Results (displaying matches 1-50 of 1823) Next
| Polynomial | $p$ | $e$ | $f$ | $c$ | Galois group | Slope content |
|---|---|---|---|---|---|---|
| x8 + x4 + x3 + x + 1 | 2 | 1 | 8 | 0 | $C_8$ (as 8T1) | $ [\ ]^{8}$ |
| x8 + 28x4 + 144 | 2 | 2 | 4 | 8 | $C_4\times C_2$ (as 8T2) | $ [2]^{4}$ |
| x8 + 2x6 + 8x3 + 16 | 2 | 2 | 4 | 8 | $((C_8 : C_2):C_2):C_2$ (as 8T27) | $ [2, 2, 2, 2]^{4}$ |
| x8 + 20x2 + 4 | 2 | 4 | 2 | 8 | $S_4$ (as 8T14) | $ [4/3, 4/3]_{3}^{2}$ |
| x8 + 2x5 + 2x4 + 4 | 2 | 4 | 2 | 8 | $A_4\wr C_2$ (as 8T42) | $ [4/3, 4/3, 4/3, 4/3]_{3}^{6}$ |
| x8 + 2x + 2 | 2 | 8 | 1 | 8 | $C_2^3:(C_7: C_3)$ (as 8T36) | $ [8/7, 8/7, 8/7]_{7}^{3}$ |
| x8 + 2x7 + 8x2 + 48 | 2 | 2 | 4 | 8 | $C_2^2:C_4$ (as 8T10) | $ [2, 2]^{4}$ |
| x8 + 2x7 + 2x6 + 16 | 2 | 2 | 4 | 8 | $C_2^3: C_4$ (as 8T20) | $ [2, 2, 2]^{4}$ |
| x8 + 2x7 + 2x6 + 8x3 + 48 | 2 | 2 | 4 | 8 | $C_8$ (as 8T1) | $ [2]^{4}$ |
| x8 + 2x7 + 8x2 + 16 | 2 | 2 | 4 | 8 | $C_8:C_2$ (as 8T7) | $ [2, 2]^{4}$ |
| x8 + 2x7 + 2x6 + 16x2 + 16 | 2 | 2 | 4 | 8 | $(C_8:C_2):C_2$ (as 8T16) | $ [2, 2, 2]^{4}$ |
| x8 + 2x6 + 4x5 + 16 | 2 | 2 | 4 | 8 | $((C_8 : C_2):C_2):C_2$ (as 8T27) | $ [2, 2, 2, 2]^{4}$ |
| x8 + 4x5 + 8x2 + 48 | 2 | 2 | 4 | 8 | $((C_8 : C_2):C_2):C_2$ (as 8T27) | $ [2, 2, 2, 2]^{4}$ |
| x8 + 6x6 + 4x5 + 16 | 2 | 2 | 4 | 8 | $((C_8 : C_2):C_2):C_2$ (as 8T27) | $ [2, 2, 2, 2]^{4}$ |
| x8 + 2x3 + 2 | 2 | 8 | 1 | 10 | $C_2^3:(C_7: C_3)$ (as 8T36) | $ [10/7, 10/7, 10/7]_{7}^{3}$ |
| x8 + 20x2 + 20 | 2 | 8 | 1 | 10 | $\textrm{GL(2,3)}$ (as 8T23) | $ [4/3, 4/3, 3/2]_{3}^{2}$ |
| x8 + 4x2 + 20 | 2 | 8 | 1 | 10 | $\textrm{GL(2,3)}$ (as 8T23) | $ [4/3, 4/3, 3/2]_{3}^{2}$ |
| x8 + 6x6 + 8x5 + 16 | 2 | 2 | 4 | 12 | $C_4\times C_2$ (as 8T2) | $ [3]^{4}$ |
| x8 + 2x6 + 112 | 2 | 2 | 4 | 12 | $((C_8 : C_2):C_2):C_2$ (as 8T27) | $ [2, 2, 2, 3]^{4}$ |
| x8 + 6x6 + 48 | 2 | 2 | 4 | 12 | $((C_8 : C_2):C_2):C_2$ (as 8T27) | $ [2, 2, 2, 3]^{4}$ |
| x8 + 2x6 + 48 | 2 | 2 | 4 | 12 | $((C_8 : C_2):C_2):C_2$ (as 8T27) | $ [2, 2, 2, 3]^{4}$ |
| x8 + 12x4 + 16 | 2 | 4 | 2 | 12 | $D_4$ (as 8T4) | $ [2, 2]^{2}$ |
| x8 + 12x4 + 144 | 2 | 4 | 2 | 12 | $D_4$ (as 8T4) | $ [2, 2]^{2}$ |
| x8 + 2x7 + 2x4 + 12 | 2 | 4 | 2 | 12 | $C_2^2:C_4$ (as 8T10) | $ [2, 2]^{4}$ |
| x8 + 24x2 + 4 | 2 | 4 | 2 | 12 | $A_4\times C_2$ (as 8T13) | $ [2, 2]^{6}$ |
| x8 + 2x7 + 2x6 + 2x4 + 4 | 2 | 4 | 2 | 12 | $C_2^4:C_6$ (as 8T33) | $ [2, 2, 2, 2]^{6}$ |
| x8 + 8x7 + 48 | 2 | 4 | 2 | 12 | $C_2^4:C_6$ (as 8T33) | $ [2, 2, 2, 2]^{6}$ |
| x8 + 12x4 + 80 | 2 | 4 | 2 | 12 | $(C_8:C_2):C_2$ (as 8T16) | $ [2, 2, 2]^{4}$ |
| x8 + 2x6 + 8x4 + 16 | 2 | 2 | 4 | 12 | $C_4\times C_2$ (as 8T2) | $ [3]^{4}$ |
| x8 + 8x6 + 12x4 + 80 | 2 | 4 | 2 | 12 | $C_2^3: C_4$ (as 8T21) | $ [2, 2, 2]^{4}$ |
| x8 + 12x6 + 12x4 + 80 | 2 | 4 | 2 | 12 | $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) | $ [2, 2, 2, 2]^{4}$ |
| x8 + 4x7 + 16x3 + 48 | 2 | 4 | 2 | 12 | $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) | $ [2, 2, 2, 2]^{4}$ |
| x8 + 8x5 + 4x4 + 48 | 2 | 4 | 2 | 12 | $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) | $ [2, 2, 2, 2]^{4}$ |
| x8 + 4x6 + 28x4 + 80 | 2 | 4 | 2 | 12 | $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) | $ [2, 2, 2, 2]^{4}$ |
| x8 + 28x2 + 4 | 2 | 8 | 1 | 12 | $S_4\times C_2$ (as 8T24) | $ [4/3, 4/3, 2]_{3}^{2}$ |
| x8 + 12x2 + 4 | 2 | 8 | 1 | 12 | $S_4\times C_2$ (as 8T24) | $ [4/3, 4/3, 2]_{3}^{2}$ |
| x8 + 4x5 + 4 | 2 | 8 | 1 | 12 | $C_2^3:(C_7: C_3)$ (as 8T36) | $ [12/7, 12/7, 12/7]_{7}^{3}$ |
| x8 + 2x5 + 2 | 2 | 8 | 1 | 12 | $C_2^3:(C_7: C_3)$ (as 8T36) | $ [12/7, 12/7, 12/7]_{7}^{3}$ |
| x8 + 28x2 + 20 | 2 | 8 | 1 | 12 | $\textrm{GL(2,3)}$ (as 8T23) | $ [4/3, 4/3, 2]_{3}^{2}$ |
| x8 + 2x6 + 16x2 + 16 | 2 | 2 | 4 | 12 | $C_2^2:C_4$ (as 8T10) | $ [2, 3]^{4}$ |
| x8 + 12x2 + 20 | 2 | 8 | 1 | 12 | $\textrm{GL(2,3)}$ (as 8T23) | $ [4/3, 4/3, 2]_{3}^{2}$ |
| x8 + 2x6 + 16 | 2 | 2 | 4 | 12 | $C_2^3: C_4$ (as 8T20) | $ [2, 2, 3]^{4}$ |
| x8 + 6x6 + 8x5 + 80 | 2 | 2 | 4 | 12 | $C_8$ (as 8T1) | $ [3]^{4}$ |
| x8 + 2x6 + 8x4 + 80 | 2 | 2 | 4 | 12 | $C_8$ (as 8T1) | $ [3]^{4}$ |
| x8 + 4x6 + 8x2 + 80 | 2 | 2 | 4 | 12 | $C_8:C_2$ (as 8T7) | $ [2, 3]^{4}$ |
| x8 + 2x6 + 80 | 2 | 2 | 4 | 12 | $(C_8:C_2):C_2$ (as 8T16) | $ [2, 2, 3]^{4}$ |
| x8 + 6x6 + 112 | 2 | 2 | 4 | 12 | $((C_8 : C_2):C_2):C_2$ (as 8T27) | $ [2, 2, 2, 3]^{4}$ |
| x8 + 2x7 + 6 | 2 | 8 | 1 | 14 | $A_4\times C_2$ (as 8T13) | $ [2, 2, 2]^{3}$ |
| x8 + 4x2 + 28 | 2 | 8 | 1 | 14 | $C_2 \wr S_4$ (as 8T44) | $ [4/3, 4/3, 2, 7/3, 7/3, 5/2]_{3}^{2}$ |
| x8 + 20x2 + 12 | 2 | 8 | 1 | 14 | $C_2 \wr S_4$ (as 8T44) | $ [4/3, 4/3, 2, 7/3, 7/3, 5/2]_{3}^{2}$ |
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