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Label Polynomial pp ee ff cc Galois group uu tt Visible slopes Slope content Unram. Ext. Eisen. Poly. Ind. of Insep. Assoc. Inertia
2.4.0.1 x4+x+1x^{4} + x + 1 22 11 44 00 C4C_4 (as 4T1) 44 11 [ ][\ ] [ ]4[\ ]^{4} t4+t+1t^{4} + t + 1 x2x - 2 [0][0] [ ][\ ]
2.4.4.1 x4+6x3+17x2+24x+13x^{4} + 6 x^{3} + 17 x^{2} + 24 x + 13 22 22 22 44 C22C_2^2 (as 4T2) 22 11 [2][2] [2]2[2]^{2} t2+t+1t^{2} + t + 1 x2+2x+2x^{2} + 2 x + 2 [1,0][1, 0] [1][1]
2.4.4.2 x4+4x3+4x2+12x^{4} + 4 x^{3} + 4 x^{2} + 12 22 22 22 44 C4C_4 (as 4T1) 22 11 [2][2] [2]2[2]^{2} t2+t+1t^{2} + t + 1 x2+2x+4t+2x^{2} + 2 x + 4 t + 2 [1,0][1, 0] [1][1]
2.4.4.3 x4+2x3+4x2+12x+12x^{4} + 2 x^{3} + 4 x^{2} + 12 x + 12 22 22 22 44 D4D_{4} (as 4T3) 22 11 [2][2] [2,2]2[2, 2]^{2} t2+t+1t^{2} + t + 1 x2+(2t+2)x+4t+2x^{2} + \left(2 t + 2\right) x + 4 t + 2 [1,0][1, 0] [1][1]
2.4.4.4 x42x3+4x2+12x+12x^{4} - 2 x^{3} + 4 x^{2} + 12 x + 12 22 22 22 44 D4D_{4} (as 4T3) 22 11 [2][2] [2,2]2[2, 2]^{2} t2+t+1t^{2} + t + 1 x2+2tx+4t+2x^{2} + 2 t x + 4 t + 2 [1,0][1, 0] [1][1]
2.4.4.5 x4+2x+2x^{4} + 2 x + 2 22 44 11 44 S4S_4 (as 4T5) 22 33 [4/3,4/3][4/3, 4/3] [4/3,4/3]32[4/3, 4/3]_{3}^{2} t+1t + 1 x4+2x+2x^{4} + 2 x + 2 [1,1,0][1, 1, 0] [1][1]
2.4.6.1 x4+2x3+31x2+30x+183x^{4} + 2 x^{3} + 31 x^{2} + 30 x + 183 22 22 22 66 C22C_2^2 (as 4T2) 22 11 [3][3] [3]2[3]^{2} t2+t+1t^{2} + t + 1 x2+14x^{2} + 14 [2,0][2, 0] [1][1]
2.4.6.2 x4+4x3+16x2+24x+12x^{4} + 4 x^{3} + 16 x^{2} + 24 x + 12 22 22 22 66 C22C_2^2 (as 4T2) 22 11 [3][3] [3]2[3]^{2} t2+t+1t^{2} + t + 1 x2+(4t+4)x+4t+2x^{2} + \left(4 t + 4\right) x + 4 t + 2 [2,0][2, 0] [1][1]
2.4.6.3 x4+8x3+28x2+48x+84x^{4} + 8 x^{3} + 28 x^{2} + 48 x + 84 22 22 22 66 C4C_4 (as 4T1) 22 11 [3][3] [3]2[3]^{2} t2+t+1t^{2} + t + 1 x2+4x+8t+10x^{2} + 4 x + 8 t + 10 [2,0][2, 0] [1][1]
2.4.6.4 x4+4x3+24x2+88x+124x^{4} + 4 x^{3} + 24 x^{2} + 88 x + 124 22 22 22 66 C4C_4 (as 4T1) 22 11 [3][3] [3]2[3]^{2} t2+t+1t^{2} + t + 1 x2+(4t+4)x+12t+10x^{2} + \left(4 t + 4\right) x + 12 t + 10 [2,0][2, 0] [1][1]
2.4.6.5 x44x3+36x2+8x+148x^{4} - 4 x^{3} + 36 x^{2} + 8 x + 148 22 22 22 66 D4D_{4} (as 4T3) 22 11 [3][3] [2,3]2[2, 3]^{2} t2+t+1t^{2} + t + 1 x2+4tx+8t+14x^{2} + 4 t x + 8 t + 14 [2,0][2, 0] [1][1]
2.4.6.6 x44x3+28x224x+36x^{4} - 4 x^{3} + 28 x^{2} - 24 x + 36 22 22 22 66 D4D_{4} (as 4T3) 22 11 [3][3] [2,3]2[2, 3]^{2} t2+t+1t^{2} + t + 1 x2+4tx+6x^{2} + 4 t x + 6 [2,0][2, 0] [1][1]
2.4.6.7 x4+2x3+2x2+2x^{4} + 2 x^{3} + 2 x^{2} + 2 22 44 11 66 A4A_4 (as 4T4) 33 11 [2,2][2, 2] [2,2]3[2, 2]^{3} t+1t + 1 x4+2x3+2x2+2x^{4} + 2 x^{3} + 2 x^{2} + 2 [3,2,0][3, 2, 0] [3][3]
2.4.6.8 x4+2x3+2x^{4} + 2 x^{3} + 2 22 44 11 66 D4D_{4} (as 4T3) 22 11 [2,2][2, 2] [2,2]2[2, 2]^{2} t+1t + 1 x4+2x3+2x^{4} + 2 x^{3} + 2 [3,3,0][3, 3, 0] [2][2]
2.4.6.9 x4+2x3+6x^{4} + 2 x^{3} + 6 22 44 11 66 D4D_{4} (as 4T3) 22 11 [2,2][2, 2] [2,2]2[2, 2]^{2} t+1t + 1 x4+2x3+6x^{4} + 2 x^{3} + 6 [3,3,0][3, 3, 0] [2][2]
2.4.8.1 x4+2x2+4x+10x^{4} + 2 x^{2} + 4 x + 10 22 44 11 88 C22C_2^2 (as 4T2) 11 11 [2,3][2, 3] [2,3][2, 3] t+1t + 1 x4+2x2+4x+10x^{4} + 2 x^{2} + 4 x + 10 [5,2,0][5, 2, 0] [1,1][1, 1]
2.4.8.2 x4+2x2+4x+2x^{4} + 2 x^{2} + 4 x + 2 22 44 11 88 C22C_2^2 (as 4T2) 11 11 [2,3][2, 3] [2,3][2, 3] t+1t + 1 x4+2x2+4x+2x^{4} + 2 x^{2} + 4 x + 2 [5,2,0][5, 2, 0] [1,1][1, 1]
2.4.8.3 x4+6x2+4x+14x^{4} + 6 x^{2} + 4 x + 14 22 44 11 88 C22C_2^2 (as 4T2) 11 11 [2,3][2, 3] [2,3][2, 3] t+1t + 1 x4+6x2+4x+14x^{4} + 6 x^{2} + 4 x + 14 [5,2,0][5, 2, 0] [1,1][1, 1]
2.4.8.4 x4+6x2+4x+6x^{4} + 6 x^{2} + 4 x + 6 22 44 11 88 C22C_2^2 (as 4T2) 11 11 [2,3][2, 3] [2,3][2, 3] t+1t + 1 x4+6x2+4x+6x^{4} + 6 x^{2} + 4 x + 6 [5,2,0][5, 2, 0] [1,1][1, 1]
2.4.8.5 x4+2x2+4x+6x^{4} + 2 x^{2} + 4 x + 6 22 44 11 88 D4D_{4} (as 4T3) 22 11 [2,3][2, 3] [2,3]2[2, 3]^{2} t+1t + 1 x4+2x2+4x+6x^{4} + 2 x^{2} + 4 x + 6 [5,2,0][5, 2, 0] [1,1][1, 1]
2.4.8.6 x4+6x2+4x+10x^{4} + 6 x^{2} + 4 x + 10 22 44 11 88 D4D_{4} (as 4T3) 22 11 [2,3][2, 3] [2,3]2[2, 3]^{2} t+1t + 1 x4+6x2+4x+10x^{4} + 6 x^{2} + 4 x + 10 [5,2,0][5, 2, 0] [1,1][1, 1]
2.4.8.7 x4+4x2+4x+2x^{4} + 4 x^{2} + 4 x + 2 22 44 11 88 S4S_4 (as 4T5) 22 33 [8/3,8/3][8/3, 8/3] [8/3,8/3]32[8/3, 8/3]_{3}^{2} t+1t + 1 x4+4x2+4x+2x^{4} + 4 x^{2} + 4 x + 2 [5,4,0][5, 4, 0] [1][1]
2.4.8.8 x4+4x+2x^{4} + 4 x + 2 22 44 11 88 S4S_4 (as 4T5) 22 33 [8/3,8/3][8/3, 8/3] [8/3,8/3]32[8/3, 8/3]_{3}^{2} t+1t + 1 x4+4x+2x^{4} + 4 x + 2 [5,4,0][5, 4, 0] [1][1]
2.4.9.1 x4+10x2+2x^{4} + 10 x^{2} + 2 22 44 11 99 D4D_{4} (as 4T3) 11 11 [2,7/2][2, 7/2] [2,3,7/2][2, 3, 7/2] t+1t + 1 x4+10x2+2x^{4} + 10 x^{2} + 2 [6,2,0][6, 2, 0] [1,1][1, 1]
2.4.9.2 x4+2x2+2x^{4} + 2 x^{2} + 2 22 44 11 99 D4D_{4} (as 4T3) 11 11 [2,7/2][2, 7/2] [2,3,7/2][2, 3, 7/2] t+1t + 1 x4+2x2+2x^{4} + 2 x^{2} + 2 [6,2,0][6, 2, 0] [1,1][1, 1]
2.4.9.3 x4+4x3+2x2+2x^{4} + 4 x^{3} + 2 x^{2} + 2 22 44 11 99 D4D_{4} (as 4T3) 11 11 [2,7/2][2, 7/2] [2,3,7/2][2, 3, 7/2] t+1t + 1 x4+4x3+2x2+2x^{4} + 4 x^{3} + 2 x^{2} + 2 [6,2,0][6, 2, 0] [1,1][1, 1]
2.4.9.4 x4+10x2+8x+2x^{4} + 10 x^{2} + 8 x + 2 22 44 11 99 D4D_{4} (as 4T3) 11 11 [2,7/2][2, 7/2] [2,3,7/2][2, 3, 7/2] t+1t + 1 x4+10x2+8x+2x^{4} + 10 x^{2} + 8 x + 2 [6,2,0][6, 2, 0] [1,1][1, 1]
2.4.9.5 x4+10x2+8x+6x^{4} + 10 x^{2} + 8 x + 6 22 44 11 99 D4D_{4} (as 4T3) 11 11 [2,7/2][2, 7/2] [2,3,7/2][2, 3, 7/2] t+1t + 1 x4+10x2+8x+6x^{4} + 10 x^{2} + 8 x + 6 [6,2,0][6, 2, 0] [1,1][1, 1]
2.4.9.6 x4+4x3+10x2+14x^{4} + 4 x^{3} + 10 x^{2} + 14 22 44 11 99 D4D_{4} (as 4T3) 11 11 [2,7/2][2, 7/2] [2,3,7/2][2, 3, 7/2] t+1t + 1 x4+4x3+10x2+14x^{4} + 4 x^{3} + 10 x^{2} + 14 [6,2,0][6, 2, 0] [1,1][1, 1]
2.4.9.7 x4+2x2+6x^{4} + 2 x^{2} + 6 22 44 11 99 D4D_{4} (as 4T3) 11 11 [2,7/2][2, 7/2] [2,3,7/2][2, 3, 7/2] t+1t + 1 x4+2x2+6x^{4} + 2 x^{2} + 6 [6,2,0][6, 2, 0] [1,1][1, 1]
2.4.9.8 x4+10x2+6x^{4} + 10 x^{2} + 6 22 44 11 99 D4D_{4} (as 4T3) 11 11 [2,7/2][2, 7/2] [2,3,7/2][2, 3, 7/2] t+1t + 1 x4+10x2+6x^{4} + 10 x^{2} + 6 [6,2,0][6, 2, 0] [1,1][1, 1]
2.4.10.1 x4+4x3+10x^{4} + 4 x^{3} + 10 22 44 11 1010 D4D_{4} (as 4T3) 11 11 [3,7/2][3, 7/2] [2,3,7/2][2, 3, 7/2] t+1t + 1 x4+4x3+10x^{4} + 4 x^{3} + 10 [7,4,0][7, 4, 0] [1,1][1, 1]
2.4.10.2 x4+4x3+2x^{4} + 4 x^{3} + 2 22 44 11 1010 D4D_{4} (as 4T3) 11 11 [3,7/2][3, 7/2] [2,3,7/2][2, 3, 7/2] t+1t + 1 x4+4x3+2x^{4} + 4 x^{3} + 2 [7,4,0][7, 4, 0] [1,1][1, 1]
2.4.10.3 x4+4x3+8x2+2x^{4} + 4 x^{3} + 8 x^{2} + 2 22 44 11 1010 D4D_{4} (as 4T3) 11 11 [3,7/2][3, 7/2] [2,3,7/2][2, 3, 7/2] t+1t + 1 x4+4x3+8x2+2x^{4} + 4 x^{3} + 8 x^{2} + 2 [7,4,0][7, 4, 0] [1,1][1, 1]
2.4.10.4 x4+4x3+8x2+10x^{4} + 4 x^{3} + 8 x^{2} + 10 22 44 11 1010 D4D_{4} (as 4T3) 11 11 [3,7/2][3, 7/2] [2,3,7/2][2, 3, 7/2] t+1t + 1 x4+4x3+8x2+10x^{4} + 4 x^{3} + 8 x^{2} + 10 [7,4,0][7, 4, 0] [1,1][1, 1]
2.4.10.5 x4+4x3+4x2+10x^{4} + 4 x^{3} + 4 x^{2} + 10 22 44 11 1010 D4D_{4} (as 4T3) 11 11 [3,7/2][3, 7/2] [2,3,7/2][2, 3, 7/2] t+1t + 1 x4+4x3+4x2+10x^{4} + 4 x^{3} + 4 x^{2} + 10 [7,4,0][7, 4, 0] [1,1][1, 1]
2.4.10.6 x4+4x3+12x2+10x^{4} + 4 x^{3} + 12 x^{2} + 10 22 44 11 1010 D4D_{4} (as 4T3) 11 11 [3,7/2][3, 7/2] [2,3,7/2][2, 3, 7/2] t+1t + 1 x4+4x3+12x2+10x^{4} + 4 x^{3} + 12 x^{2} + 10 [7,4,0][7, 4, 0] [1,1][1, 1]
2.4.10.7 x4+4x3+4x2+2x^{4} + 4 x^{3} + 4 x^{2} + 2 22 44 11 1010 D4D_{4} (as 4T3) 11 11 [3,7/2][3, 7/2] [2,3,7/2][2, 3, 7/2] t+1t + 1 x4+4x3+4x2+2x^{4} + 4 x^{3} + 4 x^{2} + 2 [7,4,0][7, 4, 0] [1,1][1, 1]
2.4.10.8 x4+4x3+12x2+2x^{4} + 4 x^{3} + 12 x^{2} + 2 22 44 11 1010 D4D_{4} (as 4T3) 11 11 [3,7/2][3, 7/2] [2,3,7/2][2, 3, 7/2] t+1t + 1 x4+4x3+12x2+2x^{4} + 4 x^{3} + 12 x^{2} + 2 [7,4,0][7, 4, 0] [1,1][1, 1]
2.4.11.1 x4+8x3+4x2+2x^{4} + 8 x^{3} + 4 x^{2} + 2 22 44 11 1111 C4C_4 (as 4T1) 11 11 [3,4][3, 4] [3,4][3, 4] t+1t + 1 x4+8x3+4x2+2x^{4} + 8 x^{3} + 4 x^{2} + 2 [8,4,0][8, 4, 0] [1,1][1, 1]
2.4.11.2 x4+4x2+2x^{4} + 4 x^{2} + 2 22 44 11 1111 C4C_4 (as 4T1) 11 11 [3,4][3, 4] [3,4][3, 4] t+1t + 1 x4+4x2+2x^{4} + 4 x^{2} + 2 [8,4,0][8, 4, 0] [1,1][1, 1]
2.4.11.3 x4+4x2+18x^{4} + 4 x^{2} + 18 22 44 11 1111 C4C_4 (as 4T1) 11 11 [3,4][3, 4] [3,4][3, 4] t+1t + 1 x4+4x2+18x^{4} + 4 x^{2} + 18 [8,4,0][8, 4, 0] [1,1][1, 1]
2.4.11.4 x4+8x3+4x2+18x^{4} + 8 x^{3} + 4 x^{2} + 18 22 44 11 1111 C4C_4 (as 4T1) 11 11 [3,4][3, 4] [3,4][3, 4] t+1t + 1 x4+8x3+4x2+18x^{4} + 8 x^{3} + 4 x^{2} + 18 [8,4,0][8, 4, 0] [1,1][1, 1]
2.4.11.5 x4+2x^{4} + 2 22 44 11 1111 D4D_{4} (as 4T3) 11 11 [3,4][3, 4] [2,3,4][2, 3, 4] t+1t + 1 x4+2x^{4} + 2 [8,4,0][8, 4, 0] [1,1][1, 1]
2.4.11.6 x4+18x^{4} + 18 22 44 11 1111 D4D_{4} (as 4T3) 11 11 [3,4][3, 4] [2,3,4][2, 3, 4] t+1t + 1 x4+18x^{4} + 18 [8,4,0][8, 4, 0] [1,1][1, 1]
2.4.11.7 x4+8x3+4x2+26x^{4} + 8 x^{3} + 4 x^{2} + 26 22 44 11 1111 C4C_4 (as 4T1) 11 11 [3,4][3, 4] [3,4][3, 4] t+1t + 1 x4+8x3+4x2+26x^{4} + 8 x^{3} + 4 x^{2} + 26 [8,4,0][8, 4, 0] [1,1][1, 1]
2.4.11.8 x4+4x2+10x^{4} + 4 x^{2} + 10 22 44 11 1111 C4C_4 (as 4T1) 11 11 [3,4][3, 4] [3,4][3, 4] t+1t + 1 x4+4x2+10x^{4} + 4 x^{2} + 10 [8,4,0][8, 4, 0] [1,1][1, 1]
2.4.11.9 x4+8x3+4x2+10x^{4} + 8 x^{3} + 4 x^{2} + 10 22 44 11 1111 C4C_4 (as 4T1) 11 11 [3,4][3, 4] [3,4][3, 4] t+1t + 1 x4+8x3+4x2+10x^{4} + 8 x^{3} + 4 x^{2} + 10 [8,4,0][8, 4, 0] [1,1][1, 1]
2.4.11.10 x4+4x2+26x^{4} + 4 x^{2} + 26 22 44 11 1111 C4C_4 (as 4T1) 11 11 [3,4][3, 4] [3,4][3, 4] t+1t + 1 x4+4x2+26x^{4} + 4 x^{2} + 26 [8,4,0][8, 4, 0] [1,1][1, 1]
2.4.11.11 x4+10x^{4} + 10 22 44 11 1111 D4D_{4} (as 4T3) 11 11 [3,4][3, 4] [2,3,4][2, 3, 4] t+1t + 1 x4+10x^{4} + 10 [8,4,0][8, 4, 0] [1,1][1, 1]
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