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 |
---|---|---|---|---|
5.5.14641.1 | $x^{5} - x^{4} - 4 x^{3} + 3 x^{2} + 3 x - 1$ | $11^{4}$ | $C_5$ (as 5T1) | trivial |
5.5.24217.1 | $x^{5} - 5 x^{3} - x^{2} + 3 x + 1$ | $61\cdot 397$ | $S_5$ (as 5T5) | trivial |
5.5.36497.1 | $x^{5} - 2 x^{4} - 3 x^{3} + 5 x^{2} + x - 1$ | $36497$ | $S_5$ (as 5T5) | trivial |
5.5.38569.1 | $x^{5} - 5 x^{3} + 4 x - 1$ | $38569$ | $S_5$ (as 5T5) | trivial |
5.5.65657.1 | $x^{5} - x^{4} - 5 x^{3} + 2 x^{2} + 5 x + 1$ | $65657$ | $S_5$ (as 5T5) | trivial |
5.5.70601.1 | $x^{5} - x^{4} - 5 x^{3} + 2 x^{2} + 3 x - 1$ | $17\cdot 4153$ | $S_5$ (as 5T5) | trivial |
5.5.81509.1 | $x^{5} - x^{4} - 5 x^{3} + 3 x^{2} + 5 x - 2$ | $81509$ | $S_5$ (as 5T5) | trivial |
5.5.81589.1 | $x^{5} - 6 x^{3} + 8 x - 1$ | $83\cdot 983$ | $S_5$ (as 5T5) | trivial |
5.5.89417.1 | $x^{5} - 6 x^{3} - x^{2} + 8 x + 3$ | $89417$ | $S_5$ (as 5T5) | trivial |
5.5.101833.1 | $x^{5} - x^{4} - 5 x^{3} + 5 x^{2} + 2 x - 1$ | $101833$ | $S_5$ (as 5T5) | trivial |
5.5.106069.1 | $x^{5} - 2 x^{4} - 4 x^{3} + 7 x^{2} + 3 x - 4$ | $73\cdot 1453$ | $S_5$ (as 5T5) | trivial |
5.5.117688.1 | $x^{5} - x^{4} - 5 x^{3} + 4 x^{2} + 4 x - 1$ | $2^{3}\cdot 47\cdot 313$ | $S_5$ (as 5T5) | trivial |
5.5.122821.1 | $x^{5} - 2 x^{4} - 4 x^{3} + 4 x^{2} + 3 x - 1$ | $263\cdot 467$ | $S_5$ (as 5T5) | trivial |
5.5.124817.1 | $x^{5} - 7 x^{3} - 6 x^{2} + 2 x + 1$ | $7\cdot 11\cdot 1621$ | $S_5$ (as 5T5) | trivial |
5.5.126032.1 | $x^{5} - 6 x^{3} + 6 x - 2$ | $2^{4}\cdot 7877$ | $S_5$ (as 5T5) | trivial |
5.5.135076.1 | $x^{5} - x^{4} - 5 x^{3} + 4 x^{2} + 4 x - 2$ | $2^{2}\cdot 33769$ | $S_5$ (as 5T5) | trivial |
5.5.138136.1 | $x^{5} - x^{4} - 6 x^{3} + 3 x^{2} + 4 x - 2$ | $2^{3}\cdot 31\cdot 557$ | $S_5$ (as 5T5) | trivial |
5.5.138917.1 | $x^{5} - 6 x^{3} - 2 x^{2} + 3 x + 1$ | $138917$ | $S_5$ (as 5T5) | trivial |
5.5.144209.1 | $x^{5} - 6 x^{3} - x^{2} + 6 x - 1$ | $13\cdot 11093$ | $S_5$ (as 5T5) | trivial |
5.5.147109.1 | $x^{5} - 2 x^{4} - 4 x^{3} + 5 x^{2} + 3 x - 2$ | $157\cdot 937$ | $S_5$ (as 5T5) | trivial |
5.5.149169.1 | $x^{5} - 6 x^{3} - 3 x^{2} + 4 x + 1$ | $3\cdot 19\cdot 2617$ | $S_5$ (as 5T5) | trivial |
5.5.153424.1 | $x^{5} - 2 x^{4} - 4 x^{3} + 8 x^{2} - 2$ | $2^{4}\cdot 43\cdot 223$ | $S_5$ (as 5T5) | trivial |
5.5.157457.1 | $x^{5} - 2 x^{4} - 4 x^{3} + 5 x^{2} + 4 x - 1$ | $157457$ | $S_5$ (as 5T5) | trivial |
5.5.160801.1 | $x^{5} - x^{4} - 5 x^{3} + 4 x^{2} + 3 x - 1$ | $401^{2}$ | $D_{5}$ (as 5T2) | trivial |
5.5.161121.1 | $x^{5} - x^{4} - 6 x^{3} + 3 x^{2} + 5 x + 1$ | $3\cdot 43\cdot 1249$ | $S_5$ (as 5T5) | trivial |
5.5.170701.1 | $x^{5} - x^{4} - 6 x^{3} + 4 x + 1$ | $170701$ | $S_5$ (as 5T5) | trivial |
5.5.173513.1 | $x^{5} - 2 x^{4} - 5 x^{3} + 3 x^{2} + 3 x - 1$ | $167\cdot 1039$ | $S_5$ (as 5T5) | trivial |
5.5.176281.1 | $x^{5} - x^{4} - 5 x^{3} + 3 x^{2} + 4 x - 1$ | $7\cdot 25183$ | $S_5$ (as 5T5) | trivial |
5.5.176684.1 | $x^{5} - 6 x^{3} - x^{2} + 5 x - 1$ | $2^{2}\cdot 44171$ | $S_5$ (as 5T5) | trivial |
5.5.179024.1 | $x^{5} - 8 x^{3} + 6 x - 2$ | $2^{4}\cdot 67\cdot 167$ | $S_5$ (as 5T5) | trivial |
5.5.180769.1 | $x^{5} - 2 x^{4} - 4 x^{3} + 7 x^{2} - 1$ | $41\cdot 4409$ | $S_5$ (as 5T5) | trivial |
5.5.181057.1 | $x^{5} - 2 x^{4} - 4 x^{3} + 7 x^{2} + 2 x - 3$ | $331\cdot 547$ | $S_5$ (as 5T5) | trivial |
5.5.186037.1 | $x^{5} - x^{4} - 6 x^{3} + 2 x^{2} + 5 x - 2$ | $186037$ | $S_5$ (as 5T5) | trivial |
5.5.195829.1 | $x^{5} - 2 x^{4} - 5 x^{3} + 6 x^{2} + 7 x + 1$ | $113\cdot 1733$ | $S_5$ (as 5T5) | trivial |
5.5.202817.1 | $x^{5} - 2 x^{4} - 4 x^{3} + 5 x^{2} + 2 x - 1$ | $202817$ | $S_5$ (as 5T5) | trivial |
5.5.205225.1 | $x^{5} - x^{4} - 6 x^{3} + 3 x^{2} + 7 x - 3$ | $5^{2}\cdot 8209$ | $S_5$ (as 5T5) | trivial |
5.5.207184.1 | $x^{5} - x^{4} - 6 x^{3} + 2 x^{2} + 7 x - 1$ | $2^{4}\cdot 23\cdot 563$ | $S_5$ (as 5T5) | trivial |
5.5.210557.1 | $x^{5} - x^{4} - 6 x^{3} + 4 x^{2} + 8 x - 1$ | $210557$ | $S_5$ (as 5T5) | trivial |
5.5.216637.1 | $x^{5} - 2 x^{4} - 4 x^{3} + 7 x^{2} + x - 2$ | $23\cdot 9419$ | $S_5$ (as 5T5) | trivial |
5.5.218524.1 | $x^{5} - 2 x^{4} - 4 x^{3} + 5 x^{2} + 3 x - 1$ | $2^{2}\cdot 54631$ | $S_5$ (as 5T5) | trivial |
5.5.220036.1 | $x^{5} - 2 x^{4} - 5 x^{3} + 11 x^{2} - 2 x - 1$ | $2^{2}\cdot 55009$ | $S_5$ (as 5T5) | trivial |
5.5.220669.1 | $x^{5} - 7 x^{3} - 2 x^{2} + 11 x + 5$ | $149\cdot 1481$ | $S_5$ (as 5T5) | trivial |
5.5.223824.1 | $x^{5} - 2 x^{4} - 4 x^{3} + 6 x^{2} + 2 x - 2$ | $2^{4}\cdot 3\cdot 4663$ | $S_5$ (as 5T5) | trivial |
5.5.223952.1 | $x^{5} - 6 x^{3} - 2 x^{2} + 6 x + 2$ | $2^{4}\cdot 13997$ | $S_5$ (as 5T5) | trivial |
5.5.224773.1 | $x^{5} - x^{4} - 6 x^{3} + 2 x^{2} + 7 x + 2$ | $53\cdot 4241$ | $S_5$ (as 5T5) | trivial |
5.5.230224.1 | $x^{5} - 2 x^{4} - 4 x^{3} + 6 x^{2} + 3 x - 2$ | $2^{4}\cdot 14389$ | $S_5$ (as 5T5) | trivial |
5.5.233489.1 | $x^{5} - x^{4} - 6 x^{3} + x^{2} + 5 x - 1$ | $233489$ | $S_5$ (as 5T5) | trivial |
5.5.236549.1 | $x^{5} - x^{4} - 6 x^{3} + 7 x^{2} + 2 x - 1$ | $236549$ | $S_5$ (as 5T5) | trivial |
5.5.240133.1 | $x^{5} - 2 x^{4} - 4 x^{3} + 6 x^{2} + 2 x - 1$ | $439\cdot 547$ | $S_5$ (as 5T5) | trivial |
5.5.240881.1 | $x^{5} - 2 x^{4} - 5 x^{3} + 9 x^{2} + 5 x - 7$ | $240881$ | $S_5$ (as 5T5) | trivial |