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Label | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
4.2.507.1 | $x^{4} - x^{3} - x^{2} - x + 1$ | $-\,3\cdot 13^{2}$ | $D_{4}$ (as 4T3) | trivial |
4.0.1257.1 | $x^{4} - x^{2} - x + 2$ | $3\cdot 419$ | $S_4$ (as 4T5) | trivial |
4.2.1371.1 | $x^{4} + 2 x^{2} - x - 1$ | $-\,3\cdot 457$ | $S_4$ (as 4T5) | trivial |
4.0.1509.1 | $x^{4} - x^{3} + 2 x^{2} + 2 x + 1$ | $3\cdot 503$ | $S_4$ (as 4T5) | trivial |
4.0.1929.1 | $x^{4} - x^{3} + 4 x^{2} - 3 x + 2$ | $3\cdot 643$ | $S_4$ (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 |
4.0.2112.1 | $x^{4} - 2 x^{3} + x^{2} + 2$ | $2^{6}\cdot 3\cdot 11$ | $D_{4}$ (as 4T3) | trivial |
4.0.2112.2 | $x^{4} - 2 x^{3} + 5 x^{2} - 2 x + 1$ | $2^{6}\cdot 3\cdot 11$ | $D_{4}$ (as 4T3) | trivial |
4.0.2256.1 | $x^{4} + 2 x^{2} - 2 x + 2$ | $2^{4}\cdot 3\cdot 47$ | $S_4$ (as 4T5) | trivial |
4.0.2292.1 | $x^{4} - x^{3} + 2 x^{2} - 4 x + 4$ | $2^{2}\cdot 3\cdot 191$ | $S_4$ (as 4T5) | trivial |
4.2.2319.1 | $x^{4} - x^{3} - 2 x^{2} + 3 x + 2$ | $-\,3\cdot 773$ | $S_4$ (as 4T5) | trivial |
4.2.2859.1 | $x^{4} - x^{3} - x^{2} + 3 x - 3$ | $-\,3\cdot 953$ | $S_4$ (as 4T5) | trivial |
4.0.3072.1 | $x^{4} - 2 x^{2} + 3$ | $2^{10}\cdot 3$ | $D_{4}$ (as 4T3) | trivial |
4.2.3216.1 | $x^{4} - 2 x^{3} - x^{2} + 3$ | $-\,2^{4}\cdot 3\cdot 67$ | $S_4$ (as 4T5) | trivial |
4.2.3504.1 | $x^{4} - 2 x^{3} + 4 x^{2} - 1$ | $-\,2^{4}\cdot 3\cdot 73$ | $S_4$ (as 4T5) | trivial |
4.0.3624.1 | $x^{4} - x^{3} + 2 x^{2} - 3 x + 3$ | $2^{3}\cdot 3\cdot 151$ | $S_4$ (as 4T5) | trivial |
4.0.3648.2 | $x^{4} - 2 x^{3} - x^{2} + 6$ | $2^{6}\cdot 3\cdot 19$ | $D_{4}$ (as 4T3) | trivial |
4.2.3723.1 | $x^{4} - x^{3} + x^{2} + 3 x - 1$ | $-\,3\cdot 17\cdot 73$ | $S_4$ (as 4T5) | trivial |
4.0.3732.1 | $x^{4} - x^{3} + 4 x^{2} + 2$ | $2^{2}\cdot 3\cdot 311$ | $S_4$ (as 4T5) | trivial |
4.2.3747.1 | $x^{4} - x^{3} + x^{2} - 3 x - 1$ | $-\,3\cdot 1249$ | $S_4$ (as 4T5) | trivial |
4.2.3891.1 | $x^{4} - x^{3} - 4 x^{2} + 3$ | $-\,3\cdot 1297$ | $S_4$ (as 4T5) | trivial |
4.4.3981.1 | $x^{4} - x^{3} - 4 x^{2} + 2 x + 1$ | $3\cdot 1327$ | $S_4$ (as 4T5) | trivial |
4.2.3984.1 | $x^{4} - 2 x^{3} + 2 x^{2} + 6 x - 3$ | $-\,2^{4}\cdot 3\cdot 83$ | $S_4$ (as 4T5) | trivial |
4.0.3993.1 | $x^{4} - x^{3} - x^{2} + 2 x + 4$ | $3\cdot 11^{3}$ | $D_{4}$ (as 4T3) | trivial |
4.2.4152.1 | $x^{4} - x^{3} + x^{2} - 4$ | $-\,2^{3}\cdot 3\cdot 173$ | $S_4$ (as 4T5) | trivial |
4.0.4281.1 | $x^{4} - x^{3} - x^{2} + 3$ | $3\cdot 1427$ | $S_4$ (as 4T5) | trivial |
4.2.4287.1 | $x^{4} - x^{3} + 2 x^{2} - x - 2$ | $-\,3\cdot 1429$ | $S_4$ (as 4T5) | trivial |
4.0.4344.1 | $x^{4} - x^{3} + 4 x^{2} - 3 x + 5$ | $2^{3}\cdot 3\cdot 181$ | $S_4$ (as 4T5) | trivial |
4.2.4503.1 | $x^{4} - 2 x^{3} + x^{2} - 3 x - 1$ | $-\,3\cdot 19\cdot 79$ | $S_4$ (as 4T5) | trivial |
4.0.4596.1 | $x^{4} - x^{3} + x^{2} + 3 x + 2$ | $2^{2}\cdot 3\cdot 383$ | $S_4$ (as 4T5) | trivial |
4.0.4749.1 | $x^{4} - x^{3} - x^{2} + 3 x + 3$ | $3\cdot 1583$ | $S_4$ (as 4T5) | trivial |
4.2.4944.1 | $x^{4} - x^{2} - 4 x - 1$ | $-\,2^{4}\cdot 3\cdot 103$ | $S_4$ (as 4T5) | trivial |
4.0.5073.1 | $x^{4} - 2 x^{3} - x^{2} + x + 4$ | $3\cdot 19\cdot 89$ | $S_4$ (as 4T5) | trivial |
4.0.5325.1 | $x^{4} - x^{3} + 2 x^{2} + 3$ | $3\cdot 5^{2}\cdot 71$ | $S_4$ (as 4T5) | trivial |
4.2.5343.1 | $x^{4} - 2 x^{3} - x^{2} + x - 2$ | $-\,3\cdot 13\cdot 137$ | $S_4$ (as 4T5) | trivial |
4.2.5424.1 | $x^{4} - 2 x^{3} + 2 x^{2} - 3$ | $-\,2^{4}\cdot 3\cdot 113$ | $S_4$ (as 4T5) | trivial |
4.2.5448.1 | $x^{4} - x^{3} - 4 x^{2} + 5 x + 1$ | $-\,2^{3}\cdot 3\cdot 227$ | $S_4$ (as 4T5) | trivial |
4.0.5556.1 | $x^{4} - x^{3} + 4 x^{2} + 6 x + 2$ | $2^{2}\cdot 3\cdot 463$ | $S_4$ (as 4T5) | trivial |
4.2.5568.1 | $x^{4} - 2 x^{3} - 2 x^{2} + 2$ | $-\,2^{6}\cdot 3\cdot 29$ | $S_4$ (as 4T5) | trivial |
4.2.5595.1 | $x^{4} - x^{3} + 4 x^{2} - 1$ | $-\,3\cdot 5\cdot 373$ | $S_4$ (as 4T5) | trivial |
4.0.5613.1 | $x^{4} - x^{3} + 5 x^{2} - 3 x + 3$ | $3\cdot 1871$ | $S_4$ (as 4T5) | trivial |
4.0.5637.1 | $x^{4} - x^{3} + x^{2} + 3 x + 5$ | $3\cdot 1879$ | $S_4$ (as 4T5) | trivial |
4.2.5748.1 | $x^{4} - x^{2} - 8 x - 4$ | $-\,2^{2}\cdot 3\cdot 479$ | $S_4$ (as 4T5) | trivial |
4.0.5808.2 | $x^{4} + x^{2} + 3$ | $2^{4}\cdot 3\cdot 11^{2}$ | $D_{4}$ (as 4T3) | trivial |
4.0.6108.1 | $x^{4} - x^{3} + x^{2} + 6$ | $2^{2}\cdot 3\cdot 509$ | $S_4$ (as 4T5) | trivial |
4.0.6144.2 | $x^{4} + 4 x^{2} + 6$ | $2^{11}\cdot 3$ | $D_{4}$ (as 4T3) | trivial |
4.0.6348.1 | $x^{4} - x^{3} + 2 x^{2} + 2 x + 4$ | $2^{2}\cdot 3\cdot 23^{2}$ | $D_{4}$ (as 4T3) | $[3]$ |
4.2.6411.1 | $x^{4} - 2 x^{2} - 3 x - 3$ | $-\,3\cdot 2137$ | $S_4$ (as 4T5) | trivial |
4.2.6591.1 | $x^{4} - x^{3} + 2 x^{2} - 9 x + 3$ | $-\,3\cdot 13^{3}$ | $D_{4}$ (as 4T3) | trivial |
4.2.6603.1 | $x^{4} - 2 x^{2} - 3 x + 3$ | $-\,3\cdot 31\cdot 71$ | $S_4$ (as 4T5) | trivial |