Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Ind. of Insep. |
Assoc. Inertia |
19.15.0.1 |
$15$ |
x15 + x7 + 10x6 + 11x5 + 13x4 + 15x3 + 14x2 + 17 |
$19$ |
$1$ |
$15$ |
$0$ |
$C_{15}$ (as 15T1) |
$15$ |
$1$ |
$[\ ]$ |
$[\ ]^{15}$ |
$[0]$ |
$[]$ |
19.15.10.1 |
$15$ |
x15 + 95x12 + 15x11 + 51x10 + 3610x9 - 4275x8 - 28995x7 + 69100x6 - 31623x5 + 835620x4 + 700180x3 + 1194855x2 - 1636410x + 2391332 |
$19$ |
$3$ |
$5$ |
$10$ |
$C_{15}$ (as 15T1) |
$5$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{5}$ |
$[0]$ |
$[1]$ |
19.15.10.2 |
$15$ |
x15 + 651605x3 - 42093683 |
$19$ |
$3$ |
$5$ |
$10$ |
$C_{15}$ (as 15T1) |
$5$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{5}$ |
$[0]$ |
$[1]$ |
19.15.10.3 |
$15$ |
x15 + 3610x9 + 3258025x3 + 715592611 |
$19$ |
$3$ |
$5$ |
$10$ |
$C_{15}$ (as 15T1) |
$5$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{5}$ |
$[0]$ |
$[1]$ |
19.15.12.1 |
$15$ |
x15 + 20x13 + 85x12 + 160x11 + 1417x10 + 3530x9 + 7020x8 + 6890x7 + 76970x6 + 160207x5 + 1168245x4 + 470325x3 + 1653430x2 + 224615x + 1762712 |
$19$ |
$5$ |
$3$ |
$12$ |
$D_5\times C_3$ (as 15T3) |
$6$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{6}$ |
$[0]$ |
$[2]$ |
19.15.14.1 |
$15$ |
x15 + 19 |
$19$ |
$15$ |
$1$ |
$14$ |
$D_5\times C_3$ (as 15T3) |
$2$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{2}$ |
$[0]$ |
$[2]$ |
19.15.14.2 |
$15$ |
x15 + 76 |
$19$ |
$15$ |
$1$ |
$14$ |
$D_5\times C_3$ (as 15T3) |
$2$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{2}$ |
$[0]$ |
$[2]$ |
19.15.14.3 |
$15$ |
x15 + 38 |
$19$ |
$15$ |
$1$ |
$14$ |
$D_5\times C_3$ (as 15T3) |
$2$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{2}$ |
$[0]$ |
$[2]$ |