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| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 4.0.144.1 | x4 - x2 + 1 | \( 2^{4}\cdot 3^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.0.225.1 | x4 - x3 + 2x2 + x + 1 | \( 3^{2}\cdot 5^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.0.256.1 | x4 + 1 | \( 2^{8} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.0.400.1 | x4 + 3x2 + 1 | \( 2^{4}\cdot 5^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.0.441.1 | x4 - x3 - x2 - 2x + 4 | \( 3^{2}\cdot 7^{2} \) | $C_2^2$ (as 4T2) | 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 |
| 4.0.784.1 | x4 - 3x2 + 4 | \( 2^{4}\cdot 7^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.0.1089.1 | x4 - x3 - 2x2 - 3x + 9 | \( 3^{2}\cdot 11^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.0.1225.1 | x4 - x3 + 5x2 + 2x + 4 | \( 5^{2}\cdot 7^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.0.1521.1 | x4 - x3 + 4x2 + 3x + 9 | \( 3^{2}\cdot 13^{2} \) | $C_2^2$ (as 4T2) | $[2]$ |
| 4.0.1600.1 | x4 + 6x2 + 4 | \( 2^{6}\cdot 5^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.4.1600.1 | x4 - 6x2 + 4 | \( 2^{6}\cdot 5^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.0.1936.1 | x4 - 5x2 + 9 | \( 2^{4}\cdot 11^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.0.2304.1 | x4 + 4x2 + 1 | \( 2^{8}\cdot 3^{2} \) | $C_2^2$ (as 4T2) | $[2]$ |
| 4.4.2304.1 | x4 - 4x2 + 1 | \( 2^{8}\cdot 3^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.0.2304.2 | x4 + 9 | \( 2^{8}\cdot 3^{2} \) | $C_2^2$ (as 4T2) | $[2]$ |
| 4.0.2601.1 | x4 - x3 + 5x2 + 4x + 16 | \( 3^{2}\cdot 17^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.0.2704.1 | x4 + 7x2 + 9 | \( 2^{4}\cdot 13^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.0.3025.1 | x4 + 3x2 + 16 | \( 5^{2}\cdot 11^{2} \) | $C_2^2$ (as 4T2) | $[2]$ |
| 4.0.3136.2 | x4 - 2x3 + 9x2 - 8x + 2 | \( 2^{6}\cdot 7^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.0.3136.3 | x4 + 6x2 + 16 | \( 2^{6}\cdot 7^{2} \) | $C_2^2$ (as 4T2) | $[2]$ |
| 4.0.3249.1 | x4 - x3 - 4x2 - 5x + 25 | \( 3^{2}\cdot 19^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.0.3600.1 | x4 + x2 + 4 | \( 2^{4}\cdot 3^{2}\cdot 5^{2} \) | $C_2^2$ (as 4T2) | $[2]$ |
| 4.4.3600.1 | x4 - 2x3 - 7x2 + 8x + 1 | \( 2^{4}\cdot 3^{2}\cdot 5^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 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) | $[2]$ |
| 4.4.4225.1 | x4 - 9x2 + 4 | \( 5^{2}\cdot 13^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.0.4624.1 | x4 + 9x2 + 16 | \( 2^{4}\cdot 17^{2} \) | $C_2^2$ (as 4T2) | $[2]$ |
| 4.0.4761.1 | x4 - x3 - 5x2 - 6x + 36 | \( 3^{2}\cdot 23^{2} \) | $C_2^2$ (as 4T2) | $[3]$ |
| 4.0.5776.1 | x4 - 9x2 + 25 | \( 2^{4}\cdot 19^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.0.5929.1 | x4 + 9x2 + 1 | \( 7^{2}\cdot 11^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.0.6400.1 | x4 - 4x2 + 9 | \( 2^{8}\cdot 5^{2} \) | $C_2^2$ (as 4T2) | $[2]$ |
| 4.0.6400.2 | x4 + 4x2 + 9 | \( 2^{8}\cdot 5^{2} \) | $C_2^2$ (as 4T2) | $[2]$ |
| 4.0.6400.3 | x4 + 25 | \( 2^{8}\cdot 5^{2} \) | $C_2^2$ (as 4T2) | $[2]$ |
| 4.0.7056.1 | x4 + 11x2 + 25 | \( 2^{4}\cdot 3^{2}\cdot 7^{2} \) | $C_2^2$ (as 4T2) | $[2]$ |
| 4.4.7056.1 | x4 - 5x2 + 1 | \( 2^{4}\cdot 3^{2}\cdot 7^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.0.7056.2 | x4 - 2x3 - x2 + 2x + 22 | \( 2^{4}\cdot 3^{2}\cdot 7^{2} \) | $C_2^2$ (as 4T2) | $[2]$ |
| 4.0.7056.3 | x4 + 7x2 + 49 | \( 2^{4}\cdot 3^{2}\cdot 7^{2} \) | $C_2^2$ (as 4T2) | $[2]$ |
| 4.4.7225.1 | x4 - 11x2 + 9 | \( 5^{2}\cdot 17^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.0.7569.1 | x4 - x3 + 8x2 + 7x + 49 | \( 3^{2}\cdot 29^{2} \) | $C_2^2$ (as 4T2) | $[3]$ |
| 4.0.7744.1 | x4 - 2x3 + 11x2 - 10x + 3 | \( 2^{6}\cdot 11^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.0.7744.2 | x4 - 2x3 + 3x2 - 2x + 23 | \( 2^{6}\cdot 11^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.0.8281.2 | x4 - 3x2 + 25 | \( 7^{2}\cdot 13^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.0.8464.1 | x4 - 11x2 + 36 | \( 2^{4}\cdot 23^{2} \) | $C_2^2$ (as 4T2) | $[3]$ |
| 4.0.8649.1 | x4 - x3 - 7x2 - 8x + 64 | \( 3^{2}\cdot 31^{2} \) | $C_2^2$ (as 4T2) | $[3]$ |
| 4.0.9025.1 | x4 + 7x2 + 36 | \( 5^{2}\cdot 19^{2} \) | $C_2^2$ (as 4T2) | $[4]$ |
| 4.4.10816.1 | x4 - 2x3 - 9x2 + 10x - 1 | \( 2^{6}\cdot 13^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.0.10816.2 | x4 - 2x3 - x2 + 2x + 27 | \( 2^{6}\cdot 13^{2} \) | $C_2^2$ (as 4T2) | $[3]$ |
| 4.0.11025.1 | x4 - x3 + 4x2 - 15x + 15 | \( 3^{2}\cdot 5^{2}\cdot 7^{2} \) | $C_2^2$ (as 4T2) | $[2]$ |
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