Learn more

Refine search


Results (44 matches)

  displayed columns for results
Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
5.10.10.11 $x^{10} - 20 x^{6} + 10 x^{5} - 100 x^{2} - 100 x + 25$ $5$ $5$ $2$ $10$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[5/4]$ $[5/4, 5/4]_{4}^{2}$ $t^{2} + 4 t + 2$ $x^{5} + \left(10 t + 10\right) x + 5$
5.10.10.12 $x^{10} - 30 x^{6} + 10 x^{5} + 25 x^{2} - 150 x + 25$ $5$ $5$ $2$ $10$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[5/4]$ $[5/4, 5/4]_{4}^{2}$ $t^{2} + 4 t + 2$ $x^{5} + \left(10 t + 5\right) x + 5$
5.10.10.13 $x^{10} - 10 x^{6} + 10 x^{5} - 25 x^{2} - 50 x + 25$ $5$ $5$ $2$ $10$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[5/4]$ $[5/4, 5/4]_{4}^{2}$ $t^{2} + 4 t + 2$ $x^{5} + \left(5 t + 5\right) x + 5$
5.10.10.14 $x^{10} + 10 x^{6} + 10 x^{5} - 25 x^{2} + 50 x + 25$ $5$ $5$ $2$ $10$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[5/4]$ $[5/4, 5/4]_{4}^{2}$ $t^{2} + 4 t + 2$ $x^{5} + \left(5 t + 15\right) x + 5$
5.10.14.11 $x^{10} + 10 x^{8} - 25 x^{6} + 10 x^{5} + 50 x^{3} + 25$ $5$ $5$ $2$ $14$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[7/4]$ $[7/4, 7/4]_{4}^{2}$ $t^{2} + 4 t + 2$ $x^{5} + \left(5 t + 15\right) x^{3} + 5$
5.10.14.12 $x^{10} - 30 x^{8} + 25 x^{6} + 10 x^{5} - 150 x^{3} + 25$ $5$ $5$ $2$ $14$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[7/4]$ $[7/4, 7/4]_{4}^{2}$ $t^{2} + 4 t + 2$ $x^{5} + \left(10 t + 5\right) x^{3} + 5$
5.10.14.13 $x^{10} - 10 x^{8} - 25 x^{6} + 10 x^{5} - 50 x^{3} + 25$ $5$ $5$ $2$ $14$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[7/4]$ $[7/4, 7/4]_{4}^{2}$ $t^{2} + 4 t + 2$ $x^{5} + \left(5 t + 5\right) x^{3} + 5$
5.10.14.14 $x^{10} - 20 x^{8} - 100 x^{6} + 10 x^{5} - 100 x^{3} + 25$ $5$ $5$ $2$ $14$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[7/4]$ $[7/4, 7/4]_{4}^{2}$ $t^{2} + 4 t + 2$ $x^{5} + \left(10 t + 10\right) x^{3} + 5$
5.10.15.10 $x^{10} + 10 x^{8} + 20 x^{7} + 5 x^{6} + 5 x^{5} + 5$ $5$ $10$ $1$ $15$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[7/4]$ $[5/4, 7/4]_{4}^{2}$ $t + 3$ $x^{10} + 10 x^{8} + 20 x^{7} + 5 x^{6} + 5 x^{5} + 5$
5.10.15.11 $x^{10} + 15 x^{8} + 10 x^{7} + 5 x^{6} + 15 x^{5} + 5$ $5$ $10$ $1$ $15$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[7/4]$ $[5/4, 7/4]_{4}^{2}$ $t + 3$ $x^{10} + 15 x^{8} + 10 x^{7} + 5 x^{6} + 15 x^{5} + 5$
5.10.15.12 $x^{10} + 10 x^{8} + 15 x^{7} + 20 x^{6} + 15 x^{5} + 5$ $5$ $10$ $1$ $15$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[7/4]$ $[5/4, 7/4]_{4}^{2}$ $t + 3$ $x^{10} + 10 x^{8} + 15 x^{7} + 20 x^{6} + 15 x^{5} + 5$
5.10.15.21 $x^{10} + 5 x^{8} + 20 x^{7} + 10 x^{6} + 5 x^{5} + 10$ $5$ $10$ $1$ $15$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[7/4]$ $[5/4, 7/4]_{4}^{2}$ $t + 3$ $x^{10} + 5 x^{8} + 20 x^{7} + 10 x^{6} + 5 x^{5} + 10$
5.10.15.22 $x^{10} + 20 x^{8} + 5 x^{7} + 15 x^{6} + 5 x^{5} + 10$ $5$ $10$ $1$ $15$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[7/4]$ $[5/4, 7/4]_{4}^{2}$ $t + 3$ $x^{10} + 20 x^{8} + 5 x^{7} + 15 x^{6} + 5 x^{5} + 10$
5.10.15.23 $x^{10} + 20 x^{8} + 15 x^{7} + 10 x^{6} + 5 x^{5} + 10$ $5$ $10$ $1$ $15$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[7/4]$ $[5/4, 7/4]_{4}^{2}$ $t + 3$ $x^{10} + 20 x^{8} + 15 x^{7} + 10 x^{6} + 5 x^{5} + 10$
5.10.15.24 $x^{10} + 5 x^{8} + 10 x^{7} + 15 x^{6} + 5 x^{5} + 10$ $5$ $10$ $1$ $15$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[7/4]$ $[5/4, 7/4]_{4}^{2}$ $t + 3$ $x^{10} + 5 x^{8} + 10 x^{7} + 15 x^{6} + 5 x^{5} + 10$
5.10.15.9 $x^{10} + 15 x^{8} + 5 x^{7} + 20 x^{6} + 5 x^{5} + 5$ $5$ $10$ $1$ $15$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[7/4]$ $[5/4, 7/4]_{4}^{2}$ $t + 3$ $x^{10} + 15 x^{8} + 5 x^{7} + 20 x^{6} + 5 x^{5} + 5$
5.10.17.21 $x^{10} + 10 x^{9} + 10 x^{8} + 15 x^{5} + 30$ $5$ $10$ $1$ $17$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[2]$ $[3/2, 2]_{4}^{2}$ $t + 3$ $x^{10} + 10 x^{9} + 10 x^{8} + 15 x^{5} + 30$
5.10.17.22 $x^{10} + 20 x^{9} + 10 x^{8} + 5 x^{5} + 105$ $5$ $10$ $1$ $17$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[2]$ $[3/2, 2]_{4}^{2}$ $t + 3$ $x^{10} + 20 x^{9} + 10 x^{8} + 5 x^{5} + 105$
5.10.17.23 $x^{10} + 15 x^{9} + 15 x^{8} + 15 x^{5} + 5$ $5$ $10$ $1$ $17$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[2]$ $[3/2, 2]_{4}^{2}$ $t + 3$ $x^{10} + 15 x^{9} + 15 x^{8} + 15 x^{5} + 5$
5.10.17.24 $x^{10} + 5 x^{9} + 15 x^{8} + 5 x^{5} + 5$ $5$ $10$ $1$ $17$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[2]$ $[3/2, 2]_{4}^{2}$ $t + 3$ $x^{10} + 5 x^{9} + 15 x^{8} + 5 x^{5} + 5$
5.10.17.45 $x^{10} + 5 x^{9} + 5 x^{8} + 5 x^{5} + 10$ $5$ $10$ $1$ $17$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[2]$ $[3/2, 2]_{4}^{2}$ $t + 3$ $x^{10} + 5 x^{9} + 5 x^{8} + 5 x^{5} + 10$
5.10.17.46 $x^{10} + 10 x^{9} + 5 x^{8} + 5 x^{5} + 60$ $5$ $10$ $1$ $17$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[2]$ $[3/2, 2]_{4}^{2}$ $t + 3$ $x^{10} + 10 x^{9} + 5 x^{8} + 5 x^{5} + 60$
5.10.17.47 $x^{10} + 20 x^{9} + 20 x^{8} + 5 x^{5} + 110$ $5$ $10$ $1$ $17$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[2]$ $[3/2, 2]_{4}^{2}$ $t + 3$ $x^{10} + 20 x^{9} + 20 x^{8} + 5 x^{5} + 110$
5.10.17.48 $x^{10} + 15 x^{9} + 20 x^{8} + 5 x^{5} + 85$ $5$ $10$ $1$ $17$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[2]$ $[3/2, 2]_{4}^{2}$ $t + 3$ $x^{10} + 15 x^{9} + 20 x^{8} + 5 x^{5} + 85$
5.10.18.10 $x^{10} - 100 x^{7} - 200 x^{6} + 60 x^{5} - 8750 x^{4} - 20000 x^{3} - 13000 x^{2} - 6000 x + 900$ $5$ $5$ $2$ $18$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[9/4]$ $[5/4, 9/4]_{4}^{2}$ $t^{2} + 4 t + 2$ $x^{5} + \left(75 t + 100\right) x^{2} + \left(100 t + 100\right) x + 30$
5.10.18.11 $x^{10} - 150 x^{7} - 150 x^{6} + 60 x^{5} + 625 x^{4} - 3750 x^{3} - 10125 x^{2} - 4500 x + 900$ $5$ $5$ $2$ $18$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[9/4]$ $[5/4, 9/4]_{4}^{2}$ $t^{2} + 4 t + 2$ $x^{5} + \left(50 t + 25\right) x^{2} + \left(75 t + 75\right) x + 30$
5.10.18.12 $x^{10} + 50 x^{7} - 400 x^{6} + 60 x^{5} - 625 x^{4} - 20000 x^{3} + 21500 x^{2} - 12000 x + 900$ $5$ $5$ $2$ $18$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[9/4]$ $[5/4, 9/4]_{4}^{2}$ $t^{2} + 4 t + 2$ $x^{5} + \left(25 t + 75\right) x^{2} + 100 t x + 30$
5.10.18.13 $x^{10} - 100 x^{7} - 300 x^{6} + 60 x^{5} - 2500 x^{4} - 5000 x^{3} - 500 x^{2} - 9000 x + 900$ $5$ $5$ $2$ $18$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[9/4]$ $[5/4, 9/4]_{4}^{2}$ $t^{2} + 4 t + 2$ $x^{5} + \left(50 t + 50\right) x^{2} + \left(100 t + 50\right) x + 30$
5.10.18.14 $x^{10} - 150 x^{7} - 100 x^{6} + 60 x^{5} - 5625 x^{4} - 15000 x^{3} - 13250 x^{2} - 3000 x + 900$ $5$ $5$ $2$ $18$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[9/4]$ $[5/4, 9/4]_{4}^{2}$ $t^{2} + 4 t + 2$ $x^{5} + \left(75 t + 75\right) x^{2} + \left(75 t + 100\right) x + 30$
5.10.18.15 $x^{10} - 200 x^{7} - 350 x^{6} + 60 x^{5} - 10000 x^{4} - 5000 x^{3} + 4625 x^{2} - 10500 x + 900$ $5$ $5$ $2$ $18$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[9/4]$ $[5/4, 9/4]_{4}^{2}$ $t^{2} + 4 t + 2$ $x^{5} + \left(100 t + 100\right) x^{2} + \left(100 t + 25\right) x + 30$
5.10.18.6 $x^{10} - 300 x^{7} - 300 x^{6} + 60 x^{5} + 2500 x^{4} + 15000 x^{3} + 2250 x^{2} - 9000 x + 900$ $5$ $5$ $2$ $18$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[9/4]$ $[5/4, 9/4]_{4}^{2}$ $t^{2} + 4 t + 2$ $x^{5} + \left(100 t + 50\right) x^{2} + 75 t x + 30$
5.10.18.7 $x^{10} + 150 x^{7} - 250 x^{6} + 60 x^{5} + 5625 x^{4} - 18750 x^{3} + 8875 x^{2} - 7500 x + 900$ $5$ $5$ $2$ $18$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[9/4]$ $[5/4, 9/4]_{4}^{2}$ $t^{2} + 4 t + 2$ $x^{5} + 75 x^{2} + \left(75 t + 25\right) x + 30$
5.10.18.8 $x^{10} + 100 x^{7} - 250 x^{6} + 60 x^{5} + 2500 x^{4} - 12500 x^{3} - 1375 x^{2} - 7500 x + 900$ $5$ $5$ $2$ $18$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[9/4]$ $[5/4, 9/4]_{4}^{2}$ $t^{2} + 4 t + 2$ $x^{5} + 50 x^{2} + \left(100 t + 75\right) x + 30$
5.10.18.9 $x^{10} - 50 x^{7} - 200 x^{6} + 60 x^{5} - 625 x^{4} - 2500 x^{3} - 2750 x^{2} - 6000 x + 900$ $5$ $5$ $2$ $18$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[9/4]$ $[5/4, 9/4]_{4}^{2}$ $t^{2} + 4 t + 2$ $x^{5} + \left(25 t + 25\right) x^{2} + \left(75 t + 50\right) x + 30$
5.10.19.21 $x^{10} + 5 x^{5} + 100 x^{3} + 100 x + 110$ $5$ $10$ $1$ $19$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[9/4]$ $[7/4, 9/4]_{4}^{2}$ $t + 3$ $x^{10} + 5 x^{5} + 100 x^{3} + 100 x + 110$
5.10.19.22 $x^{10} + 5 x^{5} + 50 x^{3} + 50 x^{2} + 50 x + 35$ $5$ $10$ $1$ $19$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[9/4]$ $[7/4, 9/4]_{4}^{2}$ $t + 3$ $x^{10} + 5 x^{5} + 50 x^{3} + 50 x^{2} + 50 x + 35$
5.10.19.23 $x^{10} + 5 x^{5} + 50 x^{3} + 50 x^{2} + 100 x + 60$ $5$ $10$ $1$ $19$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[9/4]$ $[7/4, 9/4]_{4}^{2}$ $t + 3$ $x^{10} + 5 x^{5} + 50 x^{3} + 50 x^{2} + 100 x + 60$
5.10.19.24 $x^{10} + 5 x^{5} + 25 x^{3} + 100 x^{2} + 50 x + 110$ $5$ $10$ $1$ $19$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[9/4]$ $[7/4, 9/4]_{4}^{2}$ $t + 3$ $x^{10} + 5 x^{5} + 25 x^{3} + 100 x^{2} + 50 x + 110$
5.10.19.25 $x^{10} + 5 x^{5} + 100 x^{2} + 100 x + 10$ $5$ $10$ $1$ $19$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[9/4]$ $[7/4, 9/4]_{4}^{2}$ $t + 3$ $x^{10} + 5 x^{5} + 100 x^{2} + 100 x + 10$
5.10.19.26 $x^{10} + 5 x^{5} + 25 x^{2} + 50 x + 60$ $5$ $10$ $1$ $19$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[9/4]$ $[7/4, 9/4]_{4}^{2}$ $t + 3$ $x^{10} + 5 x^{5} + 25 x^{2} + 50 x + 60$
5.10.19.27 $x^{10} + 5 x^{5} + 75 x^{3} + 25 x^{2} + 100 x + 85$ $5$ $10$ $1$ $19$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[9/4]$ $[7/4, 9/4]_{4}^{2}$ $t + 3$ $x^{10} + 5 x^{5} + 75 x^{3} + 25 x^{2} + 100 x + 85$
5.10.19.28 $x^{10} + 5 x^{5} + 100 x^{3} + 75 x^{2} + 50 x + 10$ $5$ $10$ $1$ $19$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[9/4]$ $[7/4, 9/4]_{4}^{2}$ $t + 3$ $x^{10} + 5 x^{5} + 100 x^{3} + 75 x^{2} + 50 x + 10$
5.10.19.29 $x^{10} + 5 x^{5} + 25 x^{3} + 75 x^{2} + 100 x + 35$ $5$ $10$ $1$ $19$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[9/4]$ $[7/4, 9/4]_{4}^{2}$ $t + 3$ $x^{10} + 5 x^{5} + 25 x^{3} + 75 x^{2} + 100 x + 35$
5.10.19.30 $x^{10} + 5 x^{5} + 75 x^{3} + 50 x + 85$ $5$ $10$ $1$ $19$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[9/4]$ $[7/4, 9/4]_{4}^{2}$ $t + 3$ $x^{10} + 5 x^{5} + 75 x^{3} + 50 x + 85$
  displayed columns for results