15$ |
x15 + 15x14 + 15x13 + 5x12 + 17x10 + 5x9 + 10x7 + 22x5 + 5x4 + 10x3 + 5x + 7 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.34 |
$15$ |
x15 + 15x12 + 15x11 + 12x10 + 20x8 + 22x5 + 10x4 + 20x3 + 15x + 17 |
$5$ |
$5$ |
$3$ |
$15$ |
$(C_5^2 : C_4):C_3$ (as 15T19) |
$3$ |
$4$ |
$[5/4, 5/4]_{4}^{3}$ |
5.15.15.35 |
$15$ |
x15 + 5x14 + 15x12 + 15x11 + 2x10 + 5x9 + 20x8 + 2x5 + 5x4 + 5x3 + 20x2 + 20x + 22 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.36 |
$15$ |
x15 + 15x14 + 5x13 + 20x12 + 15x11 + 12x10 + 20x9 + 15x8 + 5x7 + 20x6 + 12x5 + 15x4 + 15x2 + 20x + 2 |
$5$ |
$5$ |
$3$ |
$15$ |
$(C_5^2 : C_4):C_3$ (as 15T19) |
$3$ |
$4$ |
$[5/4, 5/4]_{4}^{3}$ |
5.15.15.37 |
$15$ |
x15 + 5x14 + 10x13 + 15x12 + 20x11 + 12x10 + 15x9 + 15x8 + 5x7 + 17x5 + 15x4 + 15x3 + 15x + 2 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.38 |
$15$ |
x15 + 10x14 + 5x13 + 10x12 + 15x11 + 17x10 + 20x9 + 15x8 + 10x7 + 17x5 + 20x4 + 5x3 + 20x + 17 |
$5$ |
$5$ |
$3$ |
$15$ |
$F_5\times C_3$ (as 15T8) |
$3$ |
$4$ |
$[5/4]_{4}^{3}$ |
5.15.15.39 |
$15$ |
x15 + 10x14 + 15x12 + 20x11 + 2x10 + 5x9 + 10x8 + 15x7 + 15x6 + 12x5 + 20x4 + 10x3 + 10x2 + 20x + 12 |
$5$ |
$5$ |
$3$ |
$15$ |
$(C_5^2 : C_4):C_3$ (as 15T19) |
$3$ |
$4$ |
$[5/4, 5/4]_{4}^{3}$ |
5.15.15.4 |
$15$ |
x15 + 5x14 + 5x13 + 10x12 + 10x11 + 22x10 + 10x9 + 20x7 + 12x5 + 20x4 + 5x3 + 10x2 + 10x + 12 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.40 |
$15$ |
x15 + 10x14 + 5x13 + 20x12 + 20x11 + 17x10 + 10x9 + 15x8 + 12x5 + 15x3 + 10x2 + 20x + 17 |
$5$ |
$5$ |
$3$ |
$15$ |
$F_5\times C_3$ (as 15T8) |
$3$ |
$4$ |
$[5/4]_{4}^{3}$ |
5.15.15.41 |
$15$ |
x15 + 10x14 + 10x13 + 15x12 + 10x11 + 7x10 + 20x9 + 5x8 + 15x7 + 10x6 + 12x5 + 10x4 + 15x3 + 10x2 + 5x + 17 |
$5$ |
$5$ |
$3$ |
$15$ |
$(C_5^2 : C_4):C_3$ (as 15T19) |
$3$ |
$4$ |
$[5/4, 5/4]_{4}^{3}$ |
5.15.15.42 |
$15$ |
x15 + 15x14 + 15x13 + 20x12 + 5x11 + 2x10 + 20x8 + 10x7 + 10x6 + 2x5 + 15x3 + 15x2 + 15x + 17 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.43 |
$15$ |
x15 + 20x14 + 15x13 + 15x12 + 5x11 + 12x10 + 10x9 + 20x8 + 5x7 + 20x6 + 22x5 + 20x4 + 15x2 + 5x + 17 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.44 |
$15$ |
x15 + 10x14 + 15x13 + 5x12 + 20x11 + 17x10 + 10x9 + 5x7 + 5x6 + 2x5 + 10x4 + 10x2 + 20x + 2 |
$5$ |
$5$ |
$3$ |
$15$ |
$F_5\times C_3$ (as 15T8) |
$3$ |
$4$ |
$[5/4]_{4}^{3}$ |
5.15.15.45 |
$15$ |
x15 - 5x14 - 5x13 + 5x12 - 10x11 + 5x10 - 5x9 - 5x8 + 5x7 + 5x6 - 5x5 - 10x4 + 10x3 + 10x2 - 10x + 5 |
$5$ |
$15$ |
$1$ |
$15$ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
$2$ |
$12$ |
$[13/12, 13/12]_{12}^{2}$ |
5.15.15.46 |
$15$ |
x15 + 5x14 - 10x12 + 10x11 + 10x10 - 10x9 - 10x8 - 10x7 - 10x5 + 5x4 - 10x3 - 5x2 - 10x - 10 |
$5$ |
$15$ |
$1$ |
$15$ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
$2$ |
$12$ |
$[13/12, 13/12]_{12}^{2}$ |
5.15.15.47 |
$15$ |
x15 - 10x14 - 10x13 - 5x12 - 10x11 - 5x10 + 10x8 + 5x6 + 10x5 + 10x4 - 5x3 + 10x2 + 5x - 5 |
$5$ |
$15$ |
$1$ |
$15$ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
$2$ |
$12$ |
$[13/12, 13/12]_{12}^{2}$ |
5.15.15.48 |
$15$ |
x15 + 5x14 - 10x13 - 10x12 + 5x11 - 5x10 - 10x9 + 10x8 + 5x7 + 5x6 - 5x5 + 5x4 + 5x3 + 10x2 - 5x + 5 |
$5$ |
$15$ |
$1$ |
$15$ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
$2$ |
$12$ |
$[13/12, 13/12]_{12}^{2}$ |
5.15.15.5 |
$15$ |
x15 + 5x14 + 15x12 + 10x11 + 2x10 + 10x9 + 20x8 + 20x7 + 5x6 + 22x5 + 10x4 + 10x2 + 2 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.6 |
$15$ |
x15 + 20x14 + 5x13 + 10x12 + 15x11 + 2x10 + 10x9 + 5x8 + 10x7 + 15x6 + 17x5 + 5x4 + 10x3 + 15x2 + 15x + 17 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.7 |
$15$ |
x15 + 20x14 + 5x13 + 15x12 + 7x10 + 10x9 + 20x8 + 20x7 + 5x6 + 7x5 + 10x4 + 5x3 + 20x + 22 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.8 |
$15$ |
x15 + 15x14 + 5x13 + 20x11 + 7x10 + 20x9 + 5x8 + 5x6 + 17x5 + 15x4 + 10x3 + 15x2 + 5x + 17 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
5.15.15.9 |
$15$ |
x15 + 20x14 + 5x13 + 15x12 + 20x11 + 17x10 + 15x9 + 10x6 + 7x5 + 15x4 + 5x3 + 5x + 12 |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |