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 |
---|---|---|---|---|
5.1.3825936.1 | $x^{5} - 2 x^{4} - 5 x^{3} + 24 x^{2} - 42 x + 36$ | $2^{4}\cdot 3^{2}\cdot 163^{2}$ | $D_{5}$ (as 5T2) | $[11]$ |
5.1.3965816.1 | $x^{5} - 2 x^{4} + 7 x^{3} - 11 x^{2} - 6 x - 1$ | $2^{3}\cdot 337\cdot 1471$ | $S_5$ (as 5T5) | $[11]$ |
5.1.4532905.1 | $x^{5} - x^{4} + 9 x^{3} - x^{2} + 17 x - 1$ | $5\cdot 13\cdot 69737$ | $S_5$ (as 5T5) | $[11]$ |
5.1.4604992.1 | $x^{5} - 2 x^{4} + 8 x^{3} - 36 x^{2} + 67 x - 30$ | $2^{6}\cdot 7\cdot 19\cdot 541$ | $S_5$ (as 5T5) | $[11]$ |
5.1.4704080.1 | $x^{5} - x^{4} + 6 x^{3} + 4 x^{2} + 7 x - 1$ | $2^{4}\cdot 5\cdot 127\cdot 463$ | $S_5$ (as 5T5) | $[11]$ |
5.1.4718800.1 | $x^{5} - 2 x^{4} + 2 x^{3} + 10 x^{2} - 30 x + 20$ | $2^{4}\cdot 5^{2}\cdot 47\cdot 251$ | $S_5$ (as 5T5) | $[11]$ |
5.1.4892116.1 | $x^{5} - x^{4} + 4 x^{3} + 12 x^{2} - 38 x + 44$ | $2^{2}\cdot 1223029$ | $S_5$ (as 5T5) | $[12]$ |
5.1.4953845.1 | $x^{5} - 2 x^{4} + 2 x^{3} + 10 x^{2} + 5 x - 1$ | $5\cdot 13\cdot 76213$ | $S_5$ (as 5T5) | $[11]$ |
5.1.4990864.1 | $x^{5} - 3 x^{3} - 10 x^{2} + 25 x - 12$ | $2^{4}\cdot 73\cdot 4273$ | $S_5$ (as 5T5) | $[11]$ |
5.1.5360324.1 | $x^{5} - 2 x^{4} + x^{3} - 9 x^{2} + 14 x + 1$ | $2^{2}\cdot 911\cdot 1471$ | $S_5$ (as 5T5) | $[11]$ |
5.1.5415540.1 | $x^{5} - 2 x^{3} - 4 x^{2} + 3 x + 18$ | $2^{2}\cdot 3\cdot 5\cdot 13\cdot 53\cdot 131$ | $S_5$ (as 5T5) | $[13]$ |
5.1.5439349.1 | $x^{5} - x^{4} + 6 x^{3} - 10 x^{2} + 11 x - 6$ | $5439349$ | $S_5$ (as 5T5) | $[11]$ |
5.1.5574629.1 | $x^{5} - x^{4} + 5 x^{3} - 11 x^{2} + 11 x - 6$ | $113\cdot 49333$ | $S_5$ (as 5T5) | $[12]$ |
5.1.5592784.1 | $x^{5} - 2 x^{4} + 2 x^{3} + 32 x^{2} - 51 x + 50$ | $2^{4}\cdot 293\cdot 1193$ | $S_5$ (as 5T5) | $[11]$ |
5.1.5665572.1 | $x^{5} - x^{4} + 13 x^{3} - 14 x^{2} + 44 x - 44$ | $2^{2}\cdot 3^{3}\cdot 11\cdot 19\cdot 251$ | $S_5$ (as 5T5) | $[11]$ |
5.1.5718864.3 | $x^{5} - x^{4} + 10 x^{3} - 4 x^{2} + 24 x + 6$ | $2^{4}\cdot 3\cdot 283\cdot 421$ | $S_5$ (as 5T5) | $[11]$ |
5.1.5781873.1 | $x^{5} - 2 x^{4} + 7 x^{3} + 9 x^{2} + 30 x + 72$ | $3\cdot 373\cdot 5167$ | $S_5$ (as 5T5) | $[11]$ |
5.1.6017045.1 | $x^{5} - 2 x^{4} + 4 x^{3} - 17 x^{2} + 10 x - 16$ | $5\cdot 1097^{2}$ | $S_5$ (as 5T5) | $[11]$ |
5.1.6076884.1 | $x^{5} - 4 x^{3} - 24 x^{2} - 11 x - 34$ | $2^{2}\cdot 3\cdot 11\cdot 19\cdot 2423$ | $S_5$ (as 5T5) | $[11]$ |
5.1.6193913.1 | $x^{5} - x^{4} + 5 x^{3} - 8 x^{2} + 10 x + 1$ | $11\cdot 263\cdot 2141$ | $S_5$ (as 5T5) | $[13]$ |
5.1.6214788.1 | $x^{5} + x^{3} - 3 x^{2} + 8 x - 1$ | $2^{2}\cdot 3^{2}\cdot 172633$ | $S_5$ (as 5T5) | $[11]$ |
5.1.6223825.1 | $x^{5} - 6 x^{3} - 3 x^{2} + 22 x - 15$ | $5^{2}\cdot 241\cdot 1033$ | $S_5$ (as 5T5) | $[11]$ |
5.1.6226421.1 | $x^{5} + 3 x^{3} - 19 x^{2} - 12 x - 53$ | $977\cdot 6373$ | $S_5$ (as 5T5) | $[11]$ |
5.1.6265888.1 | $x^{5} - 2 x^{4} + 3 x^{3} + 6 x^{2} + 10 x + 4$ | $2^{5}\cdot 195809$ | $S_5$ (as 5T5) | $[11]$ |
5.1.6289488.2 | $x^{5} - 2 x^{4} - 2 x^{3} + 6 x^{2} + 30 x + 24$ | $2^{4}\cdot 3^{4}\cdot 23\cdot 211$ | $S_5$ (as 5T5) | $[13]$ |
5.1.6317352.1 | $x^{5} - x^{4} + 4 x^{3} + 3 x^{2} - 12 x + 6$ | $2^{3}\cdot 3^{4}\cdot 9749$ | $S_5$ (as 5T5) | $[12]$ |
5.1.6370809.1 | $x^{5} - 2 x^{4} + 12 x^{3} - 9 x^{2} + 9 x + 1$ | $3\cdot 2123603$ | $S_5$ (as 5T5) | $[11]$ |
5.1.6384096.1 | $x^{5} + 12 x^{3} - 10 x^{2} - 12 x - 36$ | $2^{5}\cdot 3^{5}\cdot 821$ | $S_5$ (as 5T5) | $[11]$ |
5.1.6401221.1 | $x^{5} - x^{4} - 4 x^{3} + 27 x^{2} - 49 x + 58$ | $31^{2}\cdot 6661$ | $S_5$ (as 5T5) | $[13]$ |
5.1.6479824.1 | $x^{5} - x^{4} + 10 x^{3} + 4 x^{2} + 3 x - 1$ | $2^{4}\cdot 13\cdot 31153$ | $S_5$ (as 5T5) | $[11]$ |
5.1.6495369.1 | $x^{5} - 2 x^{4} + 15 x^{3} - 14 x^{2} + 33 x - 48$ | $3\cdot 59\cdot 36697$ | $S_5$ (as 5T5) | $[11]$ |
5.1.6540321.1 | $x^{5} - x^{4} - 8 x^{3} - 3 x^{2} + 26 x + 24$ | $3\cdot 2180107$ | $S_5$ (as 5T5) | $[11]$ |
5.1.6571389.1 | $x^{5} - x^{4} + 8 x^{3} - 9 x^{2} + 8 x - 1$ | $3\cdot 11^{2}\cdot 43\cdot 421$ | $S_5$ (as 5T5) | $[11]$ |
5.1.6721120.1 | $x^{5} - x^{4} + 5 x^{3} - 3 x^{2} + 28$ | $2^{5}\cdot 5\cdot 7\cdot 17\cdot 353$ | $S_5$ (as 5T5) | $[11]$ |
5.1.6763644.1 | $x^{5} - x^{4} + 2 x^{3} + 7 x^{2} - 2 x - 6$ | $2^{2}\cdot 3^{2}\cdot 89\cdot 2111$ | $S_5$ (as 5T5) | $[11]$ |
5.1.6772340.1 | $x^{5} - 2 x^{4} + 4 x^{3} + 4 x^{2} - 7 x + 20$ | $2^{2}\cdot 5\cdot 53\cdot 6389$ | $S_5$ (as 5T5) | $[13]$ |
5.1.6837360.1 | $x^{5} - 2 x^{4} - x^{3} + 4 x^{2} + 15 x + 12$ | $2^{4}\cdot 3\cdot 5\cdot 31\cdot 919$ | $S_5$ (as 5T5) | $[11]$ |
5.1.6865236.1 | $x^{5} - x^{4} + 7 x^{3} - 7 x^{2} + 28 x - 64$ | $2^{2}\cdot 3^{5}\cdot 7\cdot 1009$ | $S_5$ (as 5T5) | $[13]$ |
5.1.6914516.1 | $x^{5} - x^{4} + 12 x^{3} + 4 x^{2} + 6 x - 8$ | $2^{2}\cdot 7\cdot 246947$ | $S_5$ (as 5T5) | $[12]$ |
5.1.6977012.1 | $x^{5} - 2 x^{4} - 2 x^{3} - 6 x^{2} + 67 x + 18$ | $2^{2}\cdot 7^{2}\cdot 35597$ | $S_5$ (as 5T5) | $[13]$ |
5.1.7145577.1 | $x^{5} + 3 x^{3} - 5 x^{2} - 3 x - 6$ | $3^{4}\cdot 19\cdot 4643$ | $S_5$ (as 5T5) | $[11]$ |
5.1.7307724.1 | $x^{5} + 12 x^{3} - 24 x^{2} + 19 x - 160$ | $2^{2}\cdot 3\cdot 608977$ | $S_5$ (as 5T5) | $[12]$ |
5.1.7327940.1 | $x^{5} - x^{4} + 7 x^{3} - 3 x^{2} + 2 x + 20$ | $2^{2}\cdot 5\cdot 366397$ | $S_5$ (as 5T5) | $[13]$ |
5.1.7354869.1 | $x^{5} - x^{4} + 8 x^{3} + 6 x + 1$ | $3\cdot 997\cdot 2459$ | $S_5$ (as 5T5) | $[13]$ |
5.1.7415200.1 | $x^{5} - x^{4} + 3 x^{3} + 15 x^{2} - 50$ | $2^{5}\cdot 5^{2}\cdot 13\cdot 23\cdot 31$ | $S_5$ (as 5T5) | $[11]$ |
5.1.7442928.1 | $x^{5} - 2 x^{4} + 6 x^{3} - 30 x^{2} + 60 x - 36$ | $2^{4}\cdot 3^{4}\cdot 5743$ | $S_5$ (as 5T5) | $[11]$ |
5.1.7486941.1 | $x^{5} - x^{4} - 2 x^{3} + 20 x^{2} + 39 x + 18$ | $3\cdot 7\cdot 11\cdot 32411$ | $S_5$ (as 5T5) | $[11]$ |
5.1.7489752.1 | $x^{5} - x^{4} + 9 x^{3} - 6 x^{2} + 2 x + 1$ | $2^{3}\cdot 3\cdot 312073$ | $S_5$ (as 5T5) | $[11]$ |
5.1.7500080.1 | $x^{5} - x^{4} + 2 x^{3} + 16 x^{2} + x + 1$ | $2^{4}\cdot 5\cdot 7\cdot 59\cdot 227$ | $S_5$ (as 5T5) | $[14]$ |
5.1.7616097.1 | $x^{5} - x^{4} + 8 x^{3} - 11 x^{2} - 8 x + 12$ | $3^{2}\cdot 846233$ | $S_5$ (as 5T5) | $[11]$ |