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Label | Polynomial | $p$ | $e$ | $f$ | $c$ | Galois group | Slope content |
---|---|---|---|---|---|---|---|
2.4.0.1 | x4 - x + 1 | $2$ | $1$ | $4$ | $0$ | $C_4$ (as 4T1) | $[\ ]^{4}$ |
2.4.4.1 | x4 + 8x2 + 4 | $2$ | $2$ | $2$ | $4$ | $C_2^2$ (as 4T2) | $[2]^{2}$ |
2.4.4.2 | x4 - x2 + 5 | $2$ | $2$ | $2$ | $4$ | $C_4$ (as 4T1) | $[2]^{2}$ |
2.4.4.3 | x4 + 2x2 + 4x + 4 | $2$ | $2$ | $2$ | $4$ | $D_{4}$ (as 4T3) | $[2, 2]^{2}$ |
2.4.4.4 | x4 - 5 | $2$ | $2$ | $2$ | $4$ | $D_{4}$ (as 4T3) | $[2, 2]^{2}$ |
2.4.4.5 | x4 + 2x + 2 | $2$ | $4$ | $1$ | $4$ | $S_4$ (as 4T5) | $[4/3, 4/3]_{3}^{2}$ |
2.4.6.1 | x4 - 6x2 + 4 | $2$ | $2$ | $2$ | $6$ | $C_2^2$ (as 4T2) | $[3]^{2}$ |
2.4.6.2 | x4 - 2x2 + 4 | $2$ | $2$ | $2$ | $6$ | $C_2^2$ (as 4T2) | $[3]^{2}$ |
2.4.6.3 | x4 + 2x2 + 20 | $2$ | $2$ | $2$ | $6$ | $C_4$ (as 4T1) | $[3]^{2}$ |
2.4.6.4 | x4 - 2x2 + 20 | $2$ | $2$ | $2$ | $6$ | $C_4$ (as 4T1) | $[3]^{2}$ |
2.4.6.5 | x4 + 2x2 - 4 | $2$ | $2$ | $2$ | $6$ | $D_{4}$ (as 4T3) | $[2, 3]^{2}$ |
2.4.6.6 | x4 - 20 | $2$ | $2$ | $2$ | $6$ | $D_{4}$ (as 4T3) | $[2, 3]^{2}$ |
2.4.6.7 | x4 + 2x3 + 2x2 + 2 | $2$ | $4$ | $1$ | $6$ | $A_4$ (as 4T4) | $[2, 2]^{3}$ |
2.4.6.8 | x4 + 2x3 + 2 | $2$ | $4$ | $1$ | $6$ | $D_{4}$ (as 4T3) | $[2, 2]^{2}$ |
2.4.6.9 | x4 + 2x3 + 6 | $2$ | $4$ | $1$ | $6$ | $D_{4}$ (as 4T3) | $[2, 2]^{2}$ |
2.4.8.1 | x4 + 2x2 + 4x + 10 | $2$ | $4$ | $1$ | $8$ | $C_2^2$ (as 4T2) | $[2, 3]$ |
2.4.8.2 | x4 + 6x2 + 1 | $2$ | $4$ | $1$ | $8$ | $C_2^2$ (as 4T2) | $[2, 3]$ |
2.4.8.3 | x4 + 6x2 + 4x + 14 | $2$ | $4$ | $1$ | $8$ | $C_2^2$ (as 4T2) | $[2, 3]$ |
2.4.8.4 | x4 + 6x2 + 4x + 6 | $2$ | $4$ | $1$ | $8$ | $C_2^2$ (as 4T2) | $[2, 3]$ |
2.4.8.5 | x4 + 2x2 + 4x + 6 | $2$ | $4$ | $1$ | $8$ | $D_{4}$ (as 4T3) | $[2, 3]^{2}$ |
2.4.8.6 | x4 + 6x2 + 4x + 2 | $2$ | $4$ | $1$ | $8$ | $D_{4}$ (as 4T3) | $[2, 3]^{2}$ |
2.4.8.7 | x4 + 4x2 + 4x + 2 | $2$ | $4$ | $1$ | $8$ | $S_4$ (as 4T5) | $[8/3, 8/3]_{3}^{2}$ |
2.4.8.8 | x4 + 4x + 2 | $2$ | $4$ | $1$ | $8$ | $S_4$ (as 4T5) | $[8/3, 8/3]_{3}^{2}$ |
2.4.9.1 | x4 + 6x2 + 2 | $2$ | $4$ | $1$ | $9$ | $D_{4}$ (as 4T3) | $[2, 3, 7/2]$ |
2.4.9.2 | x4 - 2x2 + 2 | $2$ | $4$ | $1$ | $9$ | $D_{4}$ (as 4T3) | $[2, 3, 7/2]$ |
2.4.9.3 | x4 + 6x2 + 10 | $2$ | $4$ | $1$ | $9$ | $D_{4}$ (as 4T3) | $[2, 3, 7/2]$ |
2.4.9.4 | x4 + 2x2 + 10 | $2$ | $4$ | $1$ | $9$ | $D_{4}$ (as 4T3) | $[2, 3, 7/2]$ |
2.4.9.5 | x4 + 2x2 - 2 | $2$ | $4$ | $1$ | $9$ | $D_{4}$ (as 4T3) | $[2, 3, 7/2]$ |
2.4.9.6 | x4 - 2x2 - 2 | $2$ | $4$ | $1$ | $9$ | $D_{4}$ (as 4T3) | $[2, 3, 7/2]$ |
2.4.9.7 | x4 + 2x2 + 6 | $2$ | $4$ | $1$ | $9$ | $D_{4}$ (as 4T3) | $[2, 3, 7/2]$ |
2.4.9.8 | x4 - 2x2 + 6 | $2$ | $4$ | $1$ | $9$ | $D_{4}$ (as 4T3) | $[2, 3, 7/2]$ |
2.4.10.1 | x4 + 2x2 - 9 | $2$ | $4$ | $1$ | $10$ | $D_{4}$ (as 4T3) | $[2, 3, 7/2]$ |
2.4.10.2 | x4 + 2x2 - 1 | $2$ | $4$ | $1$ | $10$ | $D_{4}$ (as 4T3) | $[2, 3, 7/2]$ |
2.4.10.3 | x4 + 6x2 - 9 | $2$ | $4$ | $1$ | $10$ | $D_{4}$ (as 4T3) | $[2, 3, 7/2]$ |
2.4.10.4 | x4 + 6x2 - 1 | $2$ | $4$ | $1$ | $10$ | $D_{4}$ (as 4T3) | $[2, 3, 7/2]$ |
2.4.10.5 | x4 - 6x2 + 3 | $2$ | $4$ | $1$ | $10$ | $D_{4}$ (as 4T3) | $[2, 3, 7/2]$ |
2.4.10.6 | x4 + 6x2 + 3 | $2$ | $4$ | $1$ | $10$ | $D_{4}$ (as 4T3) | $[2, 3, 7/2]$ |
2.4.10.7 | x4 - 2x2 + 3 | $2$ | $4$ | $1$ | $10$ | $D_{4}$ (as 4T3) | $[2, 3, 7/2]$ |
2.4.10.8 | x4 + 2x2 + 3 | $2$ | $4$ | $1$ | $10$ | $D_{4}$ (as 4T3) | $[2, 3, 7/2]$ |
2.4.11.1 | x4 + 12x2 + 2 | $2$ | $4$ | $1$ | $11$ | $C_4$ (as 4T1) | $[3, 4]$ |
2.4.11.10 | x4 + 8x + 6 | $2$ | $4$ | $1$ | $11$ | $C_4$ (as 4T1) | $[3, 4]$ |
2.4.11.11 | x4 + 10 | $2$ | $4$ | $1$ | $11$ | $D_{4}$ (as 4T3) | $[2, 3, 4]$ |
2.4.11.12 | x4 + 26 | $2$ | $4$ | $1$ | $11$ | $D_{4}$ (as 4T3) | $[2, 3, 4]$ |
2.4.11.13 | x4 + 4x2 + 14 | $2$ | $4$ | $1$ | $11$ | $D_{4}$ (as 4T3) | $[3, 4]^{2}$ |
2.4.11.14 | x4 + 8x + 10 | $2$ | $4$ | $1$ | $11$ | $D_{4}$ (as 4T3) | $[3, 4]^{2}$ |
2.4.11.15 | x4 + 30 | $2$ | $4$ | $1$ | $11$ | $D_{4}$ (as 4T3) | $[2, 3, 4]$ |
2.4.11.16 | x4 + 14 | $2$ | $4$ | $1$ | $11$ | $D_{4}$ (as 4T3) | $[2, 3, 4]$ |
2.4.11.17 | x4 + 4x2 + 6 | $2$ | $4$ | $1$ | $11$ | $D_{4}$ (as 4T3) | $[3, 4]^{2}$ |
2.4.11.18 | x4 + 12x2 + 6 | $2$ | $4$ | $1$ | $11$ | $D_{4}$ (as 4T3) | $[3, 4]^{2}$ |
2.4.11.19 | x4 + 22 | $2$ | $4$ | $1$ | $11$ | $D_{4}$ (as 4T3) | $[2, 3, 4]$ |