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Results (displaying matches 1-50 of 460081) Next
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 4.4.725.1 | x4 - x3 - 3x2 + x + 1 | \( 5^{2}\cdot 29 \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.1125.1 | x4 - x3 - 4x2 + 4x + 1 | \( 3^{2}\cdot 5^{3} \) | $C_4$ (as 4T1) | Trivial |
| 4.4.1600.1 | x4 - 6x2 + 4 | \( 2^{6}\cdot 5^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.4.1957.1 | x4 - 4x2 - x + 1 | \( 19\cdot 103 \) | $S_4$ (as 4T5) | Trivial |
| 4.4.2000.1 | x4 - 5x2 + 5 | \( 2^{4}\cdot 5^{3} \) | $C_4$ (as 4T1) | Trivial |
| 4.4.2048.1 | x4 - 4x2 + 2 | \( 2^{11} \) | $C_4$ (as 4T1) | Trivial |
| 4.4.2225.1 | x4 - x3 - 5x2 + 2x + 4 | \( 5^{2}\cdot 89 \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.2304.1 | x4 - 4x2 + 1 | \( 2^{8}\cdot 3^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.4.2525.1 | x4 - 2x3 - 4x2 + 5x + 5 | \( 5^{2}\cdot 101 \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.2624.1 | x4 - 2x3 - 3x2 + 2x + 1 | \( 2^{6}\cdot 41 \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.2777.1 | x4 - x3 - 4x2 + x + 2 | \( 2777 \) | $S_4$ (as 4T5) | Trivial |
| 4.4.3600.1 | x4 - 2x3 - 7x2 + 8x + 1 | \( 2^{4}\cdot 3^{2}\cdot 5^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.4.3981.1 | x4 - x3 - 4x2 + 2x + 1 | \( 3\cdot 1327 \) | $S_4$ (as 4T5) | Trivial |
| 4.4.4205.1 | x4 - x3 - 5x2 - x + 1 | \( 5\cdot 29^{2} \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.4225.1 | x4 - 9x2 + 4 | \( 5^{2}\cdot 13^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.4.4352.1 | x4 - 6x2 - 4x + 2 | \( 2^{8}\cdot 17 \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.4400.1 | x4 - 7x2 + 11 | \( 2^{4}\cdot 5^{2}\cdot 11 \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.4525.1 | x4 - x3 - 7x2 + 3x + 9 | \( 5^{2}\cdot 181 \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.4752.1 | x4 - 2x3 - 3x2 + 4x + 1 | \( 2^{4}\cdot 3^{3}\cdot 11 \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.4913.1 | x4 - x3 - 6x2 + x + 1 | \( 17^{3} \) | $C_4$ (as 4T1) | Trivial |
| 4.4.5125.1 | x4 - 2x3 - 6x2 + 7x + 11 | \( 5^{3}\cdot 41 \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.5225.1 | x4 - x3 - 8x2 + x + 11 | \( 5^{2}\cdot 11\cdot 19 \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.5725.1 | x4 - x3 - 8x2 + 6x + 11 | \( 5^{2}\cdot 229 \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.5744.1 | x4 - 5x2 - 2x + 1 | \( 2^{4}\cdot 359 \) | $S_4$ (as 4T5) | Trivial |
| 4.4.6125.1 | x4 - x3 - 9x2 + 9x + 11 | \( 5^{3}\cdot 7^{2} \) | $C_4$ (as 4T1) | Trivial |
| 4.4.6224.1 | x4 - 6x2 - 2x + 5 | \( 2^{4}\cdot 389 \) | $S_4$ (as 4T5) | Trivial |
| 4.4.6809.1 | x4 - 5x2 - x + 1 | \( 11\cdot 619 \) | $S_4$ (as 4T5) | Trivial |
| 4.4.7053.1 | x4 - 2x3 - 4x2 + 3x + 3 | \( 3\cdot 2351 \) | $S_4$ (as 4T5) | Trivial |
| 4.4.7056.1 | x4 - 5x2 + 1 | \( 2^{4}\cdot 3^{2}\cdot 7^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.4.7168.1 | x4 - 6x2 + 7 | \( 2^{10}\cdot 7 \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.7225.1 | x4 - 11x2 + 9 | \( 5^{2}\cdot 17^{2} \) | $C_2^2$ (as 4T2) | Trivial |
| 4.4.7232.1 | x4 - 2x3 - 5x2 + 4x + 4 | \( 2^{6}\cdot 113 \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.7488.1 | x4 - 2x3 - 4x2 + 2x + 1 | \( 2^{6}\cdot 3^{2}\cdot 13 \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.7537.1 | x4 - x3 - 5x2 + 4x + 3 | \( 7537 \) | $S_4$ (as 4T5) | Trivial |
| 4.4.7600.1 | x4 - 9x2 + 19 | \( 2^{4}\cdot 5^{2}\cdot 19 \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.7625.1 | x4 - x3 - 9x2 + 4x + 16 | \( 5^{3}\cdot 61 \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.8000.1 | x4 - 10x2 + 20 | \( 2^{6}\cdot 5^{3} \) | $C_4$ (as 4T1) | Trivial |
| 4.4.8069.1 | x4 - x3 - 5x2 + 5x + 1 | \( 8069 \) | $S_4$ (as 4T5) | Trivial |
| 4.4.8112.1 | x4 - 5x2 + 3 | \( 2^{4}\cdot 3\cdot 13^{2} \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.8468.1 | x4 - x3 - 5x2 + 3x + 4 | \( 2^{2}\cdot 29\cdot 73 \) | $S_4$ (as 4T5) | Trivial |
| 4.4.8525.1 | x4 - 2x3 - 8x2 + 9x + 19 | \( 5^{2}\cdot 11\cdot 31 \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.8725.1 | x4 - x3 - 10x2 + 2x + 19 | \( 5^{2}\cdot 349 \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.8768.1 | x4 - 2x3 - 5x2 + 6x + 7 | \( 2^{6}\cdot 137 \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.8789.1 | x4 - x3 - 6x2 - 2x + 1 | \( 11\cdot 17\cdot 47 \) | $S_4$ (as 4T5) | Trivial |
| 4.4.8957.1 | x4 - x3 - 5x2 + x + 1 | \( 13^{2}\cdot 53 \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.9225.1 | x4 - x3 - 10x2 + 7x + 19 | \( 3^{2}\cdot 5^{2}\cdot 41 \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.9248.1 | x4 - 5x2 + 2 | \( 2^{5}\cdot 17^{2} \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.9301.1 | x4 - x3 - 5x2 + x + 3 | \( 71\cdot 131 \) | $S_4$ (as 4T5) | Trivial |
| 4.4.9792.1 | x4 - 2x3 - 7x2 + 2x + 7 | \( 2^{6}\cdot 3^{2}\cdot 17 \) | $D_{4}$ (as 4T3) | Trivial |
| 4.4.9909.1 | x4 - 6x2 - 3x + 3 | \( 3^{3}\cdot 367 \) | $S_4$ (as 4T5) | Trivial |
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