Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Ind. of Insep. |
Assoc. Inertia |
13.15.0.1 |
$15$ |
x15 + 2x7 + 12x6 + 2x5 + 11x4 + 10x3 + 11x2 + 8x + 11 |
$13$ |
$1$ |
$15$ |
$0$ |
$C_{15}$ (as 15T1) |
$15$ |
$1$ |
$[\ ]$ |
$[\ ]^{15}$ |
$[0]$ |
$[]$ |
13.15.10.1 |
$15$ |
x15 + 65x12 + 12x11 + 33x10 + 1690x9 - 2340x8 - 12822x7 + 22234x6 - 11805x5 + 254085x4 + 160029x3 + 311358x2 - 328605x + 351148 |
$13$ |
$3$ |
$5$ |
$10$ |
$C_{15}$ (as 15T1) |
$5$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{5}$ |
$[0]$ |
$[1]$ |
13.15.10.2 |
$15$ |
x15 + 1352x9 + 456976x3 + 44926453 |
$13$ |
$3$ |
$5$ |
$10$ |
$C_{15}$ (as 15T1) |
$5$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{5}$ |
$[0]$ |
$[1]$ |
13.15.10.3 |
$15$ |
x15 + 114244x3 - 4084223 |
$13$ |
$3$ |
$5$ |
$10$ |
$C_{15}$ (as 15T1) |
$5$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{5}$ |
$[0]$ |
$[1]$ |
13.15.12.1 |
$15$ |
x15 + 10x13 + 55x12 + 40x11 + 479x10 + 1290x9 + 930x8 - 5530x7 + 16110x6 + 19349x5 + 267515x4 + 64685x3 + 204430x2 - 112095x + 176534 |
$13$ |
$5$ |
$3$ |
$12$ |
$F_5\times C_3$ (as 15T8) |
$12$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{12}$ |
$[0]$ |
$[4]$ |
13.15.14.1 |
$15$ |
x15 + 13 |
$13$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$[0]$ |
$[4]$ |
13.15.14.2 |
$15$ |
x15 + 26 |
$13$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$[0]$ |
$[4]$ |
13.15.14.3 |
$15$ |
x15 + 52 |
$13$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$[0]$ |
$[4]$ |