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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
5.15.0.1 $x^{15} + 2 x^{5} + 3 x^{3} + 3 x^{2} + 4 x + 3$ $5$ $1$ $15$ $0$ $C_{15}$ (as 15T1) $[\ ]$ $[\ ]^{15}$ $t^{15} + 2 t^{5} + 3 t^{3} + 3 t^{2} + 4 t + 3$ $x - 5$
5.15.10.1 $x^{15} + 25 x^{12} + 12 x^{11} + 9 x^{10} + 250 x^{9} - 900 x^{8} - 1302 x^{7} + 1322 x^{6} - 1773 x^{5} + 11325 x^{4} + 4989 x^{3} + 16494 x^{2} - 717 x + 2572$ $5$ $3$ $5$ $10$ $S_3 \times C_5$ (as 15T4) $[\ ]$ $[\ ]_{3}^{10}$ $t^{5} + 4 t + 3$ $x^{3} + 5$
5.15.15.1 $x^{15} - 75 x^{12} + 60 x^{11} + 15 x^{10} + 1650 x^{9} - 1950 x^{8} + 525 x^{7} + 99225 x^{6} + 29700 x^{5} - 750 x^{4} - 625 x^{3} + 4500 x^{2} + 1500 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(20 t^{2} + 5 t + 15\right) x^{2} + \left(5 t + 20\right) x + 5$
5.15.15.2 $x^{15} + 30 x^{12} - 60 x^{11} + 15 x^{10} + 300 x^{9} - 1200 x^{8} + 3675 x^{7} + 400 x^{6} - 5925 x^{5} + 35250 x^{4} + 101375 x^{3} + 17625 x^{2} - 1500 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + 10 x^{2} + \left(20 t^{2} + 15 t + 20\right) x + 5$
5.15.15.3 $x^{15} - 30 x^{12} - 90 x^{11} + 15 x^{10} + 1275 x^{9} + 2775 x^{8} + 2475 x^{7} + 51725 x^{6} + 127575 x^{5} + 110250 x^{4} + 33750 x^{3} + 13125 x^{2} - 2250 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(15 t^{2} + 10 t + 20\right) x^{2} + \left(15 t^{2} + 5 t\right) x + 5$
5.15.15.4 $x^{15} + 15 x^{12} - 45 x^{11} + 15 x^{10} + 2100 x^{9} + 1875 x^{8} + 1050 x^{7} + 3675 x^{6} + 19575 x^{5} + 27375 x^{4} + 19250 x^{3} + 4875 x^{2} - 1125 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(5 t^{2} + 20 t + 15\right) x^{2} + \left(10 t^{2} + 5 t + 5\right) x + 5$
5.15.15.5 $x^{15} + 15 x^{10} + 900 x^{9} + 2400 x^{8} + 1275 x^{7} + 23000 x^{6} + 46575 x^{5} + 30750 x^{4} + 13375 x^{3} + 6375 x^{2} + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(10 t^{2} + 10 t + 20\right) x^{2} + \left(5 t^{2} + 15 t + 10\right) x + 5$
5.15.15.6 $x^{15} - 60 x^{12} + 15 x^{10} + 3900 x^{9} + 2250 x^{8} - 375 x^{7} - 33000 x^{6} + 46575 x^{5} + 84000 x^{4} + 27875 x^{3} - 375 x^{2} + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(10 t^{2} + 20 t\right) x^{2} + \left(10 t^{2} + 5 t + 20\right) x + 5$
5.15.15.7 $x^{15} - 90 x^{12} - 30 x^{11} + 15 x^{10} + 1500 x^{9} + 3000 x^{8} + 75 x^{7} + 96700 x^{6} + 51075 x^{5} + 12750 x^{4} + 10875 x^{3} + 2625 x^{2} - 750 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(20 t^{2} + 10\right) x^{2} + \left(5 t^{2} + 10 t\right) x + 5$
5.15.15.8 $x^{15} + 30 x^{12} + 15 x^{11} + 15 x^{10} + 975 x^{9} + 750 x^{8} + 450 x^{7} - 2225 x^{6} - 675 x^{5} + 5250 x^{4} + 3875 x^{3} + 1500 x^{2} + 375 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(15 t + 10\right) x^{2} + \left(5 t + 5\right) x + 5$
5.15.15.9 $x^{15} - 30 x^{12} + 15 x^{11} + 15 x^{10} + 2325 x^{9} + 2100 x^{8} + 450 x^{7} - 27225 x^{6} - 8925 x^{5} + 26250 x^{4} + 17625 x^{3} + 3000 x^{2} + 375 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(5 t^{2} + 20 t\right) x^{2} + \left(5 t^{2} + 10 t + 15\right) x + 5$
5.15.15.10 $x^{15} - 45 x^{12} - 60 x^{11} + 15 x^{10} + 750 x^{9} + 1725 x^{8} + 525 x^{7} + 44025 x^{6} + 178200 x^{5} + 240750 x^{4} + 113750 x^{3} + 3750 x^{2} - 1500 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(15 t^{2} + 5 t + 15\right) x^{2} + \left(20 t^{2} + 5 t + 20\right) x + 5$
5.15.15.11 $x^{15} + 15 x^{10} + 300 x^{9} + 300 x^{8} + 75 x^{7} - 3000 x^{6} - 4425 x^{5} - 750 x^{4} + 1125 x^{3} + 375 x^{2} + 125$ $5$ $5$ $3$ $15$ $(C_5^2 : C_4):C_3$ (as 15T19) $[5/4]$ $[5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + 10 t x^{2} + 5 t x + 5$
5.15.15.12 $x^{15} - 45 x^{12} + 45 x^{11} + 15 x^{10} + 750 x^{9} + 1950 x^{8} + 1425 x^{7} + 45075 x^{6} + 15825 x^{5} + 43125 x^{4} + 7125 x^{3} + 8250 x^{2} + 1125 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(15 t^{2} + 5 t + 15\right) x^{2} + \left(20 t + 15\right) x + 5$
5.15.15.13 $x^{15} + 30 x^{12} + 15 x^{11} + 15 x^{10} + 525 x^{9} + 1800 x^{8} + 1575 x^{7} + 6275 x^{6} + 23700 x^{5} + 16875 x^{4} - 8875 x^{3} + 7125 x^{2} + 375 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(5 t^{2} + 5 t + 20\right) x^{2} + \left(20 t + 5\right) x + 5$
5.15.15.14 $x^{15} + 15 x^{12} - 30 x^{11} + 15 x^{10} + 150 x^{9} + 675 x^{8} + 1425 x^{7} - 175 x^{6} + 3450 x^{5} + 12000 x^{4} + 56000 x^{3} + 6750 x^{2} - 750 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(5 t + 5\right) x^{2} + \left(15 t^{2} + 10 t + 20\right) x + 5$
5.15.15.15 $x^{15} - 30 x^{12} + 15 x^{10} + 2025 x^{9} + 2550 x^{8} + 600 x^{7} + 9625 x^{6} + 54825 x^{5} + 76125 x^{4} + 35750 x^{3} + 3750 x^{2} + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(10 t^{2} + 15 t + 10\right) x^{2} + \left(10 t^{2} + 10 t + 20\right) x + 5$
5.15.15.16 $x^{15} - 75 x^{12} - 90 x^{11} + 15 x^{10} + 2775 x^{9} + 3900 x^{8} + 750 x^{7} + 93975 x^{6} + 279825 x^{5} + 294375 x^{4} + 116500 x^{3} + 5625 x^{2} - 2250 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(20 t^{2} + 10 t + 15\right) x^{2} + \left(20 t^{2} + 10\right) x + 5$
5.15.15.17 $x^{15} - 90 x^{12} - 15 x^{11} + 15 x^{10} + 3675 x^{9} + 3825 x^{8} + 450 x^{7} + 6975 x^{6} - 8550 x^{5} + 7125 x^{4} + 14000 x^{3} + 4500 x^{2} - 375 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(15 t^{2} + 10 t\right) x^{2} + \left(5 t^{2} + 15 t + 5\right) x + 5$
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) $[5/4]$ $[5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(15 t^{2} + 20 t + 10\right) x^{2} + 20 x + 5$
5.15.15.19 $x^{15} - 60 x^{12} - 75 x^{11} + 15 x^{10} + 1425 x^{9} + 5100 x^{8} + 4875 x^{7} + 3375 x^{6} + 34950 x^{5} + 97125 x^{4} + 103875 x^{3} + 25875 x^{2} - 1875 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(10 t^{2} + 5 t\right) x^{2} + \left(20 t^{2} + 20 t + 15\right) x + 5$
5.15.15.20 $x^{15} - 90 x^{12} + 30 x^{11} + 15 x^{10} + 2025 x^{9} - 225 x^{8} + 675 x^{7} + 30675 x^{6} + 40575 x^{5} + 31500 x^{4} + 14000 x^{3} + 5625 x^{2} + 750 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + 15 t^{2} x^{2} + \left(5 t^{2} + 15 t + 20\right) x + 5$
5.15.15.21 $x^{15} + 45 x^{12} + 30 x^{11} + 15 x^{10} + 750 x^{9} + 1500 x^{8} + 1950 x^{7} + 4425 x^{6} + 12075 x^{5} + 14250 x^{4} - 3500 x^{3} + 8625 x^{2} + 750 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(5 t + 15\right) x^{2} + \left(20 t + 10\right) x + 5$
5.15.15.22 $x^{15} + 45 x^{12} - 30 x^{11} + 15 x^{10} + 1875 x^{9} + 600 x^{8} + 975 x^{7} - 2925 x^{6} - 2175 x^{5} + 8250 x^{4} + 2625 x^{3} + 3750 x^{2} - 750 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(20 t + 15\right) x^{2} + \left(5 t^{2} + 5 t\right) x + 5$
5.15.15.23 $x^{15} - 30 x^{12} - 90 x^{11} + 15 x^{10} + 1800 x^{8} + 3375 x^{7} + 12100 x^{6} + 58575 x^{5} + 70500 x^{4} + 16125 x^{3} + 17625 x^{2} - 2250 x + 125$ $5$ $5$ $3$ $15$ $(C_5^2 : C_4):C_3$ (as 15T19) $[5/4]$ $[5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(10 t^{2} + 10\right) x^{2} + \left(15 t^{2} + 10 t\right) x + 5$
5.15.15.24 $x^{15} - 60 x^{12} - 60 x^{11} + 15 x^{10} + 525 x^{9} + 2175 x^{8} + 825 x^{7} + 42025 x^{6} + 78450 x^{5} + 43875 x^{4} + 15000 x^{3} + 5625 x^{2} - 1500 x + 125$ $5$ $5$ $3$ $15$ $(C_5^2 : C_4):C_3$ (as 15T19) $[5/4]$ $[5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(15 t^{2} + 10\right) x^{2} + \left(10 t^{2} + 5 t\right) x + 5$
5.15.15.25 $x^{15} - 45 x^{12} - 60 x^{11} + 15 x^{10} + 3375 x^{9} + 8400 x^{8} + 4350 x^{7} - 15475 x^{6} + 13575 x^{5} + 136875 x^{4} + 146000 x^{3} + 22875 x^{2} - 1500 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(10 t^{2} + 20 t + 5\right) x^{2} + \left(20 t^{2} + 20 t + 20\right) x + 5$
5.15.15.26 $x^{15} - 75 x^{12} + 30 x^{11} + 15 x^{10} + 2850 x^{9} - 1500 x^{8} - 525 x^{7} + 23675 x^{6} + 82200 x^{5} + 23250 x^{4} - 5875 x^{3} - 750 x^{2} + 750 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(15 t^{2} + 10 t + 5\right) x^{2} + \left(5 t^{2} + 20\right) x + 5$
5.15.15.27 $x^{15} - 60 x^{12} + 45 x^{11} + 15 x^{10} + 975 x^{9} - 750 x^{8} + 150 x^{7} + 105575 x^{6} + 16575 x^{5} + 7500 x^{4} + 375 x^{3} + 2250 x^{2} + 1125 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(20 t^{2} + 5 t + 20\right) x^{2} + \left(5 t + 15\right) x + 5$
5.15.15.28 $x^{15} - 15 x^{12} - 75 x^{11} + 15 x^{10} + 1800 x^{9} + 2250 x^{8} + 525 x^{7} + 18375 x^{6} + 94575 x^{5} + 154125 x^{4} + 113625 x^{3} + 3000 x^{2} - 1875 x + 125$ $5$ $5$ $3$ $15$ $(C_5^2 : C_4):C_3$ (as 15T19) $[5/4]$ $[5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(10 t^{2} + 15 t + 15\right) x^{2} + \left(20 t^{2} + 15\right) x + 5$
5.15.15.29 $x^{15} + 30 x^{12} - 30 x^{11} + 15 x^{10} + 2325 x^{9} + 2550 x^{8} + 1500 x^{7} + 14825 x^{6} + 36825 x^{5} + 44625 x^{4} + 25750 x^{3} + 6750 x^{2} - 750 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(5 t^{2} + 20 t + 20\right) x^{2} + \left(10 t^{2} + 10 t + 10\right) x + 5$
5.15.15.30 $x^{15} - 45 x^{11} + 15 x^{10} + 2700 x^{9} + 1800 x^{8} + 28550 x^{6} + 99075 x^{5} + 101250 x^{4} + 52875 x^{3} - 1125 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(10 t^{2} + 20 t + 20\right) x^{2} + \left(15 t^{2} + 15\right) x + 5$
5.15.15.31 $x^{15} - 15 x^{12} + 45 x^{11} + 15 x^{10} + 1350 x^{9} + 900 x^{8} + 825 x^{7} - 4675 x^{6} + 4575 x^{5} + 11625 x^{4} + 9375 x^{3} + 4500 x^{2} + 1125 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(5 t^{2} + 15 t + 5\right) x^{2} + \left(10 t + 15\right) x + 5$
5.15.15.32 $x^{15} + 30 x^{12} - 15 x^{11} + 15 x^{10} + 300 x^{9} - 300 x^{8} + 2100 x^{7} + 850 x^{6} - 1425 x^{5} + 19500 x^{4} + 17625 x^{3} + 9750 x^{2} - 375 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + 10 x^{2} + \left(10 t^{2} + 15 t + 15\right) x + 5$
5.15.15.33 $x^{15} - 45 x^{12} - 60 x^{11} + 15 x^{10} + 375 x^{9} + 2250 x^{8} + 2775 x^{7} + 11525 x^{6} + 48825 x^{5} + 72750 x^{4} + 40375 x^{3} + 15000 x^{2} - 1500 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(10 t^{2} + 5\right) x^{2} + \left(15 t^{2} + 15 t + 10\right) x + 5$
5.15.15.34 $x^{15} - 45 x^{12} - 30 x^{11} + 15 x^{10} + 1650 x^{9} + 3825 x^{8} + 1125 x^{7} + 45075 x^{6} + 37200 x^{5} - 750 x^{4} + 6750 x^{3} + 6750 x^{2} - 750 x + 125$ $5$ $5$ $3$ $15$ $(C_5^2 : C_4):C_3$ (as 15T19) $[5/4]$ $[5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(15 t^{2} + 10 t + 15\right) x^{2} + \left(5 t^{2} + 15 t\right) x + 5$
5.15.15.35 $x^{15} - 60 x^{12} + 30 x^{11} + 15 x^{10} + 2100 x^{9} + 1050 x^{8} + 375 x^{7} - 2700 x^{6} - 5925 x^{5} + 6750 x^{4} + 2875 x^{3} + 3375 x^{2} + 750 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(10 t^{2} + 10 t\right) x^{2} + \left(15 t + 10\right) x + 5$
5.15.15.36 $x^{15} - 75 x^{12} - 75 x^{11} + 15 x^{10} + 1200 x^{9} + 3075 x^{8} + 1200 x^{7} + 37625 x^{6} + 108450 x^{5} + 108000 x^{4} + 47000 x^{3} + 7875 x^{2} - 1875 x + 125$ $5$ $5$ $3$ $15$ $(C_5^2 : C_4):C_3$ (as 15T19) $[5/4]$ $[5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(15 t^{2} + 5\right) x^{2} + \left(15 t^{2} + 5 t + 5\right) x + 5$
5.15.15.37 $x^{15} - 75 x^{12} - 120 x^{11} + 15 x^{10} + 5475 x^{9} + 13200 x^{8} + 7650 x^{7} + 77175 x^{6} + 153075 x^{5} + 81375 x^{4} + 42000 x^{3} + 40125 x^{2} - 3000 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(20 t^{2} + 20 t + 15\right) x^{2} + \left(20 t^{2} + 20 t\right) x + 5$
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) $[5/4]$ $[5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(15 t^{2} + 20 t + 10\right) x^{2} + 15 x + 5$
5.15.15.39 $x^{15} - 60 x^{12} + 15 x^{10} + 900 x^{9} - 300 x^{8} - 675 x^{7} + 9000 x^{6} + 22575 x^{5} + 14250 x^{4} - 125 x^{3} - 1875 x^{2} + 125$ $5$ $5$ $3$ $15$ $(C_5^2 : C_4):C_3$ (as 15T19) $[5/4]$ $[5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + 10 t^{2} x^{2} + \left(5 t^{2} + 10\right) x + 5$
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) $[5/4]$ $[5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(15 t^{2} + 20 t + 15\right) x^{2} + 5 x + 5$
5.15.15.41 $x^{15} - 60 x^{12} - 45 x^{11} + 15 x^{10} + 4425 x^{9} + 5250 x^{8} + 975 x^{7} + 16675 x^{6} + 37200 x^{5} + 48375 x^{4} + 32375 x^{3} + 6375 x^{2} - 1125 x + 125$ $5$ $5$ $3$ $15$ $(C_5^2 : C_4):C_3$ (as 15T19) $[5/4]$ $[5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(15 t^{2} + 20 t + 10\right) x^{2} + \left(10 t^{2} + 10 t + 5\right) x + 5$
5.15.15.42 $x^{15} - 75 x^{12} - 90 x^{11} + 15 x^{10} + 3900 x^{9} + 8775 x^{8} + 4125 x^{7} + 10475 x^{6} + 73200 x^{5} + 146250 x^{4} + 110500 x^{3} + 22500 x^{2} - 2250 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(15 t^{2} + 15 t + 5\right) x^{2} + \left(20 t^{2} + 15 t + 10\right) x + 5$
5.15.15.43 $x^{15} - 60 x^{12} - 90 x^{11} + 15 x^{10} + 4800 x^{9} + 7800 x^{8} + 3000 x^{7} + 103100 x^{6} + 276075 x^{5} + 276000 x^{4} + 118000 x^{3} + 16500 x^{2} - 2250 x + 125$ $5$ $5$ $3$ $15$ $C_5^3:C_{12}$ (as 15T38) $[5/4]$ $[5/4, 5/4, 5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(20 t^{2} + 20 t + 20\right) x^{2} + \left(20 t^{2} + 10 t + 10\right) x + 5$
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) $[5/4]$ $[5/4]_{4}^{3}$ $t^{3} + 3 t + 3$ $x^{5} + \left(5 t^{2} + 10 t + 15\right) x^{2} + 10 x + 5$
5.15.15.45 $x^{15} + 10 x^{2} + 15 x + 5$ $5$ $15$ $1$ $15$ $C_5^2:(C_4\times S_3)$ (as 15T27) $[13/12]$ $[13/12, 13/12]_{12}^{2}$ $t + 3$ $x^{15} + 10 x^{2} + 15 x + 5$
5.15.15.46 $x^{15} + 10 x^{2} + 10 x + 5$ $5$ $15$ $1$ $15$ $C_5^2:(C_4\times S_3)$ (as 15T27) $[13/12]$ $[13/12, 13/12]_{12}^{2}$ $t + 3$ $x^{15} + 10 x^{2} + 10 x + 5$
5.15.15.47 $x^{15} + 15 x^{2} + 5 x + 5$ $5$ $15$ $1$ $15$ $C_5^2:(C_4\times S_3)$ (as 15T27) $[13/12]$ $[13/12, 13/12]_{12}^{2}$ $t + 3$ $x^{15} + 15 x^{2} + 5 x + 5$
5.15.15.48 $x^{15} + 10 x^{2} + 20 x + 5$ $5$ $15$ $1$ $15$ $C_5^2:(C_4\times S_3)$ (as 15T27) $[13/12]$ $[13/12, 13/12]_{12}^{2}$ $t + 3$ $x^{15} + 10 x^{2} + 20 x + 5$
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