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Label Polynomial $p$ $e$ $f$ $c$ Galois group Slope content
5.10.0.1 x10 + x2 - x + 3 5 1 10 0 $C_{10}$ (as 10T1) $ [\ ]^{10}$
5.10.5.1 x10 - 50x6 + 625x2 - 12500 5 2 5 5 $C_{10}$ (as 10T1) $ [\ ]_{2}^{5}$
5.10.5.2 x10 - 625x2 + 6250 5 2 5 5 $C_{10}$ (as 10T1) $ [\ ]_{2}^{5}$
5.10.10.1 x10 + 10x5 + 75x2 + 25 5 5 2 10 $C_5^2 : C_8$ (as 10T18) $ [5/4, 5/4]_{4}^{2}$
5.10.10.10 x10 + 10x8 + 5x6 + 10x5 - 20x4 - 20x2 + 2 5 5 2 10 $F_{5}\times C_2$ (as 10T5) $ [5/4]_{4}^{2}$
5.10.10.11 x10 + 5x6 + 10x5 + 25x2 + 25x + 25 5 5 2 10 $(C_5^2 : C_4) : C_2$ (as 10T17) $ [5/4, 5/4]_{4}^{2}$
5.10.10.12 x10 + 20x6 + 10x5 + 25x2 + 100x + 25 5 5 2 10 $(C_5^2 : C_4) : C_2$ (as 10T17) $ [5/4, 5/4]_{4}^{2}$
5.10.10.13 x10 + 15x6 + 10x5 + 100x2 + 75x + 25 5 5 2 10 $(C_5^2 : C_4) : C_2$ (as 10T17) $ [5/4, 5/4]_{4}^{2}$
5.10.10.14 x10 + 10x6 + 10x5 + 100x2 + 50x + 25 5 5 2 10 $(C_5^2 : C_4) : C_2$ (as 10T17) $ [5/4, 5/4]_{4}^{2}$
5.10.10.15 x10 + 20x + 5 5 10 1 10 $(C_5^2 : C_8):C_2$ (as 10T28) $ [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]_{8}^{2}$
5.10.10.17 x10 + 20x + 10 5 10 1 10 $(C_5^2 : C_8):C_2$ (as 10T28) $ [9/8, 9/8]_{8}^{2}$
5.10.10.18 x10 + 15x + 10 5 10 1 10 $(C_5^2 : C_8):C_2$ (as 10T28) $ [9/8, 9/8]_{8}^{2}$
5.10.10.2 x10 + 5x6 + 10x5 + 50x2 + 25x + 25 5 5 2 10 $C_5^2 : C_8$ (as 10T18) $ [5/4, 5/4]_{4}^{2}$
5.10.10.3 x10 + 10x5 + 50x2 + 25 5 5 2 10 $C_5^2 : C_8$ (as 10T18) $ [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]_{4}^{2}$
5.10.10.5 x10 + 15x6 + 10x5 + 75x2 + 75x + 25 5 5 2 10 $C_5^2 : C_8$ (as 10T18) $ [5/4, 5/4]_{4}^{2}$
5.10.10.6 x10 + 10x6 + 10x5 + 75x2 + 50x + 25 5 5 2 10 $C_5^2 : C_8$ (as 10T18) $ [5/4, 5/4]_{4}^{2}$
5.10.10.7 x10 + 10x8 + 10x5 - 20x4 - 20x2 + 12 5 5 2 10 $F_{5}\times C_2$ (as 10T5) $ [5/4]_{4}^{2}$
5.10.10.8 x10 + 10x8 + 20x6 + 10x5 - 20x4 - 20x2 + 22 5 5 2 10 $F_{5}\times C_2$ (as 10T5) $ [5/4]_{4}^{2}$
5.10.10.9 x10 + 10x8 + 10x6 + 10x5 - 20x4 - 20x2 + 17 5 5 2 10 $F_{5}\times C_2$ (as 10T5) $ [5/4]_{4}^{2}$
5.10.11.1 x10 + 20x2 + 5 5 10 1 11 $F_5$ (as 10T4) $ [5/4]_{4}$
5.10.11.2 x10 + 5x2 + 5 5 10 1 11 $F_5$ (as 10T4) $ [5/4]_{4}$
5.10.11.3 x10 + 10x2 + 5 5 10 1 11 $F_{5}\times C_2$ (as 10T5) $ [5/4]_{4}^{2}$
5.10.11.4 x10 + 15x2 + 5 5 10 1 11 $F_{5}\times C_2$ (as 10T5) $ [5/4]_{4}^{2}$
5.10.11.5 x10 + 15x2 + 10 5 10 1 11 $F_5$ (as 10T4) $ [5/4]_{4}$
5.10.11.6 x10 + 10x2 + 10 5 10 1 11 $F_5$ (as 10T4) $ [5/4]_{4}$
5.10.11.7 x10 + 5x2 + 10 5 10 1 11 $F_{5}\times C_2$ (as 10T5) $ [5/4]_{4}^{2}$
5.10.11.8 x10 + 20x2 + 10 5 10 1 11 $F_{5}\times C_2$ (as 10T5) $ [5/4]_{4}^{2}$
5.10.12.1 x10 + 10x5 + 75x4 + 25 5 5 2 12 $C_5^2 : C_8$ (as 10T18) $ [3/2, 3/2]_{2}^{4}$
5.10.12.10 x10 + 10x8 + 20x7 + 15x6 - 5x5 + 5x4 + 5x2 - 5x + 7 5 5 2 12 $D_{10}$ (as 10T3) $ [3/2]_{2}^{2}$
5.10.12.11 x10 + 5x7 + 10x5 + 25x4 + 25x2 + 25 5 5 2 12 $C_5^2 : C_4$ (as 10T10) $ [3/2, 3/2]_{2}^{2}$
5.10.12.12 x10 + 20x7 + 10x5 + 25x4 + 100x2 + 25 5 5 2 12 $C_5^2 : C_4$ (as 10T10) $ [3/2, 3/2]_{2}^{2}$
5.10.12.13 x10 + 15x7 + 10x5 + 100x4 + 75x2 + 25 5 5 2 12 $D_5^2$ (as 10T9) $ [3/2, 3/2]_{2}^{2}$
5.10.12.14 x10 + 10x7 + 10x5 + 100x4 + 50x2 + 25 5 5 2 12 $D_5^2$ (as 10T9) $ [3/2, 3/2]_{2}^{2}$
5.10.12.15 x10 + 20x3 + 5 5 10 1 12 $(C_5^2 : C_8):C_2$ (as 10T28) $ [11/8, 11/8]_{8}^{2}$
5.10.12.16 x10 + 15x3 + 10 5 10 1 12 $(C_5^2 : C_8):C_2$ (as 10T28) $ [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]_{8}^{2}$
5.10.12.18 x10 + 20x3 + 10 5 10 1 12 $(C_5^2 : C_8):C_2$ (as 10T28) $ [11/8, 11/8]_{8}^{2}$
5.10.12.2 x10 + 15x7 + 10x5 + 75x4 + 75x2 + 25 5 5 2 12 $C_5^2 : C_8$ (as 10T18) $ [3/2, 3/2]_{2}^{4}$
5.10.12.3 x10 + 5x7 + 10x5 + 50x4 + 25x2 + 25 5 5 2 12 $C_5^2 : C_8$ (as 10T18) $ [3/2, 3/2]_{2}^{4}$
5.10.12.4 x10 + 10x5 + 50x4 + 25 5 5 2 12 $C_5^2 : C_8$ (as 10T18) $ [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]_{2}^{4}$
5.10.12.6 x10 + 10x7 + 10x5 + 75x4 + 50x2 + 25 5 5 2 12 $C_5^2 : C_8$ (as 10T18) $ [3/2, 3/2]_{2}^{4}$
5.10.12.7 x10 + 10x8 + 5x7 + 15x6 + 5x4 + 5x2 - 20x + 7 5 5 2 12 $D_{10}$ (as 10T3) $ [3/2]_{2}^{2}$
5.10.12.8 x10 + 10x8 + 15x7 + 15x6 - 20x5 + 5x4 + 5x2 - 10x + 7 5 5 2 12 $F_5$ (as 10T4) $ [3/2]_{2}^{2}$
5.10.12.9 x10 + 10x8 + 10x7 + 15x6 - 10x5 + 5x4 + 5x2 - 15x + 7 5 5 2 12 $F_5$ (as 10T4) $ [3/2]_{2}^{2}$
5.10.13.1 x10 + 15x4 + 5 5 10 1 13 $D_5$ (as 10T2) $ [3/2]_{2}$
5.10.13.10 x10 + 10x4 + 10 5 10 1 13 $F_{5}\times C_2$ (as 10T5) $ [3/2]_{2}^{4}$
5.10.13.11 x10 - 15x5 + 5x4 + 10 5 10 1 13 $D_5\times C_5$ (as 10T6) $ [3/2]_{2}^{5}$
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