| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.15.12.1 |
$15$ |
$x^{15} + 5 x^{13} + 5 x^{12} + 10 x^{11} + 26 x^{10} + 20 x^{9} - 145 x^{7} + 70 x^{6} + 73 x^{5} + 315 x^{4} - 105 x^{3} + 200 x^{2} + 5 x + 1$ |
$2$ |
$5$ |
$3$ |
$12$ |
$F_5\times C_3$ (as 15T8) |
$12$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{12}$ |
$t^{3} + t + 1$ |
$x^{5} + 2$ |
$[0]$ |
$[4]$ |
| 3.15.12.1 |
$15$ |
$x^{15} + 10 x^{13} + 5 x^{12} + 40 x^{11} + 49 x^{10} + 90 x^{9} + 30 x^{8} - 130 x^{7} + 410 x^{6} + 269 x^{5} + 765 x^{4} - 515 x^{3} + 730 x^{2} + 205 x + 94$ |
$3$ |
$5$ |
$3$ |
$12$ |
$F_5\times C_3$ (as 15T8) |
$12$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{12}$ |
$t^{3} + 2 t + 1$ |
$x^{5} + 3$ |
$[0]$ |
$[4]$ |
| 3.15.24.48 |
$15$ |
$x^{15} + 6 x^{14} + 6 x^{13} + 6 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{6} + 3 x^{3} + 12$ |
$3$ |
$15$ |
$1$ |
$24$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$5$ |
$[2]$ |
$[2]_{5}^{4}$ |
$t + 1$ |
$x^{15} + 6 x^{14} + 6 x^{13} + 6 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{6} + 3 x^{3} + 12$ |
$[10, 0]$ |
$[1, 4]$ |
| 3.15.24.65 |
$15$ |
$x^{15} + 3 x^{13} + 6 x^{10} + 6 x^{9} + 21$ |
$3$ |
$15$ |
$1$ |
$24$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$5$ |
$[2]$ |
$[2]_{5}^{4}$ |
$t + 1$ |
$x^{15} + 3 x^{13} + 6 x^{10} + 6 x^{9} + 21$ |
$[10, 0]$ |
$[1, 4]$ |
| 3.15.24.83 |
$15$ |
$x^{15} + 6 x^{14} + 6 x^{13} + 3 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{6} + 6 x^{3} + 3$ |
$3$ |
$15$ |
$1$ |
$24$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$5$ |
$[2]$ |
$[2]_{5}^{4}$ |
$t + 1$ |
$x^{15} + 6 x^{14} + 6 x^{13} + 3 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{6} + 6 x^{3} + 3$ |
$[10, 0]$ |
$[1, 4]$ |
| 5.15.15.18 |
$15$ |
$x^{15} - 60 x^{12} + 60 x^{11} + 15 x^{10} + 4425 x^{9} - 2400 x^{8} + 600 x^{7} + 17725 x^{6} + 88575 x^{5} - 1875 x^{4} - 4000 x^{3} + 4500 x^{2} + 1500 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$F_5\times C_3$ (as 15T8) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(15 t^{2} + 20 t + 10\right) x^{2} + 20 x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.38 |
$15$ |
$x^{15} - 60 x^{12} + 45 x^{11} + 15 x^{10} + 4425 x^{9} - 1800 x^{8} + 75 x^{7} + 17575 x^{6} + 66450 x^{5} + 8625 x^{4} - 5625 x^{3} + 1875 x^{2} + 1125 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$F_5\times C_3$ (as 15T8) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(15 t^{2} + 20 t + 10\right) x^{2} + 15 x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.40 |
$15$ |
$x^{15} - 45 x^{12} + 15 x^{11} + 15 x^{10} + 3900 x^{9} - 450 x^{8} - 375 x^{7} + 38025 x^{6} + 19575 x^{5} + 18375 x^{4} - 2125 x^{3} - 750 x^{2} + 375 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$F_5\times C_3$ (as 15T8) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(15 t^{2} + 20 t + 15\right) x^{2} + 5 x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.15.44 |
$15$ |
$x^{15} + 15 x^{12} + 30 x^{11} + 15 x^{10} + 750 x^{9} + 300 x^{8} + 450 x^{7} + 7425 x^{6} + 7575 x^{5} + 5250 x^{4} + 2500 x^{3} + 1875 x^{2} + 750 x + 125$ |
$5$ |
$5$ |
$3$ |
$15$ |
$F_5\times C_3$ (as 15T8) |
$3$ |
$4$ |
$[5/4]$ |
$[5/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 10 t + 15\right) x^{2} + 10 x + 5$ |
$[1, 0]$ |
$[1]$ |
| 5.15.18.41 |
$15$ |
$x^{15} - 30 x^{13} + 60 x^{12} - 1185 x^{10} + 14200 x^{9} - 300 x^{8} - 11400 x^{7} + 8000 x^{6} - 5925 x^{5} + 6000 x^{4} - 750 x^{3} + 1500 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$18$ |
$F_5\times C_3$ (as 15T8) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{6}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(10 t^{2} + 10\right) x^{3} + 20 x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
| 5.15.18.44 |
$15$ |
$x^{15} + 15 x^{12} + 1725 x^{11} + 15 x^{10} + 27950 x^{9} + 8625 x^{8} + 150 x^{7} + 8750 x^{6} + 75 x^{5} + 375 x^{4} + 375 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$18$ |
$F_5\times C_3$ (as 15T8) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{6}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(10 t^{2} + 15 t + 20\right) x^{3} + 5 x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
| 5.15.21.12 |
$15$ |
$x^{15} + 1290 x^{13} + 1375 x^{12} + 6450 x^{11} + 15 x^{10} + 125 x^{9} + 6525 x^{8} + 375 x^{6} + 75 x^{5} + 375 x^{3} + 125$ |
$5$ |
$5$ |
$3$ |
$21$ |
$F_5\times C_3$ (as 15T8) |
$3$ |
$4$ |
$[7/4]$ |
$[7/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 15 t + 10\right) x^{4} + 5 x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
| 5.15.21.19 |
$15$ |
$x^{15} + 60 x^{14} + 1335 x^{13} + 11525 x^{12} + 26700 x^{11} + 24015 x^{10} + 8600 x^{9} + 6975 x^{8} + 12000 x^{7} + 6000 x^{6} + 75 x^{5} + 1500 x^{4} + 1500 x^{3} + 125$ |
$5$ |
$5$ |
$3$ |
$21$ |
$F_5\times C_3$ (as 15T8) |
$3$ |
$4$ |
$[7/4]$ |
$[7/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t + 20\right) x^{4} + 20 x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
| 5.15.21.29 |
$15$ |
$x^{15} + 30 x^{14} + 405 x^{13} + 1975 x^{12} + 4050 x^{11} + 3015 x^{10} + 1300 x^{9} + 2175 x^{8} + 3000 x^{7} + 1500 x^{6} + 75 x^{5} + 750 x^{4} + 750 x^{3} + 125$ |
$5$ |
$5$ |
$3$ |
$21$ |
$F_5\times C_3$ (as 15T8) |
$3$ |
$4$ |
$[7/4]$ |
$[7/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t + 10\right) x^{4} + 10 x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
| 5.15.21.44 |
$15$ |
$x^{15} - 75 x^{14} + 4095 x^{13} + 86625 x^{12} + 61425 x^{11} - 16860 x^{10} + 2625 x^{9} + 20700 x^{8} - 11250 x^{7} + 3375 x^{6} + 75 x^{5} - 1875 x^{4} + 1125 x^{3} + 125$ |
$5$ |
$5$ |
$3$ |
$21$ |
$F_5\times C_3$ (as 15T8) |
$3$ |
$4$ |
$[7/4]$ |
$[7/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t^{2} + 15 t + 15\right) x^{4} + 15 x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
| 5.15.24.36 |
$15$ |
$x^{15} + 30 x^{14} + 300 x^{13} + 1000 x^{12} - 360 x^{10} - 7200 x^{9} - 36000 x^{8} + 133200 x^{5} + 1332000 x^{4} + 10472000$ |
$5$ |
$5$ |
$3$ |
$24$ |
$F_5\times C_3$ (as 15T8) |
$12$ |
$1$ |
$[2]$ |
$[2]^{12}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + 10 x^{4} + 100 t^{2} + 100 t + 80$ |
$[4, 0]$ |
$[4]$ |
| 5.15.24.58 |
$15$ |
$x^{15} + 45 x^{14} + 675 x^{13} + 3375 x^{12} - 435 x^{10} - 13050 x^{9} - 97875 x^{8} + 87450 x^{5} + 1311750 x^{4} + 1338875$ |
$5$ |
$5$ |
$3$ |
$24$ |
$F_5\times C_3$ (as 15T8) |
$12$ |
$1$ |
$[2]$ |
$[2]^{12}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + 15 x^{4} + 75 t^{2} + 50 t + 5$ |
$[4, 0]$ |
$[4]$ |
| 5.15.27.32 |
$15$ |
$x^{15} - 300 x^{11} + 315 x^{10} + 5625 x^{9} - 5625 x^{8} + 73125 x^{7} + 2082625 x^{6} + 7656825 x^{5} + 14887500 x^{4} + 7737500 x^{3} + 6740625 x^{2} + 5280000 x + 1307625$ |
$5$ |
$5$ |
$3$ |
$27$ |
$F_5\times C_3$ (as 15T8) |
$3$ |
$4$ |
$[9/4]$ |
$[9/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(50 t^{2} + 25 t + 100\right) x^{2} + \left(75 t^{2} + 50\right) x + 100 t + 105$ |
$[5, 0]$ |
$[1]$ |
| 5.15.27.38 |
$15$ |
$x^{15} + 300 x^{12} + 225 x^{11} - 135 x^{10} + 31875 x^{9} + 52500 x^{8} + 10500 x^{7} + 1146625 x^{6} + 2882325 x^{5} + 2128125 x^{4} + 1106250 x^{3} + 1779375 x^{2} + 446250 x - 397375$ |
$5$ |
$5$ |
$3$ |
$27$ |
$F_5\times C_3$ (as 15T8) |
$3$ |
$4$ |
$[9/4]$ |
$[9/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(25 t + 100\right) x^{2} + \left(50 t + 75\right) x + 25 t^{2} + 50 t + 5$ |
$[5, 0]$ |
$[1]$ |
| 5.15.27.39 |
$15$ |
$x^{15} - 225 x^{12} - 135 x^{10} + 41250 x^{9} + 97500 x^{8} + 147750 x^{7} + 5776875 x^{6} + 73575 x^{5} + 9300000 x^{4} - 5512500 x^{3} - 193125 x^{2} - 5475000 x + 496375$ |
$5$ |
$5$ |
$3$ |
$27$ |
$F_5\times C_3$ (as 15T8) |
$3$ |
$4$ |
$[9/4]$ |
$[9/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(75 t^{2} + 50 t + 75\right) x^{2} + 100 t x + 50 t^{2} + 100 t + 55$ |
$[5, 0]$ |
$[1]$ |
| 5.15.27.40 |
$15$ |
$x^{15} - 300 x^{12} - 435 x^{10} + 13125 x^{9} + 28125 x^{8} + 152625 x^{7} + 5455625 x^{6} + 10418700 x^{5} + 28940625 x^{4} + 35031250 x^{3} + 37989375 x^{2} + 19012500 x + 6901375$ |
$5$ |
$5$ |
$3$ |
$27$ |
$F_5\times C_3$ (as 15T8) |
$3$ |
$4$ |
$[9/4]$ |
$[9/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(75 t^{2} + 50\right) x^{2} + \left(50 t^{2} + 75 t + 100\right) x + 100 t^{2} + 100 t + 55$ |
$[5, 0]$ |
$[1]$ |
| 5.15.27.45 |
$15$ |
$x^{15} - 450 x^{11} - 135 x^{10} + 69375 x^{7} + 23625 x^{6} - 10800 x^{5} + 2484375 x^{3} + 16143750 x^{2} + 17566875 x + 5308875$ |
$5$ |
$5$ |
$3$ |
$27$ |
$F_5\times C_3$ (as 15T8) |
$3$ |
$4$ |
$[9/4]$ |
$[9/4]_{4}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(75 t^{2} + 25 t\right) x + 75 t^{2} + 105$ |
$[5, 0]$ |
$[1]$ |
| 7.15.12.1 |
$15$ |
$x^{15} + 30 x^{14} + 360 x^{13} + 2180 x^{12} + 6960 x^{11} + 12117 x^{10} + 17860 x^{9} + 33840 x^{8} + 45000 x^{7} + 90640 x^{6} - 100029 x^{5} - 595410 x^{4} - 585880 x^{3} + 441960 x^{2} + 576240 x + 404231$ |
$7$ |
$5$ |
$3$ |
$12$ |
$F_5\times C_3$ (as 15T8) |
$12$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{12}$ |
$t^{3} + 6 t^{2} + 4$ |
$x^{5} + 7$ |
$[0]$ |
$[4]$ |
| 7.15.14.1 |
$15$ |
$x^{15} + 7$ |
$7$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$t + 4$ |
$x^{15} + 7$ |
$[0]$ |
$[4]$ |
| 7.15.14.2 |
$15$ |
$x^{15} + 14$ |
$7$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$t + 4$ |
$x^{15} + 14$ |
$[0]$ |
$[4]$ |
| 7.15.14.3 |
$15$ |
$x^{15} + 21$ |
$7$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$t + 4$ |
$x^{15} + 21$ |
$[0]$ |
$[4]$ |
| 13.15.12.1 |
$15$ |
$x^{15} + 10 x^{13} + 55 x^{12} + 40 x^{11} + 479 x^{10} + 1290 x^{9} + 930 x^{8} - 5530 x^{7} + 16110 x^{6} + 19349 x^{5} + 267515 x^{4} + 64685 x^{3} + 204430 x^{2} - 112095 x + 176534$ |
$13$ |
$5$ |
$3$ |
$12$ |
$F_5\times C_3$ (as 15T8) |
$12$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{12}$ |
$t^{3} + 2 t + 11$ |
$x^{5} + 13$ |
$[0]$ |
$[4]$ |
| 13.15.14.1 |
$15$ |
$x^{15} + 13$ |
$13$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$t + 11$ |
$x^{15} + 13$ |
$[0]$ |
$[4]$ |
| 13.15.14.2 |
$15$ |
$x^{15} + 26$ |
$13$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$t + 11$ |
$x^{15} + 26$ |
$[0]$ |
$[4]$ |
| 13.15.14.3 |
$15$ |
$x^{15} + 52$ |
$13$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$t + 11$ |
$x^{15} + 52$ |
$[0]$ |
$[4]$ |
| 17.15.12.1 |
$15$ |
$x^{15} + 5 x^{13} + 70 x^{12} + 10 x^{11} + 331 x^{10} + 1970 x^{9} + 165 x^{8} - 15535 x^{7} + 28060 x^{6} + 10318 x^{5} + 504940 x^{4} + 183500 x^{3} + 248865 x^{2} - 505940 x + 539184$ |
$17$ |
$5$ |
$3$ |
$12$ |
$F_5\times C_3$ (as 15T8) |
$12$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{12}$ |
$t^{3} + t + 14$ |
$x^{5} + 17$ |
$[0]$ |
$[4]$ |
| 23.15.12.1 |
$15$ |
$x^{15} + 10 x^{13} + 90 x^{12} + 40 x^{11} + 789 x^{10} + 3320 x^{9} + 1470 x^{8} - 17740 x^{7} + 63040 x^{6} + 52919 x^{5} + 1242580 x^{4} + 496520 x^{3} + 967900 x^{2} - 957680 x + 1956291$ |
$23$ |
$5$ |
$3$ |
$12$ |
$F_5\times C_3$ (as 15T8) |
$12$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{12}$ |
$t^{3} + 2 t + 18$ |
$x^{5} + 23$ |
$[0]$ |
$[4]$ |
| 37.15.12.1 |
$15$ |
$x^{15} + 30 x^{13} + 175 x^{12} + 360 x^{11} + 4311 x^{10} + 14410 x^{9} + 34470 x^{8} + 110430 x^{7} + 606590 x^{6} + 1451433 x^{5} + 11570595 x^{4} + 9052445 x^{3} + 25270710 x^{2} + 20317365 x + 59581290$ |
$37$ |
$5$ |
$3$ |
$12$ |
$F_5\times C_3$ (as 15T8) |
$12$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{12}$ |
$t^{3} + 6 t + 35$ |
$x^{5} + 37$ |
$[0]$ |
$[4]$ |
| 37.15.14.1 |
$15$ |
$x^{15} + 37$ |
$37$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$t + 35$ |
$x^{15} + 37$ |
$[0]$ |
$[4]$ |
| 37.15.14.2 |
$15$ |
$x^{15} + 74$ |
$37$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$t + 35$ |
$x^{15} + 74$ |
$[0]$ |
$[4]$ |
| 37.15.14.3 |
$15$ |
$x^{15} + 111$ |
$37$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$t + 35$ |
$x^{15} + 111$ |
$[0]$ |
$[4]$ |
| 43.15.12.1 |
$15$ |
$x^{15} + 5 x^{13} + 200 x^{12} + 10 x^{11} + 929 x^{10} + 16010 x^{9} + 555 x^{8} - 106795 x^{7} + 641660 x^{6} + 79348 x^{5} + 10568630 x^{4} + 12744620 x^{3} + 4923015 x^{2} - 28470110 x + 102453750$ |
$43$ |
$5$ |
$3$ |
$12$ |
$F_5\times C_3$ (as 15T8) |
$12$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{12}$ |
$t^{3} + t + 40$ |
$x^{5} + 43$ |
$[0]$ |
$[4]$ |
| 43.15.14.1 |
$15$ |
$x^{15} + 43$ |
$43$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$t + 40$ |
$x^{15} + 43$ |
$[0]$ |
$[4]$ |
| 43.15.14.2 |
$15$ |
$x^{15} + 301$ |
$43$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$t + 40$ |
$x^{15} + 301$ |
$[0]$ |
$[4]$ |
| 43.15.14.3 |
$15$ |
$x^{15} + 129$ |
$43$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$t + 40$ |
$x^{15} + 129$ |
$[0]$ |
$[4]$ |
| 47.15.12.1 |
$15$ |
$x^{15} + 15 x^{13} + 210 x^{12} + 90 x^{11} + 2661 x^{10} + 17910 x^{9} + 9225 x^{8} - 18495 x^{7} + 772020 x^{6} + 571980 x^{5} + 15667560 x^{4} + 15546900 x^{3} + 16932015 x^{2} - 5624280 x + 133145666$ |
$47$ |
$5$ |
$3$ |
$12$ |
$F_5\times C_3$ (as 15T8) |
$12$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{12}$ |
$t^{3} + 3 t + 42$ |
$x^{5} + 47$ |
$[0]$ |
$[4]$ |
| 53.15.12.1 |
$15$ |
$x^{15} + 15 x^{13} + 255 x^{12} + 90 x^{11} + 3219 x^{10} + 26280 x^{9} + 11385 x^{8} - 8775 x^{7} + 1363590 x^{6} + 832575 x^{5} + 26604180 x^{4} + 33873195 x^{3} + 28664595 x^{2} - 4091625 x + 349241507$ |
$53$ |
$5$ |
$3$ |
$12$ |
$F_5\times C_3$ (as 15T8) |
$12$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{12}$ |
$t^{3} + 3 t + 51$ |
$x^{5} + 53$ |
$[0]$ |
$[4]$ |
| 67.15.12.1 |
$15$ |
$x^{15} + 30 x^{13} + 325 x^{12} + 360 x^{11} + 8001 x^{10} + 44410 x^{9} + 64170 x^{8} + 375030 x^{7} + 3075290 x^{6} + 4976193 x^{5} + 71736045 x^{4} + 94704845 x^{3} + 159006210 x^{2} + 256433265 x + 1203312330$ |
$67$ |
$5$ |
$3$ |
$12$ |
$F_5\times C_3$ (as 15T8) |
$12$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{12}$ |
$t^{3} + 6 t + 65$ |
$x^{5} + 67$ |
$[0]$ |
$[4]$ |
| 67.15.14.1 |
$15$ |
$x^{15} + 67$ |
$67$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$t + 65$ |
$x^{15} + 67$ |
$[0]$ |
$[4]$ |
| 67.15.14.2 |
$15$ |
$x^{15} + 268$ |
$67$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$t + 65$ |
$x^{15} + 268$ |
$[0]$ |
$[4]$ |
| 67.15.14.3 |
$15$ |
$x^{15} + 134$ |
$67$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$t + 65$ |
$x^{15} + 134$ |
$[0]$ |
$[4]$ |
| 73.15.12.1 |
$15$ |
$x^{15} + 10 x^{13} + 340 x^{12} + 40 x^{11} + 2939 x^{10} + 46320 x^{9} + 5970 x^{8} - 169240 x^{7} + 3161040 x^{6} + 719819 x^{5} + 58158080 x^{4} + 106666520 x^{3} + 43707400 x^{2} - 130474680 x + 1457452241$ |
$73$ |
$5$ |
$3$ |
$12$ |
$F_5\times C_3$ (as 15T8) |
$12$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{12}$ |
$t^{3} + 2 t + 68$ |
$x^{5} + 73$ |
$[0]$ |
$[4]$ |
| 73.15.14.1 |
$15$ |
$x^{15} + 73$ |
$73$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$t + 68$ |
$x^{15} + 73$ |
$[0]$ |
$[4]$ |
| 73.15.14.2 |
$15$ |
$x^{15} + 292$ |
$73$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$t + 68$ |
$x^{15} + 292$ |
$[0]$ |
$[4]$ |
| 73.15.14.3 |
$15$ |
$x^{15} + 146$ |
$73$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$t + 68$ |
$x^{15} + 146$ |
$[0]$ |
$[4]$ |
