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 |
---|---|---|---|---|
5.1.1609.1 | $x^{5} - x^{3} - x^{2} + x + 1$ | $1609$ | $S_5$ (as 5T5) | trivial |
5.1.1649.1 | $x^{5} - x^{4} + x^{2} - x + 1$ | $17\cdot 97$ | $S_5$ (as 5T5) | trivial |
5.1.1777.1 | $x^{5} - x^{4} + x^{3} - 2 x^{2} + x - 1$ | $1777$ | $S_5$ (as 5T5) | trivial |
5.1.2209.1 | $x^{5} - 2 x^{4} + 2 x^{3} - x^{2} + 1$ | $47^{2}$ | $D_{5}$ (as 5T2) | trivial |
5.1.2297.1 | $x^{5} - x^{4} + x^{3} - x^{2} - 1$ | $2297$ | $S_5$ (as 5T5) | trivial |
5.1.2617.1 | $x^{5} + x^{3} - 2 x^{2} - 1$ | $2617$ | $S_5$ (as 5T5) | trivial |
5.1.2665.1 | $x^{5} - x^{4} + x^{3} - x^{2} + 2 x - 1$ | $5\cdot 13\cdot 41$ | $S_5$ (as 5T5) | trivial |
5.1.2869.1 | $x^{5} - x - 1$ | $19\cdot 151$ | $S_5$ (as 5T5) | trivial |
5.1.3017.1 | $x^{5} - x^{2} + 1$ | $7\cdot 431$ | $S_5$ (as 5T5) | trivial |
5.1.3089.1 | $x^{5} - x^{3} + 2 x - 1$ | $3089$ | $S_5$ (as 5T5) | trivial |
5.1.3233.1 | $x^{5} - x^{2} - 1$ | $53\cdot 61$ | $S_5$ (as 5T5) | trivial |
5.1.3369.1 | $x^{5} + x^{3} - x^{2} - x - 1$ | $3\cdot 1123$ | $S_5$ (as 5T5) | trivial |
5.1.3857.1 | $x^{5} - x^{4} + x^{3} - x^{2} + 1$ | $7\cdot 19\cdot 29$ | $S_5$ (as 5T5) | trivial |
5.1.3889.1 | $x^{5} - x^{4} + x^{3} + x - 1$ | $3889$ | $S_5$ (as 5T5) | trivial |
5.1.4169.1 | $x^{5} + 2 x^{3} - x^{2} + 2 x - 1$ | $11\cdot 379$ | $S_5$ (as 5T5) | trivial |
5.1.4261.1 | $x^{5} - 2 x^{2} - 2 x - 1$ | $4261$ | $S_5$ (as 5T5) | trivial |
5.1.4409.1 | $x^{5} - x^{4} + x^{2} + x - 1$ | $4409$ | $S_5$ (as 5T5) | trivial |
5.1.4417.1 | $x^{5} - 2 x^{4} + 2 x^{3} - x^{2} - 1$ | $7\cdot 631$ | $S_5$ (as 5T5) | trivial |
5.1.4429.1 | $x^{5} - x^{4} + 2 x^{3} - x^{2} + 1$ | $43\cdot 103$ | $S_5$ (as 5T5) | trivial |
5.1.4432.1 | $x^{5} - x^{4} + 2 x^{2} - x + 1$ | $2^{4}\cdot 277$ | $S_5$ (as 5T5) | trivial |
5.1.4477.1 | $x^{5} + x^{3} + x - 1$ | $11^{2}\cdot 37$ | $S_5$ (as 5T5) | trivial |
5.3.4511.1 | $x^{5} - x^{3} - 2 x^{2} + 1$ | $-\,13\cdot 347$ | $S_5$ (as 5T5) | trivial |
5.1.4549.1 | $x^{5} - x^{4} + 2 x^{3} - 2 x^{2} - 1$ | $4549$ | $S_5$ (as 5T5) | trivial |
5.1.4597.1 | $x^{5} + x^{3} - 2 x^{2} - x - 1$ | $4597$ | $S_5$ (as 5T5) | trivial |
5.1.4757.1 | $x^{5} - x^{4} + 2 x^{3} - x^{2} + 2 x - 1$ | $67\cdot 71$ | $S_5$ (as 5T5) | trivial |
5.1.4817.1 | $x^{5} - 2 x^{4} + 2 x^{3} - x^{2} + 2 x - 1$ | $4817$ | $S_5$ (as 5T5) | trivial |
5.1.4897.1 | $x^{5} - x^{4} - x^{3} + x^{2} + 1$ | $59\cdot 83$ | $S_5$ (as 5T5) | trivial |
5.3.4903.1 | $x^{5} - x^{4} - x^{3} + 2 x^{2} - x - 1$ | $-\,4903$ | $S_5$ (as 5T5) | trivial |
5.1.5025.1 | $x^{5} - x^{4} - x^{2} + x + 1$ | $3\cdot 5^{2}\cdot 67$ | $S_5$ (as 5T5) | trivial |
5.1.5164.1 | $x^{5} - x^{4} - x^{3} + 2 x + 1$ | $2^{2}\cdot 1291$ | $S_5$ (as 5T5) | trivial |
5.1.5437.1 | $x^{5} - 2 x^{4} + 2 x^{3} - 2 x^{2} - 1$ | $5437$ | $S_5$ (as 5T5) | trivial |
5.1.5501.1 | $x^{5} - 2 x^{4} + 2 x^{2} - x + 1$ | $5501$ | $S_5$ (as 5T5) | trivial |
5.3.5519.1 | $x^{5} - x^{4} - x^{3} + 3 x^{2} - 1$ | $-\,5519$ | $S_5$ (as 5T5) | trivial |
5.1.5584.1 | $x^{5} - x^{4} + x + 1$ | $2^{4}\cdot 349$ | $S_5$ (as 5T5) | trivial |
5.1.5653.1 | $x^{5} - x^{4} + 2 x - 1$ | $5653$ | $S_5$ (as 5T5) | trivial |
5.1.5753.1 | $x^{5} - x^{4} - x^{3} + 2 x^{2} - x + 1$ | $11\cdot 523$ | $S_5$ (as 5T5) | trivial |
5.3.5783.1 | $x^{5} - 2 x^{4} + x^{3} + 2 x^{2} - 2 x - 1$ | $-\,5783$ | $S_5$ (as 5T5) | trivial |
5.1.5864.1 | $x^{5} - x^{4} + x^{3} + 2 x^{2} - 2 x + 1$ | $2^{3}\cdot 733$ | $S_5$ (as 5T5) | trivial |
5.1.5913.1 | $x^{5} - x^{4} + 2 x^{3} - x^{2} + x + 1$ | $3^{4}\cdot 73$ | $S_5$ (as 5T5) | trivial |
5.1.6241.1 | $x^{5} - x^{4} + x^{3} - 2 x^{2} + 3 x - 1$ | $79^{2}$ | $D_{5}$ (as 5T2) | trivial |
5.1.6449.1 | $x^{5} - x^{4} + x^{3} - 3 x^{2} - 1$ | $6449$ | $S_5$ (as 5T5) | trivial |
5.1.6581.1 | $x^{5} - 2 x^{2} - 1$ | $6581$ | $S_5$ (as 5T5) | trivial |
5.1.6757.1 | $x^{5} - x^{4} + 3 x^{2} - 2 x + 1$ | $29\cdot 233$ | $S_5$ (as 5T5) | trivial |
5.1.6793.1 | $x^{5} - x^{4} + x^{3} + x + 1$ | $6793$ | $S_5$ (as 5T5) | trivial |
5.3.7031.1 | $x^{5} - x^{3} - x^{2} - x + 1$ | $-\,79\cdot 89$ | $S_5$ (as 5T5) | trivial |
5.1.7096.1 | $x^{5} - x^{2} + x + 1$ | $2^{3}\cdot 887$ | $S_5$ (as 5T5) | trivial |
5.1.7177.1 | $x^{5} - x^{4} + 3 x^{3} - x^{2} + 2 x - 1$ | $7177$ | $S_5$ (as 5T5) | trivial |
5.1.7265.1 | $x^{5} - x^{4} + x^{3} + 2 x^{2} - x + 1$ | $5\cdot 1453$ | $S_5$ (as 5T5) | trivial |
5.1.7333.1 | $x^{5} - 2 x^{4} + 2 x^{3} - 2 x^{2} + 3 x - 1$ | $7333$ | $S_5$ (as 5T5) | trivial |
5.3.7367.1 | $x^{5} - 2 x^{4} + 3 x^{2} - 2 x - 1$ | $-\,53\cdot 139$ | $S_5$ (as 5T5) | trivial |