Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
2.19.0.1 |
$19$ |
$x^{19} + x^{5} + x^{2} + x + 1$ |
$2$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + t^{5} + t^{2} + t + 1$ |
$x - 2$ |
$[0]$ |
$[]$ |
3.19.0.1 |
$19$ |
$x^{19} + 2 x^{2} + 1$ |
$3$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 2 t^{2} + 1$ |
$x - 3$ |
$[0]$ |
$[]$ |
5.19.0.1 |
$19$ |
$x^{19} + x^{3} + 2 x + 3$ |
$5$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + t^{3} + 2 t + 3$ |
$x - 5$ |
$[0]$ |
$[]$ |
7.19.0.1 |
$19$ |
$x^{19} + 5 x^{2} + 4$ |
$7$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 5 t^{2} + 4$ |
$x - 7$ |
$[0]$ |
$[]$ |
11.19.0.1 |
$19$ |
$x^{19} + 8 x^{2} + 2 x + 9$ |
$11$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 8 t^{2} + 2 t + 9$ |
$x - 11$ |
$[0]$ |
$[]$ |
13.19.0.1 |
$19$ |
$x^{19} + 9 x + 11$ |
$13$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 9 t + 11$ |
$x - 13$ |
$[0]$ |
$[]$ |
17.19.0.1 |
$19$ |
$x^{19} + 11 x + 14$ |
$17$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 11 t + 14$ |
$x - 17$ |
$[0]$ |
$[]$ |
19.19.0.1 |
$19$ |
$x^{19} + 18 x + 17$ |
$19$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 18 t + 17$ |
$x - 19$ |
$[0]$ |
$[]$ |
19.19.36.1 |
$19$ |
$x^{19} + 342 x^{18} + 19$ |
$19$ |
$19$ |
$1$ |
$36$ |
$C_{19}$ (as 19T1) |
$1$ |
$1$ |
$[2]$ |
$[2]$ |
$t + 17$ |
$x^{19} + 342 x^{18} + 19$ |
$[18, 0]$ |
$[1]$ |
19.19.36.10 |
$19$ |
$x^{19} + 342 x^{18} + 3268$ |
$19$ |
$19$ |
$1$ |
$36$ |
$C_{19}$ (as 19T1) |
$1$ |
$1$ |
$[2]$ |
$[2]$ |
$t + 17$ |
$x^{19} + 342 x^{18} + 3268$ |
$[18, 0]$ |
$[1]$ |
19.19.36.11 |
$19$ |
$x^{19} + 342 x^{18} + 3629$ |
$19$ |
$19$ |
$1$ |
$36$ |
$C_{19}$ (as 19T1) |
$1$ |
$1$ |
$[2]$ |
$[2]$ |
$t + 17$ |
$x^{19} + 342 x^{18} + 3629$ |
$[18, 0]$ |
$[1]$ |
19.19.36.12 |
$19$ |
$x^{19} + 342 x^{18} + 3990$ |
$19$ |
$19$ |
$1$ |
$36$ |
$C_{19}$ (as 19T1) |
$1$ |
$1$ |
$[2]$ |
$[2]$ |
$t + 17$ |
$x^{19} + 342 x^{18} + 3990$ |
$[18, 0]$ |
$[1]$ |
19.19.36.13 |
$19$ |
$x^{19} + 342 x^{18} + 4351$ |
$19$ |
$19$ |
$1$ |
$36$ |
$C_{19}$ (as 19T1) |
$1$ |
$1$ |
$[2]$ |
$[2]$ |
$t + 17$ |
$x^{19} + 342 x^{18} + 4351$ |
$[18, 0]$ |
$[1]$ |
19.19.36.14 |
$19$ |
$x^{19} + 342 x^{18} + 4712$ |
$19$ |
$19$ |
$1$ |
$36$ |
$C_{19}$ (as 19T1) |
$1$ |
$1$ |
$[2]$ |
$[2]$ |
$t + 17$ |
$x^{19} + 342 x^{18} + 4712$ |
$[18, 0]$ |
$[1]$ |
19.19.36.15 |
$19$ |
$x^{19} + 342 x^{18} + 5073$ |
$19$ |
$19$ |
$1$ |
$36$ |
$C_{19}$ (as 19T1) |
$1$ |
$1$ |
$[2]$ |
$[2]$ |
$t + 17$ |
$x^{19} + 342 x^{18} + 5073$ |
$[18, 0]$ |
$[1]$ |
19.19.36.16 |
$19$ |
$x^{19} + 342 x^{18} + 5434$ |
$19$ |
$19$ |
$1$ |
$36$ |
$C_{19}$ (as 19T1) |
$1$ |
$1$ |
$[2]$ |
$[2]$ |
$t + 17$ |
$x^{19} + 342 x^{18} + 5434$ |
$[18, 0]$ |
$[1]$ |
19.19.36.17 |
$19$ |
$x^{19} + 342 x^{18} + 5795$ |
$19$ |
$19$ |
$1$ |
$36$ |
$C_{19}$ (as 19T1) |
$1$ |
$1$ |
$[2]$ |
$[2]$ |
$t + 17$ |
$x^{19} + 342 x^{18} + 5795$ |
$[18, 0]$ |
$[1]$ |
19.19.36.18 |
$19$ |
$x^{19} + 342 x^{18} + 6156$ |
$19$ |
$19$ |
$1$ |
$36$ |
$C_{19}$ (as 19T1) |
$1$ |
$1$ |
$[2]$ |
$[2]$ |
$t + 17$ |
$x^{19} + 342 x^{18} + 6156$ |
$[18, 0]$ |
$[1]$ |
19.19.36.19 |
$19$ |
$x^{19} + 342 x^{18} + 6517$ |
$19$ |
$19$ |
$1$ |
$36$ |
$C_{19}$ (as 19T1) |
$1$ |
$1$ |
$[2]$ |
$[2]$ |
$t + 17$ |
$x^{19} + 342 x^{18} + 6517$ |
$[18, 0]$ |
$[1]$ |
19.19.36.2 |
$19$ |
$x^{19} + 342 x^{18} + 380$ |
$19$ |
$19$ |
$1$ |
$36$ |
$C_{19}$ (as 19T1) |
$1$ |
$1$ |
$[2]$ |
$[2]$ |
$t + 17$ |
$x^{19} + 342 x^{18} + 380$ |
$[18, 0]$ |
$[1]$ |
19.19.36.3 |
$19$ |
$x^{19} + 342 x^{18} + 741$ |
$19$ |
$19$ |
$1$ |
$36$ |
$C_{19}$ (as 19T1) |
$1$ |
$1$ |
$[2]$ |
$[2]$ |
$t + 17$ |
$x^{19} + 342 x^{18} + 741$ |
$[18, 0]$ |
$[1]$ |
19.19.36.4 |
$19$ |
$x^{19} + 342 x^{18} + 1102$ |
$19$ |
$19$ |
$1$ |
$36$ |
$C_{19}$ (as 19T1) |
$1$ |
$1$ |
$[2]$ |
$[2]$ |
$t + 17$ |
$x^{19} + 342 x^{18} + 1102$ |
$[18, 0]$ |
$[1]$ |
19.19.36.5 |
$19$ |
$x^{19} + 342 x^{18} + 1463$ |
$19$ |
$19$ |
$1$ |
$36$ |
$C_{19}$ (as 19T1) |
$1$ |
$1$ |
$[2]$ |
$[2]$ |
$t + 17$ |
$x^{19} + 342 x^{18} + 1463$ |
$[18, 0]$ |
$[1]$ |
19.19.36.6 |
$19$ |
$x^{19} + 342 x^{18} + 1824$ |
$19$ |
$19$ |
$1$ |
$36$ |
$C_{19}$ (as 19T1) |
$1$ |
$1$ |
$[2]$ |
$[2]$ |
$t + 17$ |
$x^{19} + 342 x^{18} + 1824$ |
$[18, 0]$ |
$[1]$ |
19.19.36.7 |
$19$ |
$x^{19} + 342 x^{18} + 2185$ |
$19$ |
$19$ |
$1$ |
$36$ |
$C_{19}$ (as 19T1) |
$1$ |
$1$ |
$[2]$ |
$[2]$ |
$t + 17$ |
$x^{19} + 342 x^{18} + 2185$ |
$[18, 0]$ |
$[1]$ |
19.19.36.8 |
$19$ |
$x^{19} + 342 x^{18} + 2546$ |
$19$ |
$19$ |
$1$ |
$36$ |
$C_{19}$ (as 19T1) |
$1$ |
$1$ |
$[2]$ |
$[2]$ |
$t + 17$ |
$x^{19} + 342 x^{18} + 2546$ |
$[18, 0]$ |
$[1]$ |
19.19.36.9 |
$19$ |
$x^{19} + 342 x^{18} + 2907$ |
$19$ |
$19$ |
$1$ |
$36$ |
$C_{19}$ (as 19T1) |
$1$ |
$1$ |
$[2]$ |
$[2]$ |
$t + 17$ |
$x^{19} + 342 x^{18} + 2907$ |
$[18, 0]$ |
$[1]$ |
23.19.0.1 |
$19$ |
$x^{19} + 5 x + 18$ |
$23$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 5 t + 18$ |
$x - 23$ |
$[0]$ |
$[]$ |
29.19.0.1 |
$19$ |
$x^{19} + 4 x + 27$ |
$29$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 4 t + 27$ |
$x - 29$ |
$[0]$ |
$[]$ |
31.19.0.1 |
$19$ |
$x^{19} + 7 x + 28$ |
$31$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 7 t + 28$ |
$x - 31$ |
$[0]$ |
$[]$ |
37.19.0.1 |
$19$ |
$x^{19} + 36 x^{2} + 23 x + 35$ |
$37$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 36 t^{2} + 23 t + 35$ |
$x - 37$ |
$[0]$ |
$[]$ |
41.19.0.1 |
$19$ |
$x^{19} + 10 x + 35$ |
$41$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 10 t + 35$ |
$x - 41$ |
$[0]$ |
$[]$ |
43.19.0.1 |
$19$ |
$x^{19} + 30 x + 40$ |
$43$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 30 t + 40$ |
$x - 43$ |
$[0]$ |
$[]$ |
47.19.0.1 |
$19$ |
$x^{19} + 35 x + 42$ |
$47$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 35 t + 42$ |
$x - 47$ |
$[0]$ |
$[]$ |
53.19.0.1 |
$19$ |
$x^{19} + 11 x + 51$ |
$53$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 11 t + 51$ |
$x - 53$ |
$[0]$ |
$[]$ |
59.19.0.1 |
$19$ |
$x^{19} + 11 x + 57$ |
$59$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 11 t + 57$ |
$x - 59$ |
$[0]$ |
$[]$ |
61.19.0.1 |
$19$ |
$x^{19} + 2 x + 59$ |
$61$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 2 t + 59$ |
$x - 61$ |
$[0]$ |
$[]$ |
67.19.0.1 |
$19$ |
$x^{19} + 18 x + 65$ |
$67$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 18 t + 65$ |
$x - 67$ |
$[0]$ |
$[]$ |
71.19.0.1 |
$19$ |
$x^{19} + 4 x + 64$ |
$71$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 4 t + 64$ |
$x - 71$ |
$[0]$ |
$[]$ |
73.19.0.1 |
$19$ |
$x^{19} + 25 x + 68$ |
$73$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 25 t + 68$ |
$x - 73$ |
$[0]$ |
$[]$ |
79.19.0.1 |
$19$ |
$x^{19} + 25 x + 76$ |
$79$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 25 t + 76$ |
$x - 79$ |
$[0]$ |
$[]$ |
83.19.0.1 |
$19$ |
$x^{19} + 47 x + 81$ |
$83$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 47 t + 81$ |
$x - 83$ |
$[0]$ |
$[]$ |
89.19.0.1 |
$19$ |
$x^{19} + 34 x + 86$ |
$89$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 34 t + 86$ |
$x - 89$ |
$[0]$ |
$[]$ |
97.19.0.1 |
$19$ |
$x^{19} + 15 x + 92$ |
$97$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 15 t + 92$ |
$x - 97$ |
$[0]$ |
$[]$ |
101.19.0.1 |
$19$ |
$x^{19} + 24 x + 99$ |
$101$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 24 t + 99$ |
$x - 101$ |
$[0]$ |
$[]$ |
103.19.0.1 |
$19$ |
$x^{19} + 2 x + 98$ |
$103$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 2 t + 98$ |
$x - 103$ |
$[0]$ |
$[]$ |
107.19.0.1 |
$19$ |
$x^{19} + 24 x + 105$ |
$107$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 24 t + 105$ |
$x - 107$ |
$[0]$ |
$[]$ |
109.19.0.1 |
$19$ |
$x^{19} + 15 x + 103$ |
$109$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 15 t + 103$ |
$x - 109$ |
$[0]$ |
$[]$ |
113.19.0.1 |
$19$ |
$x^{19} + 22 x + 110$ |
$113$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 22 t + 110$ |
$x - 113$ |
$[0]$ |
$[]$ |
127.19.0.1 |
$19$ |
$x^{19} + 30 x + 124$ |
$127$ |
$1$ |
$19$ |
$0$ |
$C_{19}$ (as 19T1) |
$19$ |
$1$ |
$[\ ]$ |
$[\ ]^{19}$ |
$t^{19} + 30 t + 124$ |
$x - 127$ |
$[0]$ |
$[]$ |