| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 5.15.15.1 |
$15$ |
$x^{15} - 75 x^{12} + 60 x^{11} + 15 x^{10} + 1650 x^{9} - 1950 x^{8} + 525 x^{7} + 99225 x^{6} + 29700 x^{5} - 750 x^{4} - 625 x^{3} + 4500 x^{2} + 1500 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t^{2} + 5 t + 15\right) x^{2} + \left(5 t + 20\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.10 |
$15$ |
$x^{15} - 45 x^{12} - 60 x^{11} + 15 x^{10} + 750 x^{9} + 1725 x^{8} + 525 x^{7} + 44025 x^{6} + 178200 x^{5} + 240750 x^{4} + 113750 x^{3} + 3750 x^{2} - 1500 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(15 t^{2} + 5 t + 15\right) x^{2} + \left(20 t^{2} + 5 t + 20\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.12 |
$15$ |
$x^{15} - 45 x^{12} + 45 x^{11} + 15 x^{10} + 750 x^{9} + 1950 x^{8} + 1425 x^{7} + 45075 x^{6} + 15825 x^{5} + 43125 x^{4} + 7125 x^{3} + 8250 x^{2} + 1125 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(15 t^{2} + 5 t + 15\right) x^{2} + \left(20 t + 15\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.13 |
$15$ |
$x^{15} + 30 x^{12} + 15 x^{11} + 15 x^{10} + 525 x^{9} + 1800 x^{8} + 1575 x^{7} + 6275 x^{6} + 23700 x^{5} + 16875 x^{4} - 8875 x^{3} + 7125 x^{2} + 375 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 5 t + 20\right) x^{2} + \left(20 t + 5\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.14 |
$15$ |
$x^{15} + 15 x^{12} - 30 x^{11} + 15 x^{10} + 150 x^{9} + 675 x^{8} + 1425 x^{7} - 175 x^{6} + 3450 x^{5} + 12000 x^{4} + 56000 x^{3} + 6750 x^{2} - 750 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t + 5\right) x^{2} + \left(15 t^{2} + 10 t + 20\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.15 |
$15$ |
$x^{15} - 30 x^{12} + 15 x^{10} + 2025 x^{9} + 2550 x^{8} + 600 x^{7} + 9625 x^{6} + 54825 x^{5} + 76125 x^{4} + 35750 x^{3} + 3750 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(10 t^{2} + 15 t + 10\right) x^{2} + \left(10 t^{2} + 10 t + 20\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.16 |
$15$ |
$x^{15} - 75 x^{12} - 90 x^{11} + 15 x^{10} + 2775 x^{9} + 3900 x^{8} + 750 x^{7} + 93975 x^{6} + 279825 x^{5} + 294375 x^{4} + 116500 x^{3} + 5625 x^{2} - 2250 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t^{2} + 10 t + 15\right) x^{2} + \left(20 t^{2} + 10\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.17 |
$15$ |
$x^{15} - 90 x^{12} - 15 x^{11} + 15 x^{10} + 3675 x^{9} + 3825 x^{8} + 450 x^{7} + 6975 x^{6} - 8550 x^{5} + 7125 x^{4} + 14000 x^{3} + 4500 x^{2} - 375 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(15 t^{2} + 10 t\right) x^{2} + \left(5 t^{2} + 15 t + 5\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.19 |
$15$ |
$x^{15} - 60 x^{12} - 75 x^{11} + 15 x^{10} + 1425 x^{9} + 5100 x^{8} + 4875 x^{7} + 3375 x^{6} + 34950 x^{5} + 97125 x^{4} + 103875 x^{3} + 25875 x^{2} - 1875 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(10 t^{2} + 5 t\right) x^{2} + \left(20 t^{2} + 20 t + 15\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.2 |
$15$ |
$x^{15} + 30 x^{12} - 60 x^{11} + 15 x^{10} + 300 x^{9} - 1200 x^{8} + 3675 x^{7} + 400 x^{6} - 5925 x^{5} + 35250 x^{4} + 101375 x^{3} + 17625 x^{2} - 1500 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + 10 x^{2} + \left(20 t^{2} + 15 t + 20\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.20 |
$15$ |
$x^{15} - 90 x^{12} + 30 x^{11} + 15 x^{10} + 2025 x^{9} - 225 x^{8} + 675 x^{7} + 30675 x^{6} + 40575 x^{5} + 31500 x^{4} + 14000 x^{3} + 5625 x^{2} + 750 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + 15 t^{2} x^{2} + \left(5 t^{2} + 15 t + 20\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.21 |
$15$ |
$x^{15} + 45 x^{12} + 30 x^{11} + 15 x^{10} + 750 x^{9} + 1500 x^{8} + 1950 x^{7} + 4425 x^{6} + 12075 x^{5} + 14250 x^{4} - 3500 x^{3} + 8625 x^{2} + 750 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t + 15\right) x^{2} + \left(20 t + 10\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.22 |
$15$ |
$x^{15} + 45 x^{12} - 30 x^{11} + 15 x^{10} + 1875 x^{9} + 600 x^{8} + 975 x^{7} - 2925 x^{6} - 2175 x^{5} + 8250 x^{4} + 2625 x^{3} + 3750 x^{2} - 750 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t + 15\right) x^{2} + \left(5 t^{2} + 5 t\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.25 |
$15$ |
$x^{15} - 45 x^{12} - 60 x^{11} + 15 x^{10} + 3375 x^{9} + 8400 x^{8} + 4350 x^{7} - 15475 x^{6} + 13575 x^{5} + 136875 x^{4} + 146000 x^{3} + 22875 x^{2} - 1500 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(10 t^{2} + 20 t + 5\right) x^{2} + \left(20 t^{2} + 20 t + 20\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.26 |
$15$ |
$x^{15} - 75 x^{12} + 30 x^{11} + 15 x^{10} + 2850 x^{9} - 1500 x^{8} - 525 x^{7} + 23675 x^{6} + 82200 x^{5} + 23250 x^{4} - 5875 x^{3} - 750 x^{2} + 750 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(15 t^{2} + 10 t + 5\right) x^{2} + \left(5 t^{2} + 20\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.27 |
$15$ |
$x^{15} - 60 x^{12} + 45 x^{11} + 15 x^{10} + 975 x^{9} - 750 x^{8} + 150 x^{7} + 105575 x^{6} + 16575 x^{5} + 7500 x^{4} + 375 x^{3} + 2250 x^{2} + 1125 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t^{2} + 5 t + 20\right) x^{2} + \left(5 t + 15\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.29 |
$15$ |
$x^{15} + 30 x^{12} - 30 x^{11} + 15 x^{10} + 2325 x^{9} + 2550 x^{8} + 1500 x^{7} + 14825 x^{6} + 36825 x^{5} + 44625 x^{4} + 25750 x^{3} + 6750 x^{2} - 750 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 20 t + 20\right) x^{2} + \left(10 t^{2} + 10 t + 10\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.3 |
$15$ |
$x^{15} - 30 x^{12} - 90 x^{11} + 15 x^{10} + 1275 x^{9} + 2775 x^{8} + 2475 x^{7} + 51725 x^{6} + 127575 x^{5} + 110250 x^{4} + 33750 x^{3} + 13125 x^{2} - 2250 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(15 t^{2} + 10 t + 20\right) x^{2} + \left(15 t^{2} + 5 t\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.30 |
$15$ |
$x^{15} - 45 x^{11} + 15 x^{10} + 2700 x^{9} + 1800 x^{8} + 28550 x^{6} + 99075 x^{5} + 101250 x^{4} + 52875 x^{3} - 1125 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(10 t^{2} + 20 t + 20\right) x^{2} + \left(15 t^{2} + 15\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.31 |
$15$ |
$x^{15} - 15 x^{12} + 45 x^{11} + 15 x^{10} + 1350 x^{9} + 900 x^{8} + 825 x^{7} - 4675 x^{6} + 4575 x^{5} + 11625 x^{4} + 9375 x^{3} + 4500 x^{2} + 1125 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 15 t + 5\right) x^{2} + \left(10 t + 15\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.32 |
$15$ |
$x^{15} + 30 x^{12} - 15 x^{11} + 15 x^{10} + 300 x^{9} - 300 x^{8} + 2100 x^{7} + 850 x^{6} - 1425 x^{5} + 19500 x^{4} + 17625 x^{3} + 9750 x^{2} - 375 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + 10 x^{2} + \left(10 t^{2} + 15 t + 15\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.33 |
$15$ |
$x^{15} - 45 x^{12} - 60 x^{11} + 15 x^{10} + 375 x^{9} + 2250 x^{8} + 2775 x^{7} + 11525 x^{6} + 48825 x^{5} + 72750 x^{4} + 40375 x^{3} + 15000 x^{2} - 1500 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(10 t^{2} + 5\right) x^{2} + \left(15 t^{2} + 15 t + 10\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.35 |
$15$ |
$x^{15} - 60 x^{12} + 30 x^{11} + 15 x^{10} + 2100 x^{9} + 1050 x^{8} + 375 x^{7} - 2700 x^{6} - 5925 x^{5} + 6750 x^{4} + 2875 x^{3} + 3375 x^{2} + 750 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(10 t^{2} + 10 t\right) x^{2} + \left(15 t + 10\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.37 |
$15$ |
$x^{15} - 75 x^{12} - 120 x^{11} + 15 x^{10} + 5475 x^{9} + 13200 x^{8} + 7650 x^{7} + 77175 x^{6} + 153075 x^{5} + 81375 x^{4} + 42000 x^{3} + 40125 x^{2} - 3000 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t^{2} + 20 t + 15\right) x^{2} + \left(20 t^{2} + 20 t\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.4 |
$15$ |
$x^{15} + 15 x^{12} - 45 x^{11} + 15 x^{10} + 2100 x^{9} + 1875 x^{8} + 1050 x^{7} + 3675 x^{6} + 19575 x^{5} + 27375 x^{4} + 19250 x^{3} + 4875 x^{2} - 1125 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 20 t + 15\right) x^{2} + \left(10 t^{2} + 5 t + 5\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.42 |
$15$ |
$x^{15} - 75 x^{12} - 90 x^{11} + 15 x^{10} + 3900 x^{9} + 8775 x^{8} + 4125 x^{7} + 10475 x^{6} + 73200 x^{5} + 146250 x^{4} + 110500 x^{3} + 22500 x^{2} - 2250 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(15 t^{2} + 15 t + 5\right) x^{2} + \left(20 t^{2} + 15 t + 10\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.43 |
$15$ |
$x^{15} - 60 x^{12} - 90 x^{11} + 15 x^{10} + 4800 x^{9} + 7800 x^{8} + 3000 x^{7} + 103100 x^{6} + 276075 x^{5} + 276000 x^{4} + 118000 x^{3} + 16500 x^{2} - 2250 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t^{2} + 20 t + 20\right) x^{2} + \left(20 t^{2} + 10 t + 10\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.5 |
$15$ |
$x^{15} + 15 x^{10} + 900 x^{9} + 2400 x^{8} + 1275 x^{7} + 23000 x^{6} + 46575 x^{5} + 30750 x^{4} + 13375 x^{3} + 6375 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(10 t^{2} + 10 t + 20\right) x^{2} + \left(5 t^{2} + 15 t + 10\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.6 |
$15$ |
$x^{15} - 60 x^{12} + 15 x^{10} + 3900 x^{9} + 2250 x^{8} - 375 x^{7} - 33000 x^{6} + 46575 x^{5} + 84000 x^{4} + 27875 x^{3} - 375 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(10 t^{2} + 20 t\right) x^{2} + \left(10 t^{2} + 5 t + 20\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.7 |
$15$ |
$x^{15} - 90 x^{12} - 30 x^{11} + 15 x^{10} + 1500 x^{9} + 3000 x^{8} + 75 x^{7} + 96700 x^{6} + 51075 x^{5} + 12750 x^{4} + 10875 x^{3} + 2625 x^{2} - 750 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t^{2} + 10\right) x^{2} + \left(5 t^{2} + 10 t\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.8 |
$15$ |
$x^{15} + 30 x^{12} + 15 x^{11} + 15 x^{10} + 975 x^{9} + 750 x^{8} + 450 x^{7} - 2225 x^{6} - 675 x^{5} + 5250 x^{4} + 3875 x^{3} + 1500 x^{2} + 375 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(15 t + 10\right) x^{2} + \left(5 t + 5\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.9 |
$15$ |
$x^{15} - 30 x^{12} + 15 x^{11} + 15 x^{10} + 2325 x^{9} + 2100 x^{8} + 450 x^{7} - 27225 x^{6} - 8925 x^{5} + 26250 x^{4} + 17625 x^{3} + 3000 x^{2} + 375 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 20 t\right) x^{2} + \left(5 t^{2} + 10 t + 15\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.18.1 |
$15$ |
$x^{15} - 60 x^{13} + 45 x^{12} + 3375 x^{11} + 915 x^{10} + 108350 x^{9} + 47775 x^{8} + 19950 x^{7} + 21750 x^{6} + 4575 x^{5} + 4875 x^{4} - 1500 x^{3} + 1125 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$18$ |
$C_5^3:C_{12}$ (as 15T38) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{6}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t^{2} + 15 t + 20\right) x^{3} + \left(10 t + 15\right) x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
| 5.15.18.13 |
$15$ |
$x^{15} - 75 x^{13} - 105 x^{12} + 5475 x^{11} + 12465 x^{10} + 85650 x^{9} + 179625 x^{8} + 117075 x^{7} + 42500 x^{6} + 62325 x^{5} + 36375 x^{4} - 1875 x^{3} - 2625 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$18$ |
$C_5^3:C_{12}$ (as 15T38) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{6}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t^{2} + 20 t + 15\right) x^{3} + \left(20 t^{2} + 20 t + 5\right) x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
| 5.15.18.16 |
$15$ |
$x^{15} - 30 x^{13} - 60 x^{12} + 525 x^{11} + 2265 x^{10} + 1725 x^{9} + 10200 x^{8} + 69900 x^{7} + 109625 x^{6} + 11325 x^{5} + 10500 x^{4} - 750 x^{3} - 1500 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$18$ |
$C_5^3:C_{12}$ (as 15T38) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{6}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 5 t\right) x^{3} + \left(20 t^{2} + 10 t + 20\right) x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
| 5.15.18.18 |
$15$ |
$x^{15} - 75 x^{13} + 30 x^{12} + 4050 x^{11} + 1290 x^{10} + 89850 x^{9} + 121875 x^{8} + 49050 x^{7} + 31625 x^{6} + 6450 x^{5} + 4875 x^{4} - 1875 x^{3} + 750 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$18$ |
$C_5^3:C_{12}$ (as 15T38) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{6}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t^{2} + 15 t + 15\right) x^{3} + \left(5 t^{2} + 10 t + 20\right) x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
| 5.15.18.19 |
$15$ |
$x^{15} + 15 x^{13} - 90 x^{12} + 75 x^{11} - 885 x^{10} + 1625 x^{9} - 2100 x^{8} + 6600 x^{7} + 97375 x^{6} - 4425 x^{5} + 7500 x^{4} + 375 x^{3} - 2250 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$18$ |
$C_5^3:C_{12}$ (as 15T38) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{6}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + 5 x^{3} + \left(20 t^{2} + 10\right) x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
| 5.15.18.23 |
$15$ |
$x^{15} - 75 x^{13} - 75 x^{12} + 2850 x^{11} + 4740 x^{10} + 25025 x^{9} + 132750 x^{8} + 206625 x^{7} + 112875 x^{6} + 23700 x^{5} + 8250 x^{4} - 1875 x^{3} - 1875 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$18$ |
$C_5^3:C_{12}$ (as 15T38) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{6}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(15 t^{2} + 10 t + 5\right) x^{3} + \left(20 t^{2} + 5 t + 15\right) x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
| 5.15.18.27 |
$15$ |
$x^{15} + 15 x^{13} - 15 x^{12} + 300 x^{11} + 1440 x^{10} + 6225 x^{9} + 19650 x^{8} + 16725 x^{7} - 14875 x^{6} + 7200 x^{5} + 10500 x^{4} + 375 x^{3} - 375 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$18$ |
$C_5^3:C_{12}$ (as 15T38) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{6}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 5 t + 15\right) x^{3} + \left(5 t^{2} + 20 t + 5\right) x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
| 5.15.18.28 |
$15$ |
$x^{15} + 30 x^{13} - 45 x^{12} + 2325 x^{11} + 3840 x^{10} + 17825 x^{9} + 55425 x^{8} + 73800 x^{7} + 55500 x^{6} + 19200 x^{5} + 13500 x^{4} + 750 x^{3} - 1125 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$18$ |
$C_5^3:C_{12}$ (as 15T38) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{6}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 20 t + 20\right) x^{3} + \left(15 t^{2} + 15 t + 15\right) x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
| 5.15.18.29 |
$15$ |
$x^{15} + 45 x^{13} - 45 x^{12} + 1875 x^{11} + 1365 x^{10} - 2625 x^{9} + 48825 x^{8} - 450 x^{7} + 53250 x^{6} + 6825 x^{5} + 1125 x^{3} - 1125 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$18$ |
$C_5^3:C_{12}$ (as 15T38) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{6}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t + 15\right) x^{3} + \left(15 t^{2} + 15\right) x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
| 5.15.18.30 |
$15$ |
$x^{15} - 90 x^{13} - 45 x^{12} + 3675 x^{11} + 5640 x^{10} + 9525 x^{9} + 7350 x^{8} + 675 x^{7} + 17000 x^{6} + 28200 x^{5} + 12000 x^{4} - 2250 x^{3} - 1125 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$18$ |
$C_5^3:C_{12}$ (as 15T38) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{6}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(15 t^{2} + 10 t\right) x^{3} + \left(10 t^{2} + 15 t + 5\right) x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
| 5.15.18.31 |
$15$ |
$x^{15} + 30 x^{13} - 30 x^{12} + 300 x^{11} - 585 x^{10} + 1000 x^{9} - 2700 x^{8} - 300 x^{7} + 14500 x^{6} - 2925 x^{5} + 750 x^{3} - 750 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$18$ |
$C_5^3:C_{12}$ (as 15T38) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{6}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + 10 x^{3} + \left(10 t^{2} + 10\right) x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
| 5.15.18.33 |
$15$ |
$x^{15} + 30 x^{13} - 60 x^{12} + 525 x^{11} + 240 x^{10} + 9500 x^{9} + 37050 x^{8} + 130275 x^{7} + 110000 x^{6} + 1200 x^{5} + 16875 x^{4} + 750 x^{3} - 1500 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$18$ |
$C_5^3:C_{12}$ (as 15T38) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{6}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 5 t + 20\right) x^{3} + \left(20 t^{2} + 15 t + 20\right) x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
| 5.15.18.35 |
$15$ |
$x^{15} - 15 x^{13} + 750 x^{11} + 2415 x^{10} + 2150 x^{9} - 2025 x^{8} - 6750 x^{7} - 2375 x^{6} + 12075 x^{5} + 10125 x^{4} - 375 x^{3} + 125$ |
$5$ |
$5$ |
$3$ |
$18$ |
$C_5^3:C_{12}$ (as 15T38) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{6}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 10 t + 5\right) x^{3} + \left(5 t^{2} + 20 t + 10\right) x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
| 5.15.18.36 |
$15$ |
$x^{15} - 60 x^{13} - 30 x^{12} + 2100 x^{11} + 3015 x^{10} - 1800 x^{9} + 11400 x^{8} + 26700 x^{7} + 23500 x^{6} + 15075 x^{5} + 6000 x^{4} - 1500 x^{3} - 750 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$18$ |
$C_5^3:C_{12}$ (as 15T38) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{6}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(10 t^{2} + 10 t\right) x^{3} + \left(10 t^{2} + 10 t + 10\right) x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
| 5.15.18.38 |
$15$ |
$x^{15} - 30 x^{13} + 60 x^{12} + 1575 x^{11} + 1515 x^{10} - 9975 x^{9} - 13800 x^{8} - 11400 x^{7} + 15875 x^{6} + 7575 x^{5} + 12000 x^{4} - 750 x^{3} + 1500 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$18$ |
$C_5^3:C_{12}$ (as 15T38) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{6}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 15 t\right) x^{3} + \left(20 t + 20\right) x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
| 5.15.18.39 |
$15$ |
$x^{15} - 30 x^{13} - 60 x^{12} + 525 x^{11} + 1440 x^{10} + 150 x^{9} + 8325 x^{8} + 36900 x^{7} + 45250 x^{6} + 7200 x^{5} + 2625 x^{4} - 750 x^{3} - 1500 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$18$ |
$C_5^3:C_{12}$ (as 15T38) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{6}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 5 t\right) x^{3} + \left(15 t^{2} + 10\right) x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
| 5.15.21.10 |
$15$ |
$x^{15} + 60 x^{14} + 1170 x^{13} + 6800 x^{12} - 8475 x^{11} + 70515 x^{10} + 56975 x^{9} + 5700 x^{8} - 6000 x^{7} + 17625 x^{6} + 75 x^{5} + 1500 x^{4} - 750 x^{3} + 125$ |
$5$ |
$5$ |
$3$ |
$21$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[7/4]$ |
$[7/4, 7/4, 7/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + 20 x^{4} + \left(15 t^{2} + 20 t + 20\right) x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
| 5.15.21.11 |
$15$ |
$x^{15} - 30 x^{14} + 165 x^{13} + 1725 x^{12} + 18000 x^{11} + 78015 x^{10} + 103700 x^{9} + 525 x^{8} + 3000 x^{7} + 75 x^{5} - 750 x^{4} - 1500 x^{3} + 125$ |
$5$ |
$5$ |
$3$ |
$21$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[7/4]$ |
$[7/4, 7/4, 7/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + 5 t^{2} x^{4} + \left(20 t^{2} + 20\right) x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
