Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Ind. of Insep. |
Assoc. Inertia |
7.15.0.1 |
$15$ |
x15 + 5x6 + 6x5 + 6x4 + 4x3 + x2 + 2x + 4 |
$7$ |
$1$ |
$15$ |
$0$ |
$C_{15}$ (as 15T1) |
$15$ |
$1$ |
$[\ ]$ |
$[\ ]^{15}$ |
$[0]$ |
$[]$ |
7.15.10.1 |
$15$ |
x15 + 35x12 + 3x11 + 12x10 + 490x9 - 315x8 - 2517x7 + 3454x6 - 834x5 + 26565x4 + 12846x3 + 13662x2 - 19944x + 16290 |
$7$ |
$3$ |
$5$ |
$10$ |
$C_{15}$ (as 15T1) |
$5$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{5}$ |
$[0]$ |
$[1]$ |
7.15.10.2 |
$15$ |
x15 + 2401x3 - 67228 |
$7$ |
$3$ |
$5$ |
$10$ |
$C_{15}$ (as 15T1) |
$5$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{5}$ |
$[0]$ |
$[1]$ |
7.15.10.3 |
$15$ |
x15 + 98x9 + 2401x3 + 268912 |
$7$ |
$3$ |
$5$ |
$10$ |
$C_{15}$ (as 15T1) |
$5$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{5}$ |
$[0]$ |
$[1]$ |
7.15.12.1 |
$15$ |
x15 + 30x14 + 360x13 + 2180x12 + 6960x11 + 12117x10 + 17860x9 + 33840x8 + 45000x7 + 90640x6 - 100029x5 - 595410x4 - 585880x3 + 441960x2 + 576240x + 404231 |
$7$ |
$5$ |
$3$ |
$12$ |
$F_5\times C_3$ (as 15T8) |
$12$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{12}$ |
$[0]$ |
$[4]$ |
7.15.14.1 |
$15$ |
x15 + 7 |
$7$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$[0]$ |
$[4]$ |
7.15.14.2 |
$15$ |
x15 + 14 |
$7$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$[0]$ |
$[4]$ |
7.15.14.3 |
$15$ |
x15 + 21 |
$7$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$[0]$ |
$[4]$ |