Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Ind. of Insep. |
Assoc. Inertia |
7.14.0.1 |
$14$ |
x14 + 5x7 + 6x5 + 2x4 + 3x2 + 6x + 3 |
$7$ |
$1$ |
$14$ |
$0$ |
$C_{14}$ (as 14T1) |
$14$ |
$1$ |
$[\ ]$ |
$[\ ]^{14}$ |
$[0]$ |
$[]$ |
7.14.7.1 |
$14$ |
x14 + 49x12 + 1029x10 + 12017x8 + 8x7 + 82859x6 - 1176x5 + 352947x4 + 13720x3 + 881203x2 - 19160x + 794999 |
$7$ |
$2$ |
$7$ |
$7$ |
$C_{14}$ (as 14T1) |
$7$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{7}$ |
$[0]$ |
$[1]$ |
7.14.7.2 |
$14$ |
x14 - 756x13 + 407484x12 - 120759324x11 + 18245133144x10 - 1371646043208x9 + 45234910589400x8 - 365498518846944x7 - 160150981540032x6 - 9636001680480x5 - 1806831694584x4 - 187090145760x3 - 8419197738x2 - 138355224x - 3294172 |
$7$ |
$2$ |
$7$ |
$7$ |
$C_{14}$ (as 14T1) |
$7$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{7}$ |
$[0]$ |
$[1]$ |
7.14.14.1 |
$14$ |
x14 + 14x9 - 28x8 + 14x7 - 245x4 - 1372x3 - 882x2 - 196x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$C_7^2:(C_2\times C_6)$ (as 14T24) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6, 7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.10 |
$14$ |
x14 - 14x9 - 70x8 + 14x7 - 245x4 - 1274x3 - 1519x2 - 490x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$C_7^2:C_{12}$ (as 14T23) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6, 7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.11 |
$14$ |
x14 - 238x9 - 14x8 + 14x7 + 3577x4 - 1862x3 - 1911x2 - 98x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$C_7^2:(C_2\times C_6)$ (as 14T24) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6, 7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.12 |
$14$ |
x14 - 84x8 + 14x7 + 588x2 - 588x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$C_7^2:C_{12}$ (as 14T23) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6, 7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.13 |
$14$ |
x14 + 28x9 - 154x8 + 14x7 + 196x4 - 2156x3 - 1225x2 - 1078x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$C_7^2:C_{12}$ (as 14T23) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6, 7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.14 |
$14$ |
x14 - 14x9 - 140x8 + 14x7 - 245x4 - 1372x3 + 98x2 - 980x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$C_7^2:(C_2\times C_6)$ (as 14T24) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6, 7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.15 |
$14$ |
x14 - 168x9 + 14x7 - 3528x4 - 7056x3 - 2352x2 + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$C_7^2:(C_2\times C_6)$ (as 14T24) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6, 7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.16 |
$14$ |
x14 - 42x9 - 126x8 + 14x7 - 735x4 - 882x3 + 1029x2 - 882x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$C_7^2:C_{12}$ (as 14T23) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6, 7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.17 |
$14$ |
x14 - 84x9 - 28x8 + 14x7 + 588x4 - 686x2 - 196x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$C_7^2:C_{12}$ (as 14T23) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6, 7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.18 |
$14$ |
x14 + 28x8 + 14x7 - 98x2 + 196x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$C_7^2:C_{12}$ (as 14T23) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6, 7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.19 |
$14$ |
x14 - 42x9 + 42x8 + 14x7 - 735x4 - 882x3 + 147x2 + 294x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$F_7 \times C_2$ (as 14T7) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.2 |
$14$ |
x14 - 84x9 - 140x8 + 14x7 + 588x4 - 3038x2 - 980x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$C_7^2:C_{12}$ (as 14T23) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6, 7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.20 |
$14$ |
x14 - 210x9 - 168x8 + 14x7 + 3675x4 + 2940x3 - 1764x2 - 1176x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$C_7^2:(C_2\times C_6)$ (as 14T24) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6, 7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.21 |
$14$ |
x14 - 14x9 + 14x8 + 14x7 - 1127x4 - 98x3 - 49x2 + 98x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$F_7 \times C_2$ (as 14T7) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.22 |
$14$ |
x14 + 14x9 - 182x8 + 14x7 + 49x4 - 1274x3 - 2205x2 - 1274x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$C_7^2:(C_2\times C_6)$ (as 14T24) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6, 7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.23 |
$14$ |
x14 - 28x9 - 42x8 + 14x7 - 98x4 - 49x2 - 294x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$C_7^2:C_{12}$ (as 14T23) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6, 7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.24 |
$14$ |
x14 - 14x9 + 84x8 + 14x7 - 245x4 - 588x3 + 1666x2 + 588x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$F_7 \times C_2$ (as 14T7) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.25 |
$14$ |
x14 - 56x9 + 70x8 + 14x7 - 1862x4 - 1960x3 + 833x2 + 490x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$F_7 \times C_2$ (as 14T7) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.26 |
$14$ |
x14 - 154x9 - 112x8 + 14x7 - 1421x4 - 196x3 - 588x2 - 784x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$C_7^2:C_{12}$ (as 14T23) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6, 7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.27 |
$14$ |
x14 - 70x9 - 98x8 + 14x7 + 49x4 - 1274x3 - 2793x2 - 686x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$C_7^2:(C_2\times C_6)$ (as 14T24) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6, 7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.28 |
$14$ |
x14 + 28x2 + 14x + 21 |
$7$ |
$14$ |
$1$ |
$14$ |
$C_7^2:(C_3\times D_4)$ (as 14T32) |
$2$ |
$12$ |
$[13/12]$ |
$[13/12, 13/12]_{12}^{2}$ |
$[1, 0]$ |
$[1, 1]$ |
7.14.14.29 |
$14$ |
x14 + 35x2 + 7x + 21 |
$7$ |
$14$ |
$1$ |
$14$ |
$C_7^2:(C_3\times D_4)$ (as 14T32) |
$2$ |
$12$ |
$[13/12]$ |
$[13/12, 13/12]_{12}^{2}$ |
$[1, 0]$ |
$[1, 1]$ |
7.14.14.3 |
$14$ |
x14 + 42x9 + 42x8 + 14x7 + 441x4 + 882x3 + 441x2 + 294x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$C_7^2:C_{12}$ (as 14T23) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6, 7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.30 |
$14$ |
x14 + 42x2 + 21x + 7 |
$7$ |
$14$ |
$1$ |
$14$ |
$C_7^2:(C_3\times D_4)$ (as 14T32) |
$2$ |
$12$ |
$[13/12]$ |
$[13/12, 13/12]_{12}^{2}$ |
$[1, 0]$ |
$[1, 1]$ |
7.14.14.31 |
$14$ |
x14 + 35x2 + 14x + 7 |
$7$ |
$14$ |
$1$ |
$14$ |
$C_7^2:(C_3\times D_4)$ (as 14T32) |
$2$ |
$12$ |
$[13/12]$ |
$[13/12, 13/12]_{12}^{2}$ |
$[1, 0]$ |
$[1, 1]$ |
7.14.14.32 |
$14$ |
x14 + 7x2 + 21x + 21 |
$7$ |
$14$ |
$1$ |
$14$ |
$C_7^2:(C_3\times D_4)$ (as 14T32) |
$2$ |
$12$ |
$[13/12]$ |
$[13/12, 13/12]_{12}^{2}$ |
$[1, 0]$ |
$[1, 1]$ |
7.14.14.33 |
$14$ |
x14 + 21x2 + 7x + 7 |
$7$ |
$14$ |
$1$ |
$14$ |
$C_7^2:(C_3\times D_4)$ (as 14T32) |
$2$ |
$12$ |
$[13/12]$ |
$[13/12, 13/12]_{12}^{2}$ |
$[1, 0]$ |
$[1, 1]$ |
7.14.14.4 |
$14$ |
x14 - 14x9 + 28x8 + 14x7 - 1127x4 - 196x3 + 98x2 + 196x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$F_7 \times C_2$ (as 14T7) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.5 |
$14$ |
x14 - 56x9 + 56x8 + 14x7 - 392x4 - 1568x3 + 392x2 + 392x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$F_7 \times C_2$ (as 14T7) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.6 |
$14$ |
x14 - 196x9 - 210x8 + 14x7 + 2254x4 + 5880x3 + 2303x2 - 1470x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$C_7^2:C_{12}$ (as 14T23) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6, 7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.7 |
$14$ |
x14 - 238x9 - 196x8 + 14x7 + 3577x4 + 2156x3 - 2646x2 - 1372x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$C_7^2:(C_2\times C_6)$ (as 14T24) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6, 7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.8 |
$14$ |
x14 - 14x9 - 84x8 + 14x7 - 1127x4 - 4116x3 - 3038x2 - 588x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$C_7^2:C_{12}$ (as 14T23) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6, 7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.14.9 |
$14$ |
x14 + 14x9 - 56x8 + 14x7 + 49x4 - 392x3 - 1764x2 - 392x + 49 |
$7$ |
$7$ |
$2$ |
$14$ |
$C_7^2:(C_2\times C_6)$ (as 14T24) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6, 7/6]_{6}^{2}$ |
$[1, 0]$ |
$[1]$ |
7.14.15.1 |
$14$ |
x14 + 14x3 + 7x2 + 21 |
$7$ |
$14$ |
$1$ |
$15$ |
$F_7 \times C_2$ (as 14T7) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6]_{6}^{2}$ |
$[2, 0]$ |
$[2, 1]$ |
7.14.15.10 |
$14$ |
x14 + 21x3 + 35x2 + 21 |
$7$ |
$14$ |
$1$ |
$15$ |
$F_7$ (as 14T4) |
$1$ |
$6$ |
$[7/6]$ |
$[7/6]_{6}$ |
$[2, 0]$ |
$[1, 1]$ |
7.14.15.11 |
$14$ |
x14 + 7x3 + 42x2 + 7 |
$7$ |
$14$ |
$1$ |
$15$ |
$F_7 \times C_2$ (as 14T7) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6]_{6}^{2}$ |
$[2, 0]$ |
$[2, 1]$ |
7.14.15.12 |
$14$ |
x14 + 28x2 + 21 |
$7$ |
$14$ |
$1$ |
$15$ |
$F_7 \times C_2$ (as 14T7) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6]_{6}^{2}$ |
$[2, 0]$ |
$[2, 1]$ |
7.14.15.2 |
$14$ |
x14 + 7x3 + 35x2 + 7 |
$7$ |
$14$ |
$1$ |
$15$ |
$F_7 \times C_2$ (as 14T7) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6]_{6}^{2}$ |
$[2, 0]$ |
$[2, 1]$ |
7.14.15.3 |
$14$ |
x14 + 14x3 + 21x2 + 7 |
$7$ |
$14$ |
$1$ |
$15$ |
$F_7 \times C_2$ (as 14T7) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6]_{6}^{2}$ |
$[2, 0]$ |
$[2, 1]$ |
7.14.15.4 |
$14$ |
x14 + 14x3 + 14x2 + 21 |
$7$ |
$14$ |
$1$ |
$15$ |
$F_7 \times C_2$ (as 14T7) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6]_{6}^{2}$ |
$[2, 0]$ |
$[2, 1]$ |
7.14.15.5 |
$14$ |
x14 + 7x3 + 7x2 + 7 |
$7$ |
$14$ |
$1$ |
$15$ |
$F_7$ (as 14T4) |
$1$ |
$6$ |
$[7/6]$ |
$[7/6]_{6}$ |
$[2, 0]$ |
$[1, 1]$ |
7.14.15.6 |
$14$ |
x14 + 7x3 + 21x2 + 21 |
$7$ |
$14$ |
$1$ |
$15$ |
$F_7$ (as 14T4) |
$1$ |
$6$ |
$[7/6]$ |
$[7/6]_{6}$ |
$[2, 0]$ |
$[1, 1]$ |
7.14.15.7 |
$14$ |
x14 + 21x3 + 28x2 + 7 |
$7$ |
$14$ |
$1$ |
$15$ |
$F_7$ (as 14T4) |
$1$ |
$6$ |
$[7/6]$ |
$[7/6]_{6}$ |
$[2, 0]$ |
$[1, 1]$ |
7.14.15.8 |
$14$ |
x14 + 14x3 + 42x2 + 21 |
$7$ |
$14$ |
$1$ |
$15$ |
$F_7$ (as 14T4) |
$1$ |
$6$ |
$[7/6]$ |
$[7/6]_{6}$ |
$[2, 0]$ |
$[1, 1]$ |
7.14.15.9 |
$14$ |
x14 + 21x3 + 14x2 + 7 |
$7$ |
$14$ |
$1$ |
$15$ |
$F_7$ (as 14T4) |
$1$ |
$6$ |
$[7/6]$ |
$[7/6]_{6}$ |
$[2, 0]$ |
$[1, 1]$ |
7.14.16.1 |
$14$ |
x14 - 182x10 - 210x9 + 14x7 - 2303x6 - 2058x5 + 441x4 - 1274x3 - 1470x2 + 49 |
$7$ |
$7$ |
$2$ |
$16$ |
$C_7^2:C_6$ (as 14T14) |
$2$ |
$3$ |
$[4/3]$ |
$[4/3, 4/3]_{3}^{2}$ |
$[2, 0]$ |
$[1]$ |
7.14.16.10 |
$14$ |
x14 - 238x10 - 28x9 + 14x7 + 3577x6 - 196x5 - 98x4 - 1666x3 - 196x2 + 49 |
$7$ |
$7$ |
$2$ |
$16$ |
$C_7^2:C_{12}$ (as 14T23) |
$4$ |
$3$ |
$[4/3]$ |
$[4/3, 4/3]_{3}^{4}$ |
$[2, 0]$ |
$[2]$ |