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| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 4.0.117.1 | x4 - x3 - x2 + x + 1 | \( 3^{2}\cdot 13 \) | $D_{4}$ (as 4T3) | trivial |
| 4.0.125.1 | x4 - x3 + x2 - x + 1 | \( 5^{3} \) | $C_4$ (as 4T1) | trivial |
| 4.0.144.1 | x4 - x2 + 1 | \( 2^{4}\cdot 3^{2} \) | $C_2^2$ (as 4T2) | trivial |
| 4.0.189.1 | x4 - x3 + 2x + 1 | \( 3^{3}\cdot 7 \) | $D_{4}$ (as 4T3) | trivial |
| 4.0.225.1 | x4 - x3 + 2x2 + x + 1 | \( 3^{2}\cdot 5^{2} \) | $C_2^2$ (as 4T2) | trivial |
| 4.0.229.1 | x4 - x + 1 | \( 229 \) | $S_4$ (as 4T5) | trivial |
| 4.0.256.1 | x4 + 1 | \( 2^{8} \) | $C_2^2$ (as 4T2) | trivial |
| 4.0.257.1 | x4 + x2 - x + 1 | \( 257 \) | $S_4$ (as 4T5) | trivial |
| 4.0.272.1 | x4 + x2 - 2x + 1 | \( 2^{4}\cdot 17 \) | $D_{4}$ (as 4T3) | trivial |
| 4.2.275.1 | x4 - x3 + 2x - 1 | \( -\,5^{2}\cdot 11 \) | $D_{4}$ (as 4T3) | trivial |
| 4.2.283.1 | x4 - x - 1 | \( -\,283 \) | $S_4$ (as 4T5) | trivial |
| 4.0.320.1 | x4 - 2x3 + 2 | \( 2^{6}\cdot 5 \) | $D_{4}$ (as 4T3) | trivial |
| 4.2.331.1 | x4 - x3 + x2 + x - 1 | \( -\,331 \) | $S_4$ (as 4T5) | trivial |
| 4.0.333.1 | x4 - x3 - 2x2 + 3 | \( 3^{2}\cdot 37 \) | $D_{4}$ (as 4T3) | trivial |
| 4.0.392.1 | x4 - x3 + x + 1 | \( 2^{3}\cdot 7^{2} \) | $D_{4}$ (as 4T3) | trivial |
| 4.2.400.1 | x4 - x2 - 1 | \( -\,2^{4}\cdot 5^{2} \) | $D_{4}$ (as 4T3) | trivial |
| 4.0.400.1 | x4 + 3x2 + 1 | \( 2^{4}\cdot 5^{2} \) | $C_2^2$ (as 4T2) | trivial |
| 4.0.432.1 | x4 - 3x2 + 3 | \( 2^{4}\cdot 3^{3} \) | $D_{4}$ (as 4T3) | trivial |
| 4.0.441.1 | x4 - x3 - x2 - 2x + 4 | \( 3^{2}\cdot 7^{2} \) | $C_2^2$ (as 4T2) | trivial |
| 4.2.448.1 | x4 - 2x3 + x2 - 2x + 1 | \( -\,2^{6}\cdot 7 \) | $D_{4}$ (as 4T3) | trivial |
| 4.2.475.1 | x4 - 2x3 + 2x2 - x - 1 | \( -\,5^{2}\cdot 19 \) | $D_{4}$ (as 4T3) | trivial |
| 4.2.491.1 | x4 - x3 - x2 + 3x - 1 | \( -\,491 \) | $S_4$ (as 4T5) | trivial |
| 4.2.507.1 | x4 - x3 - x2 - x + 1 | \( -\,3\cdot 13^{2} \) | $D_{4}$ (as 4T3) | trivial |
| 4.0.512.1 | x4 - 2x2 + 2 | \( 2^{9} \) | $D_{4}$ (as 4T3) | trivial |
| 4.0.513.1 | x4 - x3 - 3x2 + 2x + 4 | \( 3^{3}\cdot 19 \) | $D_{4}$ (as 4T3) | trivial |
| 4.0.549.1 | x4 - 2x3 - 2x2 + 3x + 3 | \( 3^{2}\cdot 61 \) | $D_{4}$ (as 4T3) | trivial |
| 4.2.563.1 | x4 - x3 + x2 - x - 1 | \( -\,563 \) | $S_4$ (as 4T5) | trivial |
| 4.0.576.1 | x4 - 2x2 + 4 | \( 2^{6}\cdot 3^{2} \) | $C_2^2$ (as 4T2) | trivial |
| 4.0.576.2 | x4 + 2x2 + 4 | \( 2^{6}\cdot 3^{2} \) | $C_2^2$ (as 4T2) | trivial |
| 4.0.592.1 | x4 + 2x2 - 2x + 1 | \( 2^{4}\cdot 37 \) | $S_4$ (as 4T5) | trivial |
| 4.0.605.1 | x4 - x3 + x2 + x + 1 | \( 5\cdot 11^{2} \) | $D_{4}$ (as 4T3) | trivial |
| 4.2.643.1 | x4 - x3 - 2x + 1 | \( -\,643 \) | $S_4$ (as 4T5) | trivial |
| 4.0.656.1 | x4 - 2x3 - x2 + 2x + 2 | \( 2^{4}\cdot 41 \) | $D_{4}$ (as 4T3) | trivial |
| 4.0.657.1 | x4 - x3 + 5x2 - 2x + 4 | \( 3^{2}\cdot 73 \) | $D_{4}$ (as 4T3) | trivial |
| 4.2.688.1 | x4 - 2x - 1 | \( -\,2^{4}\cdot 43 \) | $S_4$ (as 4T5) | trivial |
| 4.0.697.1 | x4 - x3 + 2x2 - x + 2 | \( 17\cdot 41 \) | $S_4$ (as 4T5) | trivial |
| 4.4.725.1 | x4 - x3 - 3x2 + x + 1 | \( 5^{2}\cdot 29 \) | $D_{4}$ (as 4T3) | trivial |
| 4.2.731.1 | x4 - x3 + 2x2 - 1 | \( -\,17\cdot 43 \) | $S_4$ (as 4T5) | trivial |
| 4.2.751.1 | x4 - 2x3 + x2 - x - 1 | \( -\,751 \) | $S_4$ (as 4T5) | trivial |
| 4.0.761.1 | x4 - x3 + x2 + 2x + 1 | \( 761 \) | $S_4$ (as 4T5) | trivial |
| 4.2.775.1 | x4 - x3 - 3x - 1 | \( -\,5^{2}\cdot 31 \) | $D_{4}$ (as 4T3) | trivial |
| 4.0.784.1 | x4 - 3x2 + 4 | \( 2^{4}\cdot 7^{2} \) | $C_2^2$ (as 4T2) | trivial |
| 4.0.788.1 | x4 - x3 + 2x2 - 2x + 2 | \( 2^{2}\cdot 197 \) | $S_4$ (as 4T5) | trivial |
| 4.0.832.1 | x4 - 2x3 - 2x + 5 | \( 2^{6}\cdot 13 \) | $D_{4}$ (as 4T3) | trivial |
| 4.0.837.1 | x4 - x3 - 3x2 - x + 7 | \( 3^{3}\cdot 31 \) | $D_{4}$ (as 4T3) | trivial |
| 4.2.848.1 | x4 - x2 - 2x + 1 | \( -\,2^{4}\cdot 53 \) | $S_4$ (as 4T5) | trivial |
| 4.0.873.1 | x4 - x3 - 4x2 + x + 7 | \( 3^{2}\cdot 97 \) | $D_{4}$ (as 4T3) | trivial |
| 4.0.892.1 | x4 - x3 - x2 + 2 | \( 2^{2}\cdot 223 \) | $S_4$ (as 4T5) | trivial |
| 4.2.976.1 | x4 - 2x3 + 3x2 - 1 | \( -\,2^{4}\cdot 61 \) | $S_4$ (as 4T5) | trivial |
| 4.0.981.1 | x4 - x3 - 4x2 + 4x + 7 | \( 3^{2}\cdot 109 \) | $D_{4}$ (as 4T3) | trivial |