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Results (displaying matches 1-50 of at least 1000) Next
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 5.1.3825936.1 | x5 - 2x4 - 5x3 + 24x2 - 42x + 36 | \( 2^{4}\cdot 3^{2}\cdot 163^{2} \) | $D_{5}$ (as 5T2) | $[11]$ |
| 5.1.3965816.1 | x5 - 2x4 + 7x3 - 11x2 - 6x - 1 | \( 2^{3}\cdot 337\cdot 1471 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.4532905.1 | x5 - x4 + 9x3 - x2 + 17x - 1 | \( 5\cdot 13\cdot 69737 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.4604992.1 | x5 - 2x4 + 8x3 - 36x2 + 67x - 30 | \( 2^{6}\cdot 7\cdot 19\cdot 541 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.4704080.1 | x5 - x4 + 6x3 + 4x2 + 7x - 1 | \( 2^{4}\cdot 5\cdot 127\cdot 463 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.4718800.1 | x5 - 2x4 + 2x3 + 10x2 - 30x + 20 | \( 2^{4}\cdot 5^{2}\cdot 47\cdot 251 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.4892116.1 | x5 - x4 + 4x3 + 12x2 - 38x + 44 | \( 2^{2}\cdot 1223029 \) | $S_5$ (as 5T5) | $[12]$ |
| 5.1.4953845.1 | x5 - 2x4 + 2x3 + 10x2 + 5x - 1 | \( 5\cdot 13\cdot 76213 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.4990864.1 | x5 - 3x3 - 10x2 + 25x - 12 | \( 2^{4}\cdot 73\cdot 4273 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.5360324.1 | x5 - 2x4 + x3 - 9x2 + 14x + 1 | \( 2^{2}\cdot 911\cdot 1471 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.5415540.1 | x5 - 2x3 - 4x2 + 3x + 18 | \( 2^{2}\cdot 3\cdot 5\cdot 13\cdot 53\cdot 131 \) | $S_5$ (as 5T5) | $[13]$ |
| 5.1.5439349.1 | x5 - x4 + 6x3 - 10x2 + 11x - 6 | \( 5439349 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.5574629.1 | x5 - x4 + 5x3 - 11x2 + 11x - 6 | \( 113\cdot 49333 \) | $S_5$ (as 5T5) | $[12]$ |
| 5.1.5592784.1 | x5 - 2x4 + 2x3 + 32x2 - 51x + 50 | \( 2^{4}\cdot 293\cdot 1193 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.5665572.1 | x5 - x4 + 13x3 - 14x2 + 44x - 44 | \( 2^{2}\cdot 3^{3}\cdot 11\cdot 19\cdot 251 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.5718864.3 | x5 - x4 + 10x3 - 4x2 + 24x + 6 | \( 2^{4}\cdot 3\cdot 283\cdot 421 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.5781873.1 | x5 - 2x4 + 7x3 + 9x2 + 30x + 72 | \( 3\cdot 373\cdot 5167 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.6017045.1 | x5 - 2x4 + 4x3 - 17x2 + 10x - 16 | \( 5\cdot 1097^{2} \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.6076884.1 | x5 - 4x3 - 24x2 - 11x - 34 | \( 2^{2}\cdot 3\cdot 11\cdot 19\cdot 2423 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.6193913.1 | x5 - x4 + 5x3 - 8x2 + 10x + 1 | \( 11\cdot 263\cdot 2141 \) | $S_5$ (as 5T5) | $[13]$ |
| 5.1.6214788.1 | x5 + x3 - 3x2 + 8x - 1 | \( 2^{2}\cdot 3^{2}\cdot 172633 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.6223825.1 | x5 - 6x3 - 3x2 + 22x - 15 | \( 5^{2}\cdot 241\cdot 1033 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.6226421.1 | x5 + 3x3 - 19x2 - 12x - 53 | \( 977\cdot 6373 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.6265888.1 | x5 - 2x4 + 3x3 + 6x2 + 10x + 4 | \( 2^{5}\cdot 195809 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.6289488.2 | x5 - 2x4 - 2x3 + 6x2 + 30x + 24 | \( 2^{4}\cdot 3^{4}\cdot 23\cdot 211 \) | $S_5$ (as 5T5) | $[13]$ |
| 5.1.6317352.1 | x5 - x4 + 4x3 + 3x2 - 12x + 6 | \( 2^{3}\cdot 3^{4}\cdot 9749 \) | $S_5$ (as 5T5) | $[12]$ |
| 5.1.6370809.1 | x5 - 2x4 + 12x3 - 9x2 + 9x + 1 | \( 3\cdot 2123603 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.6384096.1 | x5 + 12x3 - 10x2 - 12x - 36 | \( 2^{5}\cdot 3^{5}\cdot 821 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.6401221.1 | x5 - x4 - 4x3 + 27x2 - 49x + 58 | \( 31^{2}\cdot 6661 \) | $S_5$ (as 5T5) | $[13]$ |
| 5.1.6479824.1 | x5 - x4 + 10x3 + 4x2 + 3x - 1 | \( 2^{4}\cdot 13\cdot 31153 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.6495369.1 | x5 - 2x4 + 15x3 - 14x2 + 33x - 48 | \( 3\cdot 59\cdot 36697 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.6540321.1 | x5 - x4 - 8x3 - 3x2 + 26x + 24 | \( 3\cdot 2180107 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.6571389.1 | x5 - x4 + 8x3 - 9x2 + 8x - 1 | \( 3\cdot 11^{2}\cdot 43\cdot 421 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.6721120.1 | x5 - x4 + 5x3 - 3x2 + 28 | \( 2^{5}\cdot 5\cdot 7\cdot 17\cdot 353 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.6763644.1 | x5 - x4 + 2x3 + 7x2 - 2x - 6 | \( 2^{2}\cdot 3^{2}\cdot 89\cdot 2111 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.6772340.1 | x5 - 2x4 + 4x3 + 4x2 - 7x + 20 | \( 2^{2}\cdot 5\cdot 53\cdot 6389 \) | $S_5$ (as 5T5) | $[13]$ |
| 5.1.6837360.1 | x5 - 2x4 - x3 + 4x2 + 15x + 12 | \( 2^{4}\cdot 3\cdot 5\cdot 31\cdot 919 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.6865236.1 | x5 - x4 + 7x3 - 7x2 + 28x - 64 | \( 2^{2}\cdot 3^{5}\cdot 7\cdot 1009 \) | $S_5$ (as 5T5) | $[13]$ |
| 5.1.6914516.1 | x5 - x4 + 12x3 + 4x2 + 6x - 8 | \( 2^{2}\cdot 7\cdot 246947 \) | $S_5$ (as 5T5) | $[12]$ |
| 5.1.6977012.1 | x5 - 2x4 - 2x3 - 6x2 + 67x + 18 | \( 2^{2}\cdot 7^{2}\cdot 35597 \) | $S_5$ (as 5T5) | $[13]$ |
| 5.1.7145577.1 | x5 + 3x3 - 5x2 - 3x - 6 | \( 3^{4}\cdot 19\cdot 4643 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.7307724.1 | x5 + 12x3 - 24x2 + 19x - 160 | \( 2^{2}\cdot 3\cdot 608977 \) | $S_5$ (as 5T5) | $[12]$ |
| 5.1.7327940.1 | x5 - x4 + 7x3 - 3x2 + 2x + 20 | \( 2^{2}\cdot 5\cdot 366397 \) | $S_5$ (as 5T5) | $[13]$ |
| 5.1.7354869.1 | x5 - x4 + 8x3 + 6x + 1 | \( 3\cdot 997\cdot 2459 \) | $S_5$ (as 5T5) | $[13]$ |
| 5.1.7415200.1 | x5 - x4 + 3x3 + 15x2 - 50 | \( 2^{5}\cdot 5^{2}\cdot 13\cdot 23\cdot 31 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.7442928.1 | x5 - 2x4 + 6x3 - 30x2 + 60x - 36 | \( 2^{4}\cdot 3^{4}\cdot 5743 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.7486941.1 | x5 - x4 - 2x3 + 20x2 + 39x + 18 | \( 3\cdot 7\cdot 11\cdot 32411 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.7489752.1 | x5 - x4 + 9x3 - 6x2 + 2x + 1 | \( 2^{3}\cdot 3\cdot 312073 \) | $S_5$ (as 5T5) | $[11]$ |
| 5.1.7500080.1 | x5 - x4 + 2x3 + 16x2 + x + 1 | \( 2^{4}\cdot 5\cdot 7\cdot 59\cdot 227 \) | $S_5$ (as 5T5) | $[14]$ |
| 5.1.7616097.1 | x5 - x4 + 8x3 - 11x2 - 8x + 12 | \( 3^{2}\cdot 846233 \) | $S_5$ (as 5T5) | $[11]$ |
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