Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Ind. of Insep. |
Assoc. Inertia |
17.12.0.1 |
$12$ |
x12 + x8 + 4x7 + 14x6 + 14x5 + 13x4 + 6x3 + 14x2 + 9x + 3 |
$17$ |
$1$ |
$12$ |
$0$ |
$C_{12}$ (as 12T1) |
$12$ |
$1$ |
$[\ ]$ |
$[\ ]^{12}$ |
$[0]$ |
$[]$ |
17.12.6.1 |
$12$ |
x12 + 918x11 + 351241x10 + 71712630x9 + 8244584136x8 + 506874732756x7 + 13125344775560x6 + 9625198256031x5 + 28457943732288x4 + 16844354225613x3 + 132306217741765x2 + 68598705820311x + 44162739951115 |
$17$ |
$2$ |
$6$ |
$6$ |
$C_6\times C_2$ (as 12T2) |
$6$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{6}$ |
$[0]$ |
$[1]$ |
17.12.6.2 |
$12$ |
x12 + 578x8 + 835210x4 - 4259571x2 + 72412707 |
$17$ |
$2$ |
$6$ |
$6$ |
$C_{12}$ (as 12T1) |
$6$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{6}$ |
$[0]$ |
$[1]$ |
17.12.8.1 |
$12$ |
x12 + 225x10 + 98x9 + 17904x8 + 10824x7 + 611647x6 + 498390x5 + 8494833x4 + 11764900x3 + 38205036x2 + 73669974x + 36476587 |
$17$ |
$3$ |
$4$ |
$8$ |
$C_3 : C_4$ (as 12T5) |
$4$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{4}$ |
$[0]$ |
$[1]$ |
17.12.8.2 |
$12$ |
x12 + 2023x6 - 49130x3 + 250563 |
$17$ |
$3$ |
$4$ |
$8$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$12$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{12}$ |
$[0]$ |
$[1]$ |
17.12.9.1 |
$12$ |
x12 + 4x10 + 56x9 + 57x8 + 168x7 + 1044x6 - 11256x5 + 3356x4 + 10080x3 + 97736x2 + 58576x + 57252 |
$17$ |
$4$ |
$3$ |
$9$ |
$C_{12}$ (as 12T1) |
$3$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{3}$ |
$[0]$ |
$[1]$ |
17.12.9.2 |
$12$ |
x12 - 34x8 + 289x4 + 962948 |
$17$ |
$4$ |
$3$ |
$9$ |
$C_{12}$ (as 12T1) |
$3$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{3}$ |
$[0]$ |
$[1]$ |
17.12.9.3 |
$12$ |
x12 + 289x4 - 68782 |
$17$ |
$4$ |
$3$ |
$9$ |
$C_{12}$ (as 12T1) |
$3$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{3}$ |
$[0]$ |
$[1]$ |
17.12.9.4 |
$12$ |
x12 + 153x8 + 81787x4 - 277825237 |
$17$ |
$4$ |
$3$ |
$9$ |
$C_{12}$ (as 12T1) |
$3$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{3}$ |
$[0]$ |
$[1]$ |
17.12.10.1 |
$12$ |
x12 + 96x11 + 3858x10 + 83360x9 + 1029255x8 + 7037376x7 + 22883390x6 + 21113760x5 + 9327045x4 + 3594400x3 + 16245408x2 + 100784640x + 265511268 |
$17$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$[0]$ |
$[1]$ |
17.12.10.2 |
$12$ |
x12 - 3060x6 - 197676 |
$17$ |
$6$ |
$2$ |
$10$ |
$C_6\times S_3$ (as 12T18) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$[0]$ |
$[1]$ |
17.12.10.3 |
$12$ |
x12 - 3604x6 - 719321 |
$17$ |
$6$ |
$2$ |
$10$ |
$C_3 : C_4$ (as 12T5) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$[0]$ |
$[1]$ |
17.12.10.4 |
$12$ |
x12 + 238x6 - 3468 |
$17$ |
$6$ |
$2$ |
$10$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$[0]$ |
$[1]$ |
17.12.11.1 |
$12$ |
x12 + 17 |
$17$ |
$12$ |
$1$ |
$11$ |
$S_3 \times C_4$ (as 12T11) |
$2$ |
$12$ |
$[\ ]$ |
$[\ ]_{12}^{2}$ |
$[0]$ |
$[2]$ |
17.12.11.2 |
$12$ |
x12 + 34 |
$17$ |
$12$ |
$1$ |
$11$ |
$S_3 \times C_4$ (as 12T11) |
$2$ |
$12$ |
$[\ ]$ |
$[\ ]_{12}^{2}$ |
$[0]$ |
$[2]$ |
17.12.11.3 |
$12$ |
x12 + 51 |
$17$ |
$12$ |
$1$ |
$11$ |
$S_3 \times C_4$ (as 12T11) |
$2$ |
$12$ |
$[\ ]$ |
$[\ ]_{12}^{2}$ |
$[0]$ |
$[2]$ |
17.12.11.4 |
$12$ |
x12 + 102 |
$17$ |
$12$ |
$1$ |
$11$ |
$S_3 \times C_4$ (as 12T11) |
$2$ |
$12$ |
$[\ ]$ |
$[\ ]_{12}^{2}$ |
$[0]$ |
$[2]$ |