Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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Label | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
4.0.117.1 | $x^{4} - x^{3} - x^{2} + x + 1$ | $3^{2}\cdot 13$ | $D_{4}$ (as 4T3) | trivial |
4.0.125.1 | $x^{4} - x^{3} + x^{2} - x + 1$ | $5^{3}$ | $C_4$ (as 4T1) | trivial |
4.0.144.1 | $x^{4} - x^{2} + 1$ | $2^{4}\cdot 3^{2}$ | $C_2^2$ (as 4T2) | trivial |
4.0.189.1 | $x^{4} - x^{3} + 2 x + 1$ | $3^{3}\cdot 7$ | $D_{4}$ (as 4T3) | trivial |
4.0.225.1 | $x^{4} - x^{3} + 2 x^{2} + x + 1$ | $3^{2}\cdot 5^{2}$ | $C_2^2$ (as 4T2) | trivial |
4.0.229.1 | $x^{4} - x + 1$ | $229$ | $S_4$ (as 4T5) | trivial |
4.0.256.1 | $x^{4} + 1$ | $2^{8}$ | $C_2^2$ (as 4T2) | trivial |
4.0.257.1 | $x^{4} + x^{2} - x + 1$ | $257$ | $S_4$ (as 4T5) | trivial |
4.0.272.1 | $x^{4} + x^{2} - 2 x + 1$ | $2^{4}\cdot 17$ | $D_{4}$ (as 4T3) | trivial |
4.2.275.1 | $x^{4} - x^{3} + 2 x - 1$ | $-\,5^{2}\cdot 11$ | $D_{4}$ (as 4T3) | trivial |
4.2.283.1 | $x^{4} - x - 1$ | $-\,283$ | $S_4$ (as 4T5) | trivial |
4.0.320.1 | $x^{4} - 2 x^{3} + 2$ | $2^{6}\cdot 5$ | $D_{4}$ (as 4T3) | trivial |
4.2.331.1 | $x^{4} - x^{3} + x^{2} + x - 1$ | $-\,331$ | $S_4$ (as 4T5) | trivial |
4.0.333.1 | $x^{4} - x^{3} - 2 x^{2} + 3$ | $3^{2}\cdot 37$ | $D_{4}$ (as 4T3) | trivial |
4.0.392.1 | $x^{4} - x^{3} + x + 1$ | $2^{3}\cdot 7^{2}$ | $D_{4}$ (as 4T3) | trivial |
4.2.400.1 | $x^{4} - x^{2} - 1$ | $-\,2^{4}\cdot 5^{2}$ | $D_{4}$ (as 4T3) | trivial |
4.0.400.1 | $x^{4} + 3 x^{2} + 1$ | $2^{4}\cdot 5^{2}$ | $C_2^2$ (as 4T2) | trivial |
4.0.432.1 | $x^{4} - 3 x^{2} + 3$ | $2^{4}\cdot 3^{3}$ | $D_{4}$ (as 4T3) | trivial |
4.0.441.1 | $x^{4} - x^{3} - x^{2} - 2 x + 4$ | $3^{2}\cdot 7^{2}$ | $C_2^2$ (as 4T2) | trivial |
4.2.448.1 | $x^{4} - 2 x^{3} + x^{2} - 2 x + 1$ | $-\,2^{6}\cdot 7$ | $D_{4}$ (as 4T3) | trivial |
4.2.475.1 | $x^{4} - 2 x^{3} + 2 x^{2} - x - 1$ | $-\,5^{2}\cdot 19$ | $D_{4}$ (as 4T3) | trivial |
4.2.491.1 | $x^{4} - x^{3} - x^{2} + 3 x - 1$ | $-\,491$ | $S_4$ (as 4T5) | trivial |
4.2.507.1 | $x^{4} - x^{3} - x^{2} - x + 1$ | $-\,3\cdot 13^{2}$ | $D_{4}$ (as 4T3) | trivial |
4.0.512.1 | $x^{4} - 2 x^{2} + 2$ | $2^{9}$ | $D_{4}$ (as 4T3) | trivial |
4.0.513.1 | $x^{4} - x^{3} - 3 x^{2} + 2 x + 4$ | $3^{3}\cdot 19$ | $D_{4}$ (as 4T3) | trivial |
4.0.549.1 | $x^{4} - 2 x^{3} - 2 x^{2} + 3 x + 3$ | $3^{2}\cdot 61$ | $D_{4}$ (as 4T3) | trivial |
4.2.563.1 | $x^{4} - x^{3} + x^{2} - x - 1$ | $-\,563$ | $S_4$ (as 4T5) | trivial |
4.0.576.1 | $x^{4} - 2 x^{2} + 4$ | $2^{6}\cdot 3^{2}$ | $C_2^2$ (as 4T2) | trivial |
4.0.576.2 | $x^{4} + 2 x^{2} + 4$ | $2^{6}\cdot 3^{2}$ | $C_2^2$ (as 4T2) | trivial |
4.0.592.1 | $x^{4} + 2 x^{2} - 2 x + 1$ | $2^{4}\cdot 37$ | $S_4$ (as 4T5) | trivial |
4.0.605.1 | $x^{4} - x^{3} + x^{2} + x + 1$ | $5\cdot 11^{2}$ | $D_{4}$ (as 4T3) | trivial |
4.2.643.1 | $x^{4} - x^{3} - 2 x + 1$ | $-\,643$ | $S_4$ (as 4T5) | trivial |
4.0.656.1 | $x^{4} - 2 x^{3} - x^{2} + 2 x + 2$ | $2^{4}\cdot 41$ | $D_{4}$ (as 4T3) | trivial |
4.0.657.1 | $x^{4} - x^{3} + 5 x^{2} - 2 x + 4$ | $3^{2}\cdot 73$ | $D_{4}$ (as 4T3) | trivial |
4.2.688.1 | $x^{4} - 2 x - 1$ | $-\,2^{4}\cdot 43$ | $S_4$ (as 4T5) | trivial |
4.0.697.1 | $x^{4} - x^{3} + 2 x^{2} - x + 2$ | $17\cdot 41$ | $S_4$ (as 4T5) | trivial |
4.4.725.1 | $x^{4} - x^{3} - 3 x^{2} + x + 1$ | $5^{2}\cdot 29$ | $D_{4}$ (as 4T3) | trivial |
4.2.731.1 | $x^{4} - x^{3} + 2 x^{2} - 1$ | $-\,17\cdot 43$ | $S_4$ (as 4T5) | trivial |
4.2.751.1 | $x^{4} - 2 x^{3} + x^{2} - x - 1$ | $-\,751$ | $S_4$ (as 4T5) | trivial |
4.0.761.1 | $x^{4} - x^{3} + x^{2} + 2 x + 1$ | $761$ | $S_4$ (as 4T5) | trivial |
4.2.775.1 | $x^{4} - x^{3} - 3 x - 1$ | $-\,5^{2}\cdot 31$ | $D_{4}$ (as 4T3) | trivial |
4.0.784.1 | $x^{4} - 3 x^{2} + 4$ | $2^{4}\cdot 7^{2}$ | $C_2^2$ (as 4T2) | trivial |
4.0.788.1 | $x^{4} - x^{3} + 2 x^{2} - 2 x + 2$ | $2^{2}\cdot 197$ | $S_4$ (as 4T5) | trivial |
4.0.832.1 | $x^{4} - 2 x^{3} - 2 x + 5$ | $2^{6}\cdot 13$ | $D_{4}$ (as 4T3) | trivial |
4.0.837.1 | $x^{4} - x^{3} - 3 x^{2} - x + 7$ | $3^{3}\cdot 31$ | $D_{4}$ (as 4T3) | trivial |
4.2.848.1 | $x^{4} - x^{2} - 2 x + 1$ | $-\,2^{4}\cdot 53$ | $S_4$ (as 4T5) | trivial |
4.0.873.1 | $x^{4} - x^{3} - 4 x^{2} + x + 7$ | $3^{2}\cdot 97$ | $D_{4}$ (as 4T3) | trivial |
4.0.892.1 | $x^{4} - x^{3} - x^{2} + 2$ | $2^{2}\cdot 223$ | $S_4$ (as 4T5) | trivial |
4.2.976.1 | $x^{4} - 2 x^{3} + 3 x^{2} - 1$ | $-\,2^{4}\cdot 61$ | $S_4$ (as 4T5) | trivial |
4.0.981.1 | $x^{4} - x^{3} - 4 x^{2} + 4 x + 7$ | $3^{2}\cdot 109$ | $D_{4}$ (as 4T3) | trivial |