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| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 4.0.1521.1 | x4 - x3 + 4x2 + 3x + 9 | \( 3^{2}\cdot 13^{2} \) | $C_2^2$ (as 4T2) | $[2]$ |
| 4.0.1872.1 | x4 + 7x2 + 13 | \( 2^{4}\cdot 3^{2}\cdot 13 \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.2304.1 | x4 + 4x2 + 1 | \( 2^{8}\cdot 3^{2} \) | $C_2^2$ (as 4T2) | $[2]$ |
| 4.0.2304.2 | x4 + 9 | \( 2^{8}\cdot 3^{2} \) | $C_2^2$ (as 4T2) | $[2]$ |
| 4.0.2448.1 | x4 - x2 - 6x + 10 | \( 2^{4}\cdot 3^{2}\cdot 17 \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.2457.1 | x4 - x3 + 9x2 - 4x + 16 | \( 3^{3}\cdot 7\cdot 13 \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.2457.2 | x4 - x3 - 6x2 - x + 19 | \( 3^{3}\cdot 7\cdot 13 \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.2880.1 | x4 - 2x3 - 4x2 + 2x + 13 | \( 2^{6}\cdot 3^{2}\cdot 5 \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.2889.1 | x4 - x3 + 3x2 + 2x + 1 | \( 3^{3}\cdot 107 \) | $S_4$ (as 4T5) | $[2]$ |
| 4.0.2925.1 | x4 - x3 - 8x2 + 6x + 21 | \( 3^{2}\cdot 5^{2}\cdot 13 \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.3024.2 | x4 - 9x2 + 21 | \( 2^{4}\cdot 3^{3}\cdot 7 \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.3025.1 | x4 + 3x2 + 16 | \( 5^{2}\cdot 11^{2} \) | $C_2^2$ (as 4T2) | $[2]$ |
| 4.0.3136.3 | x4 + 6x2 + 16 | \( 2^{6}\cdot 7^{2} \) | $C_2^2$ (as 4T2) | $[2]$ |
| 4.0.3528.1 | x4 - x3 + 5x2 - 5x + 4 | \( 2^{3}\cdot 3^{2}\cdot 7^{2} \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.3600.1 | x4 + x2 + 4 | \( 2^{4}\cdot 3^{2}\cdot 5^{2} \) | $C_2^2$ (as 4T2) | $[2]$ |
| 4.0.3600.2 | x4 - 7x2 + 16 | \( 2^{4}\cdot 3^{2}\cdot 5^{2} \) | $C_2^2$ (as 4T2) | $[2]$ |
| 4.0.3600.3 | x4 - 5x2 + 25 | \( 2^{4}\cdot 3^{2}\cdot 5^{2} \) | $C_2^2$ (as 4T2) | $[2]$ |
| 4.0.3625.1 | x4 - x3 + 6x2 - x + 11 | \( 5^{3}\cdot 29 \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.3636.1 | x4 - x3 - x2 + x + 4 | \( 2^{2}\cdot 3^{2}\cdot 101 \) | $S_4$ (as 4T5) | $[2]$ |
| 4.0.3700.1 | x4 - x3 + 5x2 - 3x + 4 | \( 2^{2}\cdot 5^{2}\cdot 37 \) | $S_4$ (as 4T5) | $[2]$ |
| 4.0.3897.1 | x4 - x3 - 8x2 + 9x + 27 | \( 3^{2}\cdot 433 \) | $D_{4}$ (as 4T3) | $[3]$ |
| 4.0.4225.1 | x4 - x3 - 3x + 4 | \( 5^{2}\cdot 13^{2} \) | $A_4$ (as 4T4) | $[2]$ |
| 4.0.4232.1 | x4 - x3 + 4x2 + x + 1 | \( 2^{3}\cdot 23^{2} \) | $D_{4}$ (as 4T3) | $[3]$ |
| 4.0.4257.1 | x4 - x3 + 5x2 - 2x + 1 | \( 3^{2}\cdot 11\cdot 43 \) | $S_4$ (as 4T5) | $[2]$ |
| 4.0.4329.1 | x4 - x3 - 10x2 + 7x + 31 | \( 3^{2}\cdot 13\cdot 37 \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.4329.2 | x4 - x3 + 11x2 - 2x + 28 | \( 3^{2}\cdot 13\cdot 37 \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.4352.1 | x4 - 2x2 - 4x + 6 | \( 2^{8}\cdot 17 \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.4352.2 | x4 - 8x2 + 17 | \( 2^{8}\cdot 17 \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.4400.1 | x4 + 7x2 + 11 | \( 2^{4}\cdot 5^{2}\cdot 11 \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.4608.1 | x4 - 6x2 + 18 | \( 2^{9}\cdot 3^{2} \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.4624.1 | x4 + 9x2 + 16 | \( 2^{4}\cdot 17^{2} \) | $C_2^2$ (as 4T2) | $[2]$ |
| 4.0.4725.1 | x4 - x3 + 12x2 - 4x + 31 | \( 3^{3}\cdot 5^{2}\cdot 7 \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.4752.1 | x4 + 3x2 - 6x + 6 | \( 2^{4}\cdot 3^{3}\cdot 11 \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.4761.1 | x4 - x3 - 5x2 - 6x + 36 | \( 3^{2}\cdot 23^{2} \) | $C_2^2$ (as 4T2) | $[3]$ |
| 4.0.4805.1 | x4 - 2x3 + 2x2 - x + 8 | \( 5\cdot 31^{2} \) | $D_{4}$ (as 4T3) | $[3]$ |
| 4.0.5076.1 | x4 - x3 + 3x2 - x + 4 | \( 2^{2}\cdot 3^{3}\cdot 47 \) | $S_4$ (as 4T5) | $[2]$ |
| 4.0.5225.1 | x4 - x3 + 7x2 - 4x + 16 | \( 5^{2}\cdot 11\cdot 19 \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.5328.1 | x4 + 11x2 + 37 | \( 2^{4}\cdot 3^{2}\cdot 37 \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.5400.1 | x4 - x3 + 2x + 4 | \( 2^{3}\cdot 3^{3}\cdot 5^{2} \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.5400.2 | x4 - 3x2 + 6 | \( 2^{3}\cdot 3^{3}\cdot 5^{2} \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.5440.1 | x4 - 2x3 - 4x2 - 2x + 25 | \( 2^{6}\cdot 5\cdot 17 \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.5440.2 | x4 - 2x3 - 8x + 26 | \( 2^{6}\cdot 5\cdot 17 \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.5445.1 | x4 - x3 + 4x2 - 6x + 3 | \( 3^{2}\cdot 5\cdot 11^{2} \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.5517.1 | x4 - x3 - 11x2 + 9x + 39 | \( 3^{2}\cdot 613 \) | $D_{4}$ (as 4T3) | $[3]$ |
| 4.0.5616.1 | x4 - 12x2 + 39 | \( 2^{4}\cdot 3^{3}\cdot 13 \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.5616.2 | x4 + 12x2 + 39 | \( 2^{4}\cdot 3^{3}\cdot 13 \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.5648.1 | x4 - 2x3 - 7x2 + 8x + 20 | \( 2^{4}\cdot 353 \) | $D_{4}$ (as 4T3) | $[3]$ |
| 4.0.5733.1 | x4 - x3 + 13x2 - 9x + 39 | \( 3^{2}\cdot 7^{2}\cdot 13 \) | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.5744.1 | x4 + x2 - 4x + 3 | \( 2^{4}\cdot 359 \) | $S_4$ (as 4T5) | $[2]$ |
| 4.0.5904.1 | x4 - 7x2 - 6x + 25 | \( 2^{4}\cdot 3^{2}\cdot 41 \) | $D_{4}$ (as 4T3) | $[2]$ |
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