| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.15.20.12 |
$15$ |
$x^{15} - 48 x^{14} + 1269 x^{13} - 16365 x^{12} + 105075 x^{11} - 125469 x^{10} - 254304 x^{9} + 934173 x^{8} + 810891 x^{7} - 1130166 x^{6} - 655452 x^{5} + 4781511 x^{4} + 1182357 x^{3} - 1339416 x^{2} + 6603525$ |
$3$ |
$3$ |
$5$ |
$20$ |
$C_3^4:C_5$ (as 15T26) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{5}$ |
$t^{5} + 2 t + 1$ |
$x^{3} + \left(6 t^{4} + 3 t^{3} + 3 t^{2} + 6 t\right) x^{2} + 18 t + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.15.20.30 |
$15$ |
$x^{15} + 15 x^{14} + 171 x^{13} + 1626 x^{12} + 8712 x^{11} + 33534 x^{10} + 147564 x^{9} + 412938 x^{8} + 1100547 x^{7} + 3380643 x^{6} + 3861675 x^{5} + 17036244 x^{4} + 5310198 x^{3} + 46864980 x^{2} + 54370521$ |
$3$ |
$3$ |
$5$ |
$20$ |
$C_3^4:C_5$ (as 15T26) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{5}$ |
$t^{5} + 2 t + 1$ |
$x^{3} + \left(3 t^{3} + 3 t^{2} + 3\right) x^{2} + 9 t^{4} + 18 t^{3} + 9 t^{2} + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.15.20.49 |
$15$ |
$x^{15} + 6 x^{14} + 144 x^{13} + 1005 x^{12} + 2448 x^{11} + 21627 x^{10} - 64818 x^{9} - 4050 x^{8} + 54432 x^{7} + 650052 x^{6} - 1224072 x^{5} - 95256 x^{4} + 754677 x^{3} + 10037358 x^{2} + 5447331$ |
$3$ |
$3$ |
$5$ |
$20$ |
$C_3^4:C_5$ (as 15T26) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{5}$ |
$t^{5} + 2 t + 1$ |
$x^{3} + \left(3 t^{4} + 6 t^{2} + 6\right) x^{2} + 18 t^{4} + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.15.20.87 |
$15$ |
$x^{15} - 9 x^{14} + 252 x^{13} - 3351 x^{12} + 10152 x^{11} + 8181 x^{10} + 21744 x^{9} + 4617 x^{8} + 242028 x^{7} + 229176 x^{6} + 607743 x^{5} + 322461 x^{4} + 2039661 x^{3} + 1689093 x^{2} - 5949855$ |
$3$ |
$3$ |
$5$ |
$20$ |
$C_3^4:C_5$ (as 15T26) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{5}$ |
$t^{5} + 2 t + 1$ |
$x^{3} + \left(3 t^{4} + 6 t^{2} + 6 t + 3\right) x^{2} + 9 t^{4} + 18 t^{3} + 9 t + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.15.20.88 |
$15$ |
$x^{15} + 378 x^{13} - 2451 x^{12} + 7992 x^{11} - 28431 x^{10} + 73773 x^{9} - 164025 x^{8} + 381996 x^{7} - 581715 x^{6} + 1164942 x^{5} - 1306368 x^{4} + 1476387 x^{3} - 1754703 x^{2} + 3411234$ |
$3$ |
$3$ |
$5$ |
$20$ |
$C_3^4:C_5$ (as 15T26) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{5}$ |
$t^{5} + 2 t + 1$ |
$x^{3} + \left(3 t^{3} + 6 t^{2} + 6 t\right) x^{2} + 18 t^{4} + 18 t^{3} + 18 t^{2} + 9 t + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.15.20.92 |
$15$ |
$x^{15} - 9 x^{14} + 18 x^{13} + 411 x^{12} + 2646 x^{11} + 9963 x^{10} + 36351 x^{9} + 88695 x^{8} + 140940 x^{7} + 554067 x^{6} + 176904 x^{5} + 1512432 x^{4} + 261144 x^{3} + 1936953 x^{2} + 1449495$ |
$3$ |
$3$ |
$5$ |
$20$ |
$C_3^4:C_5$ (as 15T26) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{5}$ |
$t^{5} + 2 t + 1$ |
$x^{3} + \left(3 t^{4} + 3 t^{3} + 3\right) x^{2} + 9 t^{3} + 12$ |
$[2, 0]$ |
$[1]$ |
| 3.15.20.93 |
$15$ |
$x^{15} + 30 x^{14} + 360 x^{13} + 2265 x^{12} + 7974 x^{11} + 12798 x^{10} + 20286 x^{9} + 153738 x^{8} + 259524 x^{7} + 463428 x^{6} - 456759 x^{5} - 1677915 x^{4} + 228825 x^{3} + 910035 x^{2} + 5402862$ |
$3$ |
$3$ |
$5$ |
$20$ |
$C_3^4:C_5$ (as 15T26) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{5}$ |
$t^{5} + 2 t + 1$ |
$x^{3} + \left(3 t^{3} + 6\right) x^{2} + 9 t^{4} + 18 t^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.15.20.96 |
$15$ |
$x^{15} + 195 x^{12} + 918 x^{11} + 4212 x^{10} + 17964 x^{9} + 50301 x^{8} + 200232 x^{7} + 410211 x^{6} + 1120473 x^{5} + 2318949 x^{4} + 2410236 x^{3} + 8641566 x^{2} + 19557855$ |
$3$ |
$3$ |
$5$ |
$20$ |
$C_3^4:C_5$ (as 15T26) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{5}$ |
$t^{5} + 2 t + 1$ |
$x^{3} + 3 t^{3} x^{2} + 9 t^{4} + 9 t^{3} + 18 t^{2} + 21$ |
$[2, 0]$ |
$[1]$ |
