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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content
5.10.0.1 x10 + 3x5 + 3x4 + 2x3 + 4x2 + x + 2 $5$ $1$ $10$ $0$ $C_{10}$ (as 10T1) $[\ ]$ $[\ ]^{10}$
5.10.5.1 x10 + 100x9 + 4025x8 + 82000x7 + 860258x6 + 4015486x5 + 4317350x4 + 2373700x3 + 3853141x2 + 15123594x + 12051954 $5$ $2$ $5$ $5$ $C_{10}$ (as 10T1) $[\ ]$ $[\ ]_{2}^{5}$
5.10.5.2 x10 + 2500x2 - 9375 $5$ $2$ $5$ $5$ $C_{10}$ (as 10T1) $[\ ]$ $[\ ]_{2}^{5}$
5.10.10.1 x10 + 10x5 - 50x2 + 25 $5$ $5$ $2$ $10$ $C_5^2 : C_8$ (as 10T18) $[5/4]$ $[5/4, 5/4]_{4}^{2}$
5.10.10.10 x10 + 40x6 + 10x5 - 200x4 + 400x2 + 200x + 25 $5$ $5$ $2$ $10$ $F_{5}\times C_2$ (as 10T5) $[5/4]$ $[5/4]_{4}^{2}$
5.10.10.11 x10 - 20x6 + 10x5 - 100x2 - 100x + 25 $5$ $5$ $2$ $10$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[5/4]$ $[5/4, 5/4]_{4}^{2}$
5.10.10.12 x10 - 30x6 + 10x5 + 25x2 - 150x + 25 $5$ $5$ $2$ $10$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[5/4]$ $[5/4, 5/4]_{4}^{2}$
5.10.10.13 x10 - 10x6 + 10x5 - 25x2 - 50x + 25 $5$ $5$ $2$ $10$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[5/4]$ $[5/4, 5/4]_{4}^{2}$
5.10.10.14 x10 + 10x6 + 10x5 - 25x2 + 50x + 25 $5$ $5$ $2$ $10$ $(C_5^2 : C_4) : C_2$ (as 10T17) $[5/4]$ $[5/4, 5/4]_{4}^{2}$
5.10.10.15 x10 + 5x + 5 $5$ $10$ $1$ $10$ $(C_5^2 : C_8):C_2$ (as 10T28) $[9/8]$ $[9/8, 9/8]_{8}^{2}$
5.10.10.16 x10 + 10x + 5 $5$ $10$ $1$ $10$ $(C_5^2 : C_8):C_2$ (as 10T28) $[9/8]$ $[9/8, 9/8]_{8}^{2}$
5.10.10.17 x10 + 5x + 10 $5$ $10$ $1$ $10$ $(C_5^2 : C_8):C_2$ (as 10T28) $[9/8]$ $[9/8, 9/8]_{8}^{2}$
5.10.10.18 x10 + 10x + 10 $5$ $10$ $1$ $10$ $(C_5^2 : C_8):C_2$ (as 10T28) $[9/8]$ $[9/8, 9/8]_{8}^{2}$
5.10.10.2 x10 - 20x6 + 10x5 + 50x2 - 100x + 25 $5$ $5$ $2$ $10$ $C_5^2 : C_8$ (as 10T18) $[5/4]$ $[5/4, 5/4]_{4}^{2}$
5.10.10.3 x10 + 10x5 - 200x2 + 25 $5$ $5$ $2$ $10$ $C_5^2 : C_8$ (as 10T18) $[5/4]$ $[5/4, 5/4]_{4}^{2}$
5.10.10.4 x10 + 20x6 + 10x5 + 50x2 + 100x + 25 $5$ $5$ $2$ $10$ $C_5^2 : C_8$ (as 10T18) $[5/4]$ $[5/4, 5/4]_{4}^{2}$
5.10.10.5 x10 - 10x6 + 10x5 - 175x2 - 50x + 25 $5$ $5$ $2$ $10$ $C_5^2 : C_8$ (as 10T18) $[5/4]$ $[5/4, 5/4]_{4}^{2}$
5.10.10.6 x10 - 40x6 + 10x5 + 200x2 - 200x + 25 $5$ $5$ $2$ $10$ $C_5^2 : C_8$ (as 10T18) $[5/4]$ $[5/4, 5/4]_{4}^{2}$
5.10.10.7 x10 - 50x7 + 10x6 + 10x5 + 175x4 - 250x3 - 225x2 + 50x + 25 $5$ $5$ $2$ $10$ $F_{5}\times C_2$ (as 10T5) $[5/4]$ $[5/4]_{4}^{2}$
5.10.10.8 x10 - 50x7 + 30x6 + 10x5 - 175x4 - 750x3 - 25x2 + 150x + 25 $5$ $5$ $2$ $10$ $F_{5}\times C_2$ (as 10T5) $[5/4]$ $[5/4]_{4}^{2}$
5.10.10.9 x10 + 20x6 + 10x5 - 50x4 + 100x2 + 100x + 25 $5$ $5$ $2$ $10$ $F_{5}\times C_2$ (as 10T5) $[5/4]$ $[5/4]_{4}^{2}$
5.10.11.1 x10 + 20x2 + 5 $5$ $10$ $1$ $11$ $F_5$ (as 10T4) $[5/4]$ $[5/4]_{4}$
5.10.11.2 x10 + 5x2 + 5 $5$ $10$ $1$ $11$ $F_5$ (as 10T4) $[5/4]$ $[5/4]_{4}$
5.10.11.3 x10 + 10x2 + 5 $5$ $10$ $1$ $11$ $F_{5}\times C_2$ (as 10T5) $[5/4]$ $[5/4]_{4}^{2}$
5.10.11.4 x10 + 15x2 + 5 $5$ $10$ $1$ $11$ $F_{5}\times C_2$ (as 10T5) $[5/4]$ $[5/4]_{4}^{2}$
5.10.11.5 x10 + 15x2 + 10 $5$ $10$ $1$ $11$ $F_5$ (as 10T4) $[5/4]$ $[5/4]_{4}$
5.10.11.6 x10 + 10x2 + 10 $5$ $10$ $1$ $11$ $F_5$ (as 10T4) $[5/4]$ $[5/4]_{4}$
5.10.11.7 x10 + 5x2 + 10 $5$ $10$ $1$ $11$ $F_{5}\times C_2$ (as 10T5) $[5/4]$ $[5/4]_{4}^{2}$
5.10.11.8 x10 + 20x2 + 10 $5$ $10$ $1$ $11$ $F_{5}\times C_2$ (as 10T5) $[5/4]$ $[5/4]_{4}^{2}$
5.10.12.1 x10 + 10x5 - 50x4 + 25 $5$ $5$ $2$ $12$ $C_5^2 : C_8$ (as 10T18) $[3/2]$ $[3/2, 3/2]_{2}^{4}$
5.10.12.10 x10 + 20x7 - 200x6 + 10x5 + 100x4 + 100x2 + 25 $5$ $5$ $2$ $12$ $D_{10}$ (as 10T3) $[3/2]$ $[3/2]_{2}^{2}$
5.10.12.11 x10 - 20x7 + 10x5 - 100x4 - 100x2 + 25 $5$ $5$ $2$ $12$ $C_5^2 : C_4$ (as 10T10) $[3/2]$ $[3/2, 3/2]_{2}^{2}$
5.10.12.12 x10 - 30x7 + 10x5 + 25x4 - 150x2 + 25 $5$ $5$ $2$ $12$ $C_5^2 : C_4$ (as 10T10) $[3/2]$ $[3/2, 3/2]_{2}^{2}$
5.10.12.13 x10 - 10x7 + 10x5 - 25x4 - 50x2 + 25 $5$ $5$ $2$ $12$ $D_5^2$ (as 10T9) $[3/2]$ $[3/2, 3/2]_{2}^{2}$
5.10.12.14 x10 + 10x7 + 10x5 - 25x4 + 50x2 + 25 $5$ $5$ $2$ $12$ $D_5^2$ (as 10T9) $[3/2]$ $[3/2, 3/2]_{2}^{2}$
5.10.12.15 x10 + 5x3 + 5 $5$ $10$ $1$ $12$ $(C_5^2 : C_8):C_2$ (as 10T28) $[11/8]$ $[11/8, 11/8]_{8}^{2}$
5.10.12.16 x10 + 10x3 + 10 $5$ $10$ $1$ $12$ $(C_5^2 : C_8):C_2$ (as 10T28) $[11/8]$ $[11/8, 11/8]_{8}^{2}$
5.10.12.17 x10 + 10x3 + 5 $5$ $10$ $1$ $12$ $(C_5^2 : C_8):C_2$ (as 10T28) $[11/8]$ $[11/8, 11/8]_{8}^{2}$
5.10.12.18 x10 + 5x3 + 10 $5$ $10$ $1$ $12$ $(C_5^2 : C_8):C_2$ (as 10T28) $[11/8]$ $[11/8, 11/8]_{8}^{2}$
5.10.12.2 x10 - 10x7 + 10x5 - 175x4 - 50x2 + 25 $5$ $5$ $2$ $12$ $C_5^2 : C_8$ (as 10T18) $[3/2]$ $[3/2, 3/2]_{2}^{4}$
5.10.12.3 x10 - 20x7 + 10x5 + 50x4 - 100x2 + 25 $5$ $5$ $2$ $12$ $C_5^2 : C_8$ (as 10T18) $[3/2]$ $[3/2, 3/2]_{2}^{4}$
5.10.12.4 x10 + 10x5 - 200x4 + 25 $5$ $5$ $2$ $12$ $C_5^2 : C_8$ (as 10T18) $[3/2]$ $[3/2, 3/2]_{2}^{4}$
5.10.12.5 x10 + 20x7 + 10x5 + 50x4 + 100x2 + 25 $5$ $5$ $2$ $12$ $C_5^2 : C_8$ (as 10T18) $[3/2]$ $[3/2, 3/2]_{2}^{4}$
5.10.12.6 x10 - 40x7 + 10x5 + 200x4 - 200x2 + 25 $5$ $5$ $2$ $12$ $C_5^2 : C_8$ (as 10T18) $[3/2]$ $[3/2, 3/2]_{2}^{4}$
5.10.12.7 x10 - 50x8 + 30x7 + 175x6 - 740x5 + 225x4 - 250x3 + 150x2 + 25 $5$ $5$ $2$ $12$ $D_{10}$ (as 10T3) $[3/2]$ $[3/2]_{2}^{2}$
5.10.12.8 x10 - 50x8 + 40x7 - 175x6 - 990x5 + 400x4 - 250x3 + 200x2 + 25 $5$ $5$ $2$ $12$ $F_5$ (as 10T4) $[3/2]$ $[3/2]_{2}^{2}$
5.10.12.9 x10 + 10x7 - 50x6 + 10x5 + 25x4 + 50x2 + 25 $5$ $5$ $2$ $12$ $F_5$ (as 10T4) $[3/2]$ $[3/2]_{2}^{2}$
5.10.13.1 x10 + 15x4 + 5 $5$ $10$ $1$ $13$ $D_5$ (as 10T2) $[3/2]$ $[3/2]_{2}$
5.10.13.10 x10 + 10x4 + 10 $5$ $10$ $1$ $13$ $F_{5}\times C_2$ (as 10T5) $[3/2]$ $[3/2]_{2}^{4}$
5.10.13.11 x10 + 10x5 + 5x4 + 10 $5$ $10$ $1$ $13$ $D_5\times C_5$ (as 10T6) $[3/2]$ $[3/2]_{2}^{5}$
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