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Label | Polynomial | $p$ | $e$ | $f$ | $c$ | Galois group | Slope content |
---|---|---|---|---|---|---|---|
7.4.0.1 | x4 + 5x2 + 4x + 3 | $7$ | $1$ | $4$ | $0$ | $C_4$ (as 4T1) | $[\ ]^{4}$ |
7.4.2.1 | x4 + 12x3 + 56x2 + 120x + 268 | $7$ | $2$ | $2$ | $2$ | $C_2^2$ (as 4T2) | $[\ ]_{2}^{2}$ |
7.4.2.2 | x4 - 42x2 + 147 | $7$ | $2$ | $2$ | $2$ | $C_4$ (as 4T1) | $[\ ]_{2}^{2}$ |
7.4.3.1 | x4 + 7 | $7$ | $4$ | $1$ | $3$ | $D_{4}$ (as 4T3) | $[\ ]_{4}^{2}$ |
7.4.3.2 | x4 + 21 | $7$ | $4$ | $1$ | $3$ | $D_{4}$ (as 4T3) | $[\ ]_{4}^{2}$ |