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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
5.15.15.18 $x^{15} - 60 x^{12} + 60 x^{11} + 15 x^{10} + 4425 x^{9} - 2400 x^{8} + 600 x^{7} + 17725 x^{6} + 88575 x^{5} - 1875 x^{4} - 4000 x^{3} + 4500 x^{2} + 1500 x + 125$ $5$ $5$ $3$ $15$ $F_5\times C_3$ (as 15T8) $[5/4]$ $[5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(15 t^{2} + 20 t + 10\right) x^{2} + 20 x + 5$
5.15.15.38 $x^{15} - 60 x^{12} + 45 x^{11} + 15 x^{10} + 4425 x^{9} - 1800 x^{8} + 75 x^{7} + 17575 x^{6} + 66450 x^{5} + 8625 x^{4} - 5625 x^{3} + 1875 x^{2} + 1125 x + 125$ $5$ $5$ $3$ $15$ $F_5\times C_3$ (as 15T8) $[5/4]$ $[5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(15 t^{2} + 20 t + 10\right) x^{2} + 15 x + 5$
5.15.15.40 $x^{15} - 45 x^{12} + 15 x^{11} + 15 x^{10} + 3900 x^{9} - 450 x^{8} - 375 x^{7} + 38025 x^{6} + 19575 x^{5} + 18375 x^{4} - 2125 x^{3} - 750 x^{2} + 375 x + 125$ $5$ $5$ $3$ $15$ $F_5\times C_3$ (as 15T8) $[5/4]$ $[5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(15 t^{2} + 20 t + 15\right) x^{2} + 5 x + 5$
5.15.15.44 $x^{15} + 15 x^{12} + 30 x^{11} + 15 x^{10} + 750 x^{9} + 300 x^{8} + 450 x^{7} + 7425 x^{6} + 7575 x^{5} + 5250 x^{4} + 2500 x^{3} + 1875 x^{2} + 750 x + 125$ $5$ $5$ $3$ $15$ $F_5\times C_3$ (as 15T8) $[5/4]$ $[5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(5 t^{2} + 10 t + 15\right) x^{2} + 10 x + 5$
5.15.18.41 $x^{15} - 30 x^{13} + 60 x^{12} - 1185 x^{10} + 14200 x^{9} - 300 x^{8} - 11400 x^{7} + 8000 x^{6} - 5925 x^{5} + 6000 x^{4} - 750 x^{3} + 1500 x^{2} + 125$ $5$ $5$ $3$ $18$ $F_5\times C_3$ (as 15T8) $[3/2]$ $[3/2]_{2}^{6}$ $t^{3} + 3 t + 3$ $x^{5} + \left(10 t^{2} + 10\right) x^{3} + 20 x^{2} + 5$
5.15.18.44 $x^{15} + 15 x^{12} + 1725 x^{11} + 15 x^{10} + 27950 x^{9} + 8625 x^{8} + 150 x^{7} + 8750 x^{6} + 75 x^{5} + 375 x^{4} + 375 x^{2} + 125$ $5$ $5$ $3$ $18$ $F_5\times C_3$ (as 15T8) $[3/2]$ $[3/2]_{2}^{6}$ $t^{3} + 3 t + 3$ $x^{5} + \left(10 t^{2} + 15 t + 20\right) x^{3} + 5 x^{2} + 5$
5.15.21.12 $x^{15} + 1290 x^{13} + 1375 x^{12} + 6450 x^{11} + 15 x^{10} + 125 x^{9} + 6525 x^{8} + 375 x^{6} + 75 x^{5} + 375 x^{3} + 125$ $5$ $5$ $3$ $21$ $F_5\times C_3$ (as 15T8) $[7/4]$ $[7/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(5 t^{2} + 15 t + 10\right) x^{4} + 5 x^{3} + 5$
5.15.21.19 $x^{15} + 60 x^{14} + 1335 x^{13} + 11525 x^{12} + 26700 x^{11} + 24015 x^{10} + 8600 x^{9} + 6975 x^{8} + 12000 x^{7} + 6000 x^{6} + 75 x^{5} + 1500 x^{4} + 1500 x^{3} + 125$ $5$ $5$ $3$ $21$ $F_5\times C_3$ (as 15T8) $[7/4]$ $[7/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(5 t + 20\right) x^{4} + 20 x^{3} + 5$
5.15.21.29 $x^{15} + 30 x^{14} + 405 x^{13} + 1975 x^{12} + 4050 x^{11} + 3015 x^{10} + 1300 x^{9} + 2175 x^{8} + 3000 x^{7} + 1500 x^{6} + 75 x^{5} + 750 x^{4} + 750 x^{3} + 125$ $5$ $5$ $3$ $21$ $F_5\times C_3$ (as 15T8) $[7/4]$ $[7/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(5 t + 10\right) x^{4} + 10 x^{3} + 5$
5.15.21.44 $x^{15} - 75 x^{14} + 4095 x^{13} + 86625 x^{12} + 61425 x^{11} - 16860 x^{10} + 2625 x^{9} + 20700 x^{8} - 11250 x^{7} + 3375 x^{6} + 75 x^{5} - 1875 x^{4} + 1125 x^{3} + 125$ $5$ $5$ $3$ $21$ $F_5\times C_3$ (as 15T8) $[7/4]$ $[7/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(20 t^{2} + 15 t + 15\right) x^{4} + 15 x^{3} + 5$
5.15.24.36 $x^{15} + 30 x^{14} + 300 x^{13} + 1000 x^{12} - 360 x^{10} - 7200 x^{9} - 36000 x^{8} + 133200 x^{5} + 1332000 x^{4} + 10472000$ $5$ $5$ $3$ $24$ $F_5\times C_3$ (as 15T8) $[2]$ $[2]^{12}$ $t^{3} + 3 t + 3$ $x^{5} + 10 x^{4} + 100 t^{2} + 100 t + 80$
5.15.24.58 $x^{15} + 45 x^{14} + 675 x^{13} + 3375 x^{12} - 435 x^{10} - 13050 x^{9} - 97875 x^{8} + 87450 x^{5} + 1311750 x^{4} + 1338875$ $5$ $5$ $3$ $24$ $F_5\times C_3$ (as 15T8) $[2]$ $[2]^{12}$ $t^{3} + 3 t + 3$ $x^{5} + 15 x^{4} + 75 t^{2} + 50 t + 5$
5.15.27.32 $x^{15} - 300 x^{11} + 315 x^{10} + 5625 x^{9} - 5625 x^{8} + 73125 x^{7} + 2082625 x^{6} + 7656825 x^{5} + 14887500 x^{4} + 7737500 x^{3} + 6740625 x^{2} + 5280000 x + 1307625$ $5$ $5$ $3$ $27$ $F_5\times C_3$ (as 15T8) $[9/4]$ $[9/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(50 t^{2} + 25 t + 100\right) x^{2} + \left(75 t^{2} + 50\right) x + 100 t + 105$
5.15.27.38 $x^{15} + 300 x^{12} + 225 x^{11} - 135 x^{10} + 31875 x^{9} + 52500 x^{8} + 10500 x^{7} + 1146625 x^{6} + 2882325 x^{5} + 2128125 x^{4} + 1106250 x^{3} + 1779375 x^{2} + 446250 x - 397375$ $5$ $5$ $3$ $27$ $F_5\times C_3$ (as 15T8) $[9/4]$ $[9/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(25 t + 100\right) x^{2} + \left(50 t + 75\right) x + 25 t^{2} + 50 t + 5$
5.15.27.39 $x^{15} - 225 x^{12} - 135 x^{10} + 41250 x^{9} + 97500 x^{8} + 147750 x^{7} + 5776875 x^{6} + 73575 x^{5} + 9300000 x^{4} - 5512500 x^{3} - 193125 x^{2} - 5475000 x + 496375$ $5$ $5$ $3$ $27$ $F_5\times C_3$ (as 15T8) $[9/4]$ $[9/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(75 t^{2} + 50 t + 75\right) x^{2} + 100 t x + 50 t^{2} + 100 t + 55$
5.15.27.40 $x^{15} - 300 x^{12} - 435 x^{10} + 13125 x^{9} + 28125 x^{8} + 152625 x^{7} + 5455625 x^{6} + 10418700 x^{5} + 28940625 x^{4} + 35031250 x^{3} + 37989375 x^{2} + 19012500 x + 6901375$ $5$ $5$ $3$ $27$ $F_5\times C_3$ (as 15T8) $[9/4]$ $[9/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(75 t^{2} + 50\right) x^{2} + \left(50 t^{2} + 75 t + 100\right) x + 100 t^{2} + 100 t + 55$
5.15.27.45 $x^{15} - 450 x^{11} - 135 x^{10} + 69375 x^{7} + 23625 x^{6} - 10800 x^{5} + 2484375 x^{3} + 16143750 x^{2} + 17566875 x + 5308875$ $5$ $5$ $3$ $27$ $F_5\times C_3$ (as 15T8) $[9/4]$ $[9/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(75 t^{2} + 25 t\right) x + 75 t^{2} + 105$
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