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 |
---|---|---|---|---|
4.2.275.1 | $x^{4} - x^{3} + 2 x - 1$ | $-\,5^{2}\cdot 11$ | $D_{4}$ (as 4T3) | trivial |
4.2.283.1 | $x^{4} - x - 1$ | $-\,283$ | $S_4$ (as 4T5) | trivial |
4.2.331.1 | $x^{4} - x^{3} + x^{2} + x - 1$ | $-\,331$ | $S_4$ (as 4T5) | trivial |
4.2.400.1 | $x^{4} - x^{2} - 1$ | $-\,2^{4}\cdot 5^{2}$ | $D_{4}$ (as 4T3) | 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 |
4.2.563.1 | $x^{4} - x^{3} + x^{2} - x - 1$ | $-\,563$ | $S_4$ (as 4T5) | trivial |
4.2.643.1 | $x^{4} - x^{3} - 2 x + 1$ | $-\,643$ | $S_4$ (as 4T5) | trivial |
4.2.688.1 | $x^{4} - 2 x - 1$ | $-\,2^{4}\cdot 43$ | $S_4$ (as 4T5) | 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 |
4.2.775.1 | $x^{4} - x^{3} - 3 x - 1$ | $-\,5^{2}\cdot 31$ | $D_{4}$ (as 4T3) | trivial |
4.2.848.1 | $x^{4} - x^{2} - 2 x + 1$ | $-\,2^{4}\cdot 53$ | $S_4$ (as 4T5) | trivial |
4.2.976.1 | $x^{4} - 2 x^{3} + 3 x^{2} - 1$ | $-\,2^{4}\cdot 61$ | $S_4$ (as 4T5) | trivial |
4.2.1024.1 | $x^{4} - 2 x^{2} - 1$ | $-\,2^{10}$ | $D_{4}$ (as 4T3) | trivial |
4.2.1099.1 | $x^{4} - x^{3} + x^{2} - 3 x + 1$ | $-\,7\cdot 157$ | $S_4$ (as 4T5) | trivial |
4.2.1107.1 | $x^{4} - x^{3} - 2 x - 1$ | $-\,3^{3}\cdot 41$ | $S_4$ (as 4T5) | trivial |
4.2.1156.1 | $x^{4} - x^{3} - 2 x^{2} - x + 1$ | $-\,2^{2}\cdot 17^{2}$ | $D_{4}$ (as 4T3) | trivial |
4.2.1192.1 | $x^{4} - x^{3} + 2 x^{2} + x - 1$ | $-\,2^{3}\cdot 149$ | $S_4$ (as 4T5) | trivial |
4.2.1255.1 | $x^{4} - x^{2} - 3 x - 1$ | $-\,5\cdot 251$ | $S_4$ (as 4T5) | trivial |
4.2.1323.1 | $x^{4} - x^{3} - 3 x^{2} - x + 1$ | $-\,3^{3}\cdot 7^{2}$ | $D_{4}$ (as 4T3) | trivial |
4.2.1328.1 | $x^{4} - 3 x^{2} - 2 x + 1$ | $-\,2^{4}\cdot 83$ | $S_4$ (as 4T5) | trivial |
4.2.1371.1 | $x^{4} + 2 x^{2} - x - 1$ | $-\,3\cdot 457$ | $S_4$ (as 4T5) | trivial |
4.2.1375.1 | $x^{4} - x^{3} + x^{2} + 4 x - 4$ | $-\,5^{3}\cdot 11$ | $D_{4}$ (as 4T3) | trivial |
4.2.1399.1 | $x^{4} - x^{3} + x - 2$ | $-\,1399$ | $S_4$ (as 4T5) | trivial |
4.2.1423.1 | $x^{4} - x^{3} + x^{2} - 2 x - 1$ | $-\,1423$ | $S_4$ (as 4T5) | trivial |
4.2.1424.1 | $x^{4} + x^{2} - 2 x - 1$ | $-\,2^{4}\cdot 89$ | $S_4$ (as 4T5) | trivial |
4.2.1456.1 | $x^{4} - 2 x^{2} - 2 x + 1$ | $-\,2^{4}\cdot 7\cdot 13$ | $S_4$ (as 4T5) | trivial |
4.2.1472.1 | $x^{4} - 2 x^{3} + 2 x^{2} - 2$ | $-\,2^{6}\cdot 23$ | $S_4$ (as 4T5) | trivial |
4.2.1472.2 | $x^{4} - 2 x^{3} + 3 x^{2} - 2 x - 1$ | $-\,2^{6}\cdot 23$ | $D_{4}$ (as 4T3) | trivial |
4.2.1475.1 | $x^{4} - x^{3} - x^{2} + 5 x - 5$ | $-\,5^{2}\cdot 59$ | $D_{4}$ (as 4T3) | trivial |
4.2.1588.1 | $x^{4} - x^{3} - 3 x^{2} + 2$ | $-\,2^{2}\cdot 397$ | $S_4$ (as 4T5) | trivial |
4.2.1600.1 | $x^{4} - 2 x^{2} - 4$ | $-\,2^{6}\cdot 5^{2}$ | $D_{4}$ (as 4T3) | trivial |
4.2.1728.1 | $x^{4} - 2 x^{3} - 2 x + 1$ | $-\,2^{6}\cdot 3^{3}$ | $D_{4}$ (as 4T3) | trivial |
4.2.1732.1 | $x^{4} - x^{3} + 3 x - 1$ | $-\,2^{2}\cdot 433$ | $S_4$ (as 4T5) | trivial |
4.2.1775.1 | $x^{4} - 2 x^{3} + 3 x^{2} - 2 x - 4$ | $-\,5^{2}\cdot 71$ | $D_{4}$ (as 4T3) | trivial |
4.2.1791.1 | $x^{4} - x^{3} - x^{2} - 2 x + 1$ | $-\,3^{2}\cdot 199$ | $S_4$ (as 4T5) | trivial |
4.2.1792.1 | $x^{4} - 2 x^{2} - 4 x - 2$ | $-\,2^{8}\cdot 7$ | $D_{4}$ (as 4T3) | trivial |
4.2.1823.1 | $x^{4} - x^{3} + 3 x - 2$ | $-\,1823$ | $S_4$ (as 4T5) | trivial |
4.2.1856.1 | $x^{4} - 2 x^{3} + x^{2} - 2 x - 1$ | $-\,2^{6}\cdot 29$ | $S_4$ (as 4T5) | trivial |
4.2.1879.1 | $x^{4} - x^{3} - 2 x^{2} - 3 x + 1$ | $-\,1879$ | $S_4$ (as 4T5) | trivial |
4.2.1927.1 | $x^{4} - 2 x^{3} + x^{2} - 3 x + 1$ | $-\,41\cdot 47$ | $S_4$ (as 4T5) | trivial |
4.2.1931.1 | $x^{4} - 3 x + 1$ | $-\,1931$ | $S_4$ (as 4T5) | trivial |
4.2.1963.1 | $x^{4} - x^{3} + 2 x^{2} - 2 x - 1$ | $-\,13\cdot 151$ | $S_4$ (as 4T5) | trivial |
4.2.1968.1 | $x^{4} - 4 x^{2} - 2 x + 2$ | $-\,2^{4}\cdot 3\cdot 41$ | $S_4$ (as 4T5) | trivial |
4.2.1975.1 | $x^{4} - 2 x^{3} + x^{2} - 5$ | $-\,5^{2}\cdot 79$ | $D_{4}$ (as 4T3) | trivial |
4.2.1984.1 | $x^{4} - 2 x^{3} + x^{2} - 2$ | $-\,2^{6}\cdot 31$ | $D_{4}$ (as 4T3) | trivial |
4.2.1984.2 | $x^{4} - 2 x^{3} + 2 x^{2} + 2 x - 1$ | $-\,2^{6}\cdot 31$ | $S_4$ (as 4T5) | trivial |