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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.10.10.15 $x^{10} + 2 x + 2$ $2$ $10$ $1$ $10$ $(C_2^4 : C_5):C_4$ (as 10T24) $[6/5]$ $[6/5, 6/5, 6/5, 6/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x + 2$
2.10.10.16 $x^{10} + 2 x^{2} + 2 x + 2$ $2$ $10$ $1$ $10$ $(C_2^4 : C_5):C_4$ (as 10T25) $[6/5]$ $[6/5, 6/5, 6/5, 6/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{2} + 2 x + 2$
2.10.12.1 $x^{10} + 2 x^{6} + 2 x^{3} + 2$ $2$ $10$ $1$ $12$ $(C_2^4 : C_5):C_4$ (as 10T24) $[8/5]$ $[8/5, 8/5, 8/5, 8/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{6} + 2 x^{3} + 2$
2.10.12.2 $x^{10} + 2 x^{6} + 2 x^{5} + 2 x^{3} + 2$ $2$ $10$ $1$ $12$ $(C_2^4 : C_5):C_4$ (as 10T24) $[8/5]$ $[8/5, 8/5, 8/5, 8/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{6} + 2 x^{5} + 2 x^{3} + 2$
2.10.12.3 $x^{10} + 2 x^{3} + 2$ $2$ $10$ $1$ $12$ $(C_2^4 : C_5):C_4$ (as 10T25) $[8/5]$ $[8/5, 8/5, 8/5, 8/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{3} + 2$
2.10.12.4 $x^{10} + 2 x^{5} + 2 x^{3} + 2$ $2$ $10$ $1$ $12$ $(C_2^4 : C_5):C_4$ (as 10T25) $[8/5]$ $[8/5, 8/5, 8/5, 8/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{5} + 2 x^{3} + 2$
2.10.14.1 $x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{5} + 2 x^{4} + 2$ $2$ $10$ $1$ $14$ $F_{5}\times C_2$ (as 10T5) $[2]$ $[2]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{5} + 2 x^{4} + 2$
2.10.14.2 $x^{10} + 2 x^{9} + 2 x^{5} + 2$ $2$ $10$ $1$ $14$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[2]$ $[6/5, 6/5, 6/5, 6/5, 2]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{5} + 2$
2.10.14.3 $x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{5} + 2$ $2$ $10$ $1$ $14$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[2]$ $[8/5, 8/5, 8/5, 8/5, 2]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{5} + 2$
2.10.14.4 $x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{5} + 2$ $2$ $10$ $1$ $14$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[2]$ $[8/5, 8/5, 8/5, 8/5, 2]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{5} + 2$
2.10.14.5 $x^{10} + 2 x^{5} + 6$ $2$ $10$ $1$ $14$ $F_{5}\times C_2$ (as 10T5) $[2]$ $[2]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{5} + 6$
2.10.14.6 $x^{10} + 2 x^{9} + 2 x^{7} + 2 x^{5} + 2 x^{4} + 6$ $2$ $10$ $1$ $14$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[2]$ $[6/5, 6/5, 6/5, 6/5, 2]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{7} + 2 x^{5} + 2 x^{4} + 6$
2.10.14.7 $x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 2 x^{5} + 2 x^{4} + 2$ $2$ $10$ $1$ $14$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[2]$ $[8/5, 8/5, 8/5, 8/5, 2]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 2 x^{5} + 2 x^{4} + 2$
2.10.14.8 $x^{10} + 2 x^{5} + 2 x^{4} + 6$ $2$ $10$ $1$ $14$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[2]$ $[8/5, 8/5, 8/5, 8/5, 2]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{5} + 2 x^{4} + 6$
2.10.16.1 $x^{10} + 2 x^{7} + 4 x^{4} + 4 x^{2} + 2$ $2$ $10$ $1$ $16$ $(C_2^4 : C_5):C_4$ (as 10T24) $[12/5]$ $[12/5, 12/5, 12/5, 12/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{7} + 4 x^{4} + 4 x^{2} + 2$
2.10.16.10 $x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 2$ $2$ $10$ $1$ $16$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[12/5]$ $[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 2$
2.10.16.11 $x^{10} + 2 x^{9} + 2 x^{7} + 4 x^{3} + 6$ $2$ $10$ $1$ $16$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[12/5]$ $[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{7} + 4 x^{3} + 6$
2.10.16.12 $x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{4} + 4 x^{3} + 4 x^{2} + 2$ $2$ $10$ $1$ $16$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[12/5]$ $[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{4} + 4 x^{3} + 4 x^{2} + 2$
2.10.16.13 $x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 6 x^{4} + 4 x^{3} + 4 x + 6$ $2$ $10$ $1$ $16$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[12/5]$ $[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 6 x^{4} + 4 x^{3} + 4 x + 6$
2.10.16.14 $x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 4 x^{4} + 4 x^{3} + 4 x + 2$ $2$ $10$ $1$ $16$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[12/5]$ $[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 4 x^{4} + 4 x^{3} + 4 x + 2$
2.10.16.15 $x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{4} + 4 x^{2} + 2$ $2$ $10$ $1$ $16$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[12/5]$ $[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{4} + 4 x^{2} + 2$
2.10.16.16 $x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 4 x^{4} + 4 x^{2} + 2$ $2$ $10$ $1$ $16$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[12/5]$ $[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 4 x^{4} + 4 x^{2} + 2$
2.10.16.2 $x^{10} + 2 x^{8} + 2 x^{7} + 4 x^{3} + 4 x^{2} + 6$ $2$ $10$ $1$ $16$ $(C_2^4 : C_5):C_4$ (as 10T24) $[12/5]$ $[12/5, 12/5, 12/5, 12/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{8} + 2 x^{7} + 4 x^{3} + 4 x^{2} + 6$
2.10.16.3 $x^{10} + 2 x^{7} + 4 x^{4} + 4 x^{2} + 6$ $2$ $10$ $1$ $16$ $(C_2^4 : C_5):C_4$ (as 10T24) $[12/5]$ $[12/5, 12/5, 12/5, 12/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{7} + 4 x^{4} + 4 x^{2} + 6$
2.10.16.4 $x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{4} + 4 x^{2} + 4 x + 2$ $2$ $10$ $1$ $16$ $(C_2^4 : C_5):C_4$ (as 10T24) $[12/5]$ $[12/5, 12/5, 12/5, 12/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{4} + 4 x^{2} + 4 x + 2$
2.10.16.5 $x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 4 x^{2} + 2$ $2$ $10$ $1$ $16$ $(C_2^4 : C_5):C_4$ (as 10T25) $[12/5]$ $[12/5, 12/5, 12/5, 12/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 4 x^{2} + 2$
2.10.16.6 $x^{10} + 2 x^{8} + 2 x^{7} + 4 x^{4} + 4 x + 2$ $2$ $10$ $1$ $16$ $(C_2^4 : C_5):C_4$ (as 10T25) $[12/5]$ $[12/5, 12/5, 12/5, 12/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{8} + 2 x^{7} + 4 x^{4} + 4 x + 2$
2.10.16.7 $x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 4 x + 6$ $2$ $10$ $1$ $16$ $(C_2^4 : C_5):C_4$ (as 10T25) $[12/5]$ $[12/5, 12/5, 12/5, 12/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 4 x + 6$
2.10.16.8 $x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{4} + 4 x^{2} + 4 x + 6$ $2$ $10$ $1$ $16$ $(C_2^4 : C_5):C_4$ (as 10T25) $[12/5]$ $[12/5, 12/5, 12/5, 12/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{4} + 4 x^{2} + 4 x + 6$
2.10.16.9 $x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 6 x^{4} + 6$ $2$ $10$ $1$ $16$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[12/5]$ $[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 6 x^{4} + 6$
2.10.18.1 $x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x + 2$ $2$ $10$ $1$ $18$ $(C_2^4 : C_5):C_4$ (as 10T24) $[14/5]$ $[14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x + 2$
2.10.18.10 $x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{6} + 4 x + 2$ $2$ $10$ $1$ $18$ $(C_2^4 : C_5):C_4$ (as 10T25) $[14/5]$ $[14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{6} + 4 x + 2$
2.10.18.11 $x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2$ $2$ $10$ $1$ $18$ $(C_2^4 : C_5):C_4$ (as 10T25) $[14/5]$ $[14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2$
2.10.18.12 $x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 2$ $2$ $10$ $1$ $18$ $(C_2^4 : C_5):C_4$ (as 10T25) $[14/5]$ $[14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 2$
2.10.18.13 $x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{7} + 4 x^{6} + 4 x + 2$ $2$ $10$ $1$ $18$ $(C_2^4 : C_5):C_4$ (as 10T25) $[14/5]$ $[14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{7} + 4 x^{6} + 4 x + 2$
2.10.18.14 $x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x + 2$ $2$ $10$ $1$ $18$ $(C_2^4 : C_5):C_4$ (as 10T25) $[14/5]$ $[14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x + 2$
2.10.18.15 $x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 2$ $2$ $10$ $1$ $18$ $(C_2^4 : C_5):C_4$ (as 10T25) $[14/5]$ $[14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 2$
2.10.18.16 $x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{6} + 4 x^{5} + 4 x + 2$ $2$ $10$ $1$ $18$ $(C_2^4 : C_5):C_4$ (as 10T25) $[14/5]$ $[14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{6} + 4 x^{5} + 4 x + 2$
2.10.18.17 $x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{3} + 4 x^{2} + 4 x + 2$ $2$ $10$ $1$ $18$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[14/5]$ $[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{3} + 4 x^{2} + 4 x + 2$
2.10.18.18 $x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{4} + 2$ $2$ $10$ $1$ $18$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[14/5]$ $[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{4} + 2$
2.10.18.19 $x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 4 x + 2$ $2$ $10$ $1$ $18$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[14/5]$ $[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 4 x + 2$
2.10.18.2 $x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x + 2$ $2$ $10$ $1$ $18$ $(C_2^4 : C_5):C_4$ (as 10T24) $[14/5]$ $[14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x + 2$
2.10.18.20 $x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{6} + 4 x^{3} + 4 x^{2} + 4 x + 2$ $2$ $10$ $1$ $18$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[14/5]$ $[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{6} + 4 x^{3} + 4 x^{2} + 4 x + 2$
2.10.18.21 $x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{5} + 4 x^{4} + 2$ $2$ $10$ $1$ $18$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[14/5]$ $[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{5} + 4 x^{4} + 2$
2.10.18.22 $x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{4} + 2$ $2$ $10$ $1$ $18$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[14/5]$ $[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{4} + 2$
2.10.18.23 $x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 2$ $2$ $10$ $1$ $18$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[14/5]$ $[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 2$
2.10.18.24 $x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 4 x + 2$ $2$ $10$ $1$ $18$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[14/5]$ $[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 4 x + 2$
2.10.18.25 $x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 4 x + 2$ $2$ $10$ $1$ $18$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[14/5]$ $[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 4 x + 2$
2.10.18.26 $x^{10} + 2 x^{9} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 2$ $2$ $10$ $1$ $18$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[14/5]$ $[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 2$
2.10.18.27 $x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 4 x + 2$ $2$ $10$ $1$ $18$ $((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) $[14/5]$ $[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 4 x + 2$
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