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Label | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
4.0.2889.1 | $x^{4} - x^{3} + 3 x^{2} + 2 x + 1$ | $3^{3}\cdot 107$ | $S_4$ (as 4T5) | $[2]$ |
4.2.18083.1 | $x^{4} - x^{3} + 5 x^{2} - 17 x + 3$ | $-\,13^{2}\cdot 107$ | $D_{4}$ (as 4T3) | trivial |
4.0.20544.2 | $x^{4} - 2 x^{3} + 2 x^{2} + 6 x + 3$ | $2^{6}\cdot 3\cdot 107$ | $S_4$ (as 4T5) | trivial |
4.0.20544.4 | $x^{4} - 2 x^{3} + 2 x^{2} + 10 x + 7$ | $2^{6}\cdot 3\cdot 107$ | $S_4$ (as 4T5) | trivial |
4.0.20544.5 | $x^{4} - 2 x^{3} - 3 x^{2} - 6 x + 27$ | $2^{6}\cdot 3\cdot 107$ | $D_{4}$ (as 4T3) | trivial |
4.0.20865.1 | $x^{4} + 5 x^{2} - 3 x + 3$ | $3\cdot 5\cdot 13\cdot 107$ | $S_4$ (as 4T5) | trivial |
4.0.20972.1 | $x^{4} - x^{3} + 7 x^{2} + 8 x + 22$ | $2^{2}\cdot 7^{2}\cdot 107$ | $D_{4}$ (as 4T3) | trivial |
4.0.21293.1 | $x^{4} - x^{3} + 6 x^{2} - 7 x + 9$ | $107\cdot 199$ | $S_4$ (as 4T5) | trivial |
4.2.23219.1 | $x^{4} - x^{3} + 2 x^{2} - 9$ | $-\,7\cdot 31\cdot 107$ | $S_4$ (as 4T5) | trivial |
4.2.23647.1 | $x^{4} - x^{3} - 3 x^{2} - 2 x + 7$ | $-\,13\cdot 17\cdot 107$ | $S_4$ (as 4T5) | trivial |
4.0.27713.1 | $x^{4} + 5 x^{2} - 3 x + 5$ | $7\cdot 37\cdot 107$ | $S_4$ (as 4T5) | $[3]$ |
4.2.31244.1 | $x^{4} - x^{3} + 6 x - 2$ | $-\,2^{2}\cdot 73\cdot 107$ | $S_4$ (as 4T5) | trivial |
4.2.31244.2 | $x^{4} - x^{3} - 6 x^{2} - 4 x + 2$ | $-\,2^{2}\cdot 73\cdot 107$ | $S_4$ (as 4T5) | trivial |
4.2.31244.3 | $x^{4} - x^{3} + 4 x^{2} + 8 x - 16$ | $-\,2^{2}\cdot 73\cdot 107$ | $S_4$ (as 4T5) | trivial |
4.2.32635.1 | $x^{4} - x^{3} - 2 x^{2} + 6 x + 1$ | $-\,5\cdot 61\cdot 107$ | $S_4$ (as 4T5) | trivial |
4.2.35524.1 | $x^{4} - x^{3} - x^{2} + 7 x - 10$ | $-\,2^{2}\cdot 83\cdot 107$ | $S_4$ (as 4T5) | trivial |
4.0.38841.1 | $x^{4} - x^{2} - 11 x + 14$ | $3\cdot 11^{2}\cdot 107$ | $S_4$ (as 4T5) | $[2]$ |
4.2.40767.1 | $x^{4} - 2 x^{3} + x^{2} - 3 x - 4$ | $-\,3\cdot 107\cdot 127$ | $S_4$ (as 4T5) | trivial |
4.2.42800.2 | $x^{4} - 2 x^{3} - 2 x^{2} - 2 x - 19$ | $-\,2^{4}\cdot 5^{2}\cdot 107$ | $S_4$ (as 4T5) | $[2]$ |
4.4.46224.1 | $x^{4} - 2 x^{3} - 15 x^{2} + 16 x + 16$ | $2^{4}\cdot 3^{3}\cdot 107$ | $D_{4}$ (as 4T3) | trivial |
4.2.52216.1 | $x^{4} - x^{3} - 7 x^{2} + 18 x - 18$ | $-\,2^{3}\cdot 61\cdot 107$ | $S_4$ (as 4T5) | trivial |
4.4.54249.1 | $x^{4} - x^{3} - 16 x^{2} - 13 x + 13$ | $3\cdot 13^{2}\cdot 107$ | $D_{4}$ (as 4T3) | trivial |
4.2.56496.1 | $x^{4} - 8 x^{2} - 6 x + 6$ | $-\,2^{4}\cdot 3\cdot 11\cdot 107$ | $S_4$ (as 4T5) | trivial |
4.2.57459.1 | $x^{4} - 2 x^{3} - 4 x^{2} - x - 3$ | $-\,3\cdot 107\cdot 179$ | $S_4$ (as 4T5) | trivial |
4.0.57673.2 | $x^{4} - 2 x^{3} - 5 x^{2} + 6 x + 72$ | $7^{2}\cdot 11\cdot 107$ | $D_{4}$ (as 4T3) | trivial |
4.0.57780.1 | $x^{4} - 2 x^{3} - 14 x + 40$ | $2^{2}\cdot 3^{3}\cdot 5\cdot 107$ | $S_4$ (as 4T5) | $[2]$ |
4.2.61632.1 | $x^{4} - 2 x^{2} - 107$ | $-\,2^{6}\cdot 3^{2}\cdot 107$ | $D_{4}$ (as 4T3) | trivial |
4.2.64307.1 | $x^{4} - x^{3} + 8 x^{2} + 13 x - 29$ | $-\,107\cdot 601$ | $S_4$ (as 4T5) | trivial |
4.2.65484.1 | $x^{4} - x^{3} - 2 x^{2} + 12 x - 12$ | $-\,2^{2}\cdot 3^{2}\cdot 17\cdot 107$ | $S_4$ (as 4T5) | trivial |
4.0.72225.1 | $x^{4} - 2 x^{3} - 3 x^{2} + 4 x + 19$ | $3^{3}\cdot 5^{2}\cdot 107$ | $D_{4}$ (as 4T3) | $[2]$ |
4.0.72332.1 | $x^{4} - x^{3} - 9 x^{2} + 4 x + 28$ | $2^{2}\cdot 13^{2}\cdot 107$ | $S_4$ (as 4T5) | $[3]$ |
4.0.75328.1 | $x^{4} - 2 x^{3} - 9 x^{2} - 8 x + 86$ | $2^{6}\cdot 11\cdot 107$ | $D_{4}$ (as 4T3) | $[3]$ |
4.0.76184.1 | $x^{4} - x^{3} - 2 x^{2} - 13 x + 27$ | $2^{3}\cdot 89\cdot 107$ | $S_4$ (as 4T5) | $[9]$ |
4.0.81320.1 | $x^{4} - x^{3} + 12 x^{2} - 15 x + 5$ | $2^{3}\cdot 5\cdot 19\cdot 107$ | $S_4$ (as 4T5) | trivial |
4.0.82176.1 | $x^{4} - 16 x^{2} - 8 x + 89$ | $2^{8}\cdot 3\cdot 107$ | $D_{4}$ (as 4T3) | $[2]$ |
4.0.84316.1 | $x^{4} - x^{3} - 6 x^{2} - 9 x + 37$ | $2^{2}\cdot 107\cdot 197$ | $S_4$ (as 4T5) | trivial |
4.2.87419.1 | $x^{4} - 2 x^{3} + 9 x^{2} - 4 x - 9$ | $-\,19\cdot 43\cdot 107$ | $S_4$ (as 4T5) | trivial |
4.2.89131.2 | $x^{4} - 6 x^{2} - 13 x - 10$ | $-\,7^{2}\cdot 17\cdot 107$ | $S_4$ (as 4T5) | trivial |
4.2.89131.3 | $x^{4} - 12 x^{2} - 27 x - 19$ | $-\,7^{2}\cdot 17\cdot 107$ | $S_4$ (as 4T5) | trivial |
4.2.89559.1 | $x^{4} - 2 x^{3} + 3 x^{2} + 5 x - 16$ | $-\,3^{3}\cdot 31\cdot 107$ | $S_4$ (as 4T5) | trivial |
4.2.89987.1 | $x^{4} - 2 x^{3} + x - 7$ | $-\,29^{2}\cdot 107$ | $D_{4}$ (as 4T3) | trivial |
4.0.92448.1 | $x^{4} - 3 x^{2} - 6 x + 18$ | $2^{5}\cdot 3^{3}\cdot 107$ | $S_4$ (as 4T5) | trivial |
4.2.92555.1 | $x^{4} - x^{3} + 11 x^{2} - 2 x - 32$ | $-\,5\cdot 107\cdot 173$ | $S_4$ (as 4T5) | trivial |
4.2.100580.1 | $x^{4} - x^{3} - 7 x^{2} + 8 x - 32$ | $-\,2^{2}\cdot 5\cdot 47\cdot 107$ | $S_4$ (as 4T5) | trivial |
4.0.101329.1 | $x^{4} + 9 x^{2} - 12 x + 13$ | $107\cdot 947$ | $S_4$ (as 4T5) | $[4]$ |
4.4.101329.1 | $x^{4} - x^{3} - 12 x^{2} + 11 x + 5$ | $107\cdot 947$ | $S_4$ (as 4T5) | trivial |
4.0.102292.1 | $x^{4} - x^{3} - x^{2} + 9 x + 26$ | $2^{2}\cdot 107\cdot 239$ | $S_4$ (as 4T5) | trivial |
4.0.104325.1 | $x^{4} - x^{3} + 5 x^{2} - x + 19$ | $3\cdot 5^{2}\cdot 13\cdot 107$ | $S_4$ (as 4T5) | trivial |
4.2.106572.1 | $x^{4} - x^{3} - 2 x^{2} - 12 x + 6$ | $-\,2^{2}\cdot 3\cdot 83\cdot 107$ | $S_4$ (as 4T5) | trivial |
4.2.107000.1 | $x^{4} - x^{3} - 4 x^{2} + 14 x - 4$ | $-\,2^{3}\cdot 5^{3}\cdot 107$ | $S_4$ (as 4T5) | $[2]$ |