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 |
---|---|---|---|---|
5.3.4511.1 | $x^{5} - x^{3} - 2 x^{2} + 1$ | $-\,13\cdot 347$ | $S_5$ (as 5T5) | trivial |
5.3.4903.1 | $x^{5} - x^{4} - x^{3} + 2 x^{2} - x - 1$ | $-\,4903$ | $S_5$ (as 5T5) | trivial |
5.3.5519.1 | $x^{5} - x^{4} - x^{3} + 3 x^{2} - 1$ | $-\,5519$ | $S_5$ (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 |
5.3.7031.1 | $x^{5} - x^{3} - x^{2} - x + 1$ | $-\,79\cdot 89$ | $S_5$ (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 |
5.3.7463.1 | $x^{5} - 2 x^{4} + x^{3} - 2 x + 1$ | $-\,17\cdot 439$ | $S_5$ (as 5T5) | trivial |
5.3.8519.1 | $x^{5} - x^{4} - x^{2} - x + 1$ | $-\,7\cdot 1217$ | $S_5$ (as 5T5) | trivial |
5.3.8647.1 | $x^{5} - 3 x^{3} - 2 x^{2} + 2 x + 1$ | $-\,8647$ | $S_5$ (as 5T5) | trivial |
5.3.9439.1 | $x^{5} - x^{4} - x^{3} + x^{2} - 2 x + 1$ | $-\,9439$ | $S_5$ (as 5T5) | trivial |
5.3.9759.1 | $x^{5} - 2 x^{4} + x^{2} - 2 x - 1$ | $-\,3\cdot 3253$ | $S_5$ (as 5T5) | trivial |
5.3.10407.1 | $x^{5} - x^{4} - 3 x^{3} + 3 x - 1$ | $-\,3\cdot 3469$ | $S_5$ (as 5T5) | trivial |
5.3.11119.1 | $x^{5} - 2 x^{4} + x^{3} + x^{2} - 3 x + 1$ | $-\,11119$ | $S_5$ (as 5T5) | trivial |
5.3.11243.1 | $x^{5} - x^{4} - 2 x + 1$ | $-\,11243$ | $S_5$ (as 5T5) | trivial |
5.3.11551.1 | $x^{5} - x^{4} - 2 x^{3} + 3 x^{2} - x - 1$ | $-\,11551$ | $S_5$ (as 5T5) | trivial |
5.3.12447.1 | $x^{5} + x^{3} - x^{2} - 3 x - 1$ | $-\,3^{3}\cdot 461$ | $S_5$ (as 5T5) | trivial |
5.3.13219.1 | $x^{5} - 2 x^{2} - x + 1$ | $-\,13219$ | $S_5$ (as 5T5) | trivial |
5.3.13523.1 | $x^{5} - x^{4} - x^{3} - x^{2} - 3 x + 1$ | $-\,13523$ | $S_5$ (as 5T5) | trivial |
5.3.13799.1 | $x^{5} - x^{4} - x^{3} + 2 x^{2} - 3 x + 1$ | $-\,13799$ | $S_5$ (as 5T5) | trivial |
5.3.13883.1 | $x^{5} - x^{4} - 2 x^{3} + x + 2$ | $-\,13883$ | $S_5$ (as 5T5) | trivial |
5.3.14103.1 | $x^{5} - 2 x^{4} + 2 x^{3} - x^{2} - 2 x + 1$ | $-\,3^{2}\cdot 1567$ | $S_5$ (as 5T5) | trivial |
5.3.14631.1 | $x^{5} - x^{4} - 3 x^{3} + 3 x^{2} - 1$ | $-\,3\cdot 4877$ | $S_5$ (as 5T5) | trivial |
5.3.14891.1 | $x^{5} - x^{4} - 3 x^{3} + 3 x^{2} + x - 2$ | $-\,14891$ | $S_5$ (as 5T5) | trivial |
5.3.14911.1 | $x^{5} - x^{4} - 2 x^{3} - x^{2} + 3 x + 1$ | $-\,13\cdot 31\cdot 37$ | $S_5$ (as 5T5) | trivial |
5.3.15536.1 | $x^{5} - 2 x^{4} + 2$ | $-\,2^{4}\cdot 971$ | $S_5$ (as 5T5) | trivial |
5.3.15919.1 | $x^{5} - 2 x^{3} - 3 x^{2} + 1$ | $-\,15919$ | $S_5$ (as 5T5) | trivial |
5.3.16816.1 | $x^{5} - 2 x^{3} - 2 x^{2} - 4 x - 2$ | $-\,2^{4}\cdot 1051$ | $S_5$ (as 5T5) | trivial |
5.3.17151.1 | $x^{5} - x^{3} - 2 x - 1$ | $-\,3\cdot 5717$ | $S_5$ (as 5T5) | trivial |
5.3.17348.1 | $x^{5} - x^{4} - 2 x^{3} - x^{2} + 2 x + 2$ | $-\,2^{2}\cdot 4337$ | $S_5$ (as 5T5) | trivial |
5.3.18063.1 | $x^{5} - x^{4} + x^{3} - 2 x^{2} - x + 1$ | $-\,3^{4}\cdot 223$ | $S_5$ (as 5T5) | trivial |
5.3.18463.1 | $x^{5} - x^{4} - 3 x^{3} + 4 x^{2} + x - 1$ | $-\,37\cdot 499$ | $S_5$ (as 5T5) | trivial |
5.3.18583.1 | $x^{5} - x^{4} - x^{3} - 2 x^{2} + x + 1$ | $-\,18583$ | $S_5$ (as 5T5) | trivial |
5.3.18839.1 | $x^{5} - x^{4} + 3 x^{2} - x - 1$ | $-\,18839$ | $S_5$ (as 5T5) | trivial |
5.3.19015.1 | $x^{5} - 2 x^{3} - x^{2} - 2 x - 1$ | $-\,5\cdot 3803$ | $S_5$ (as 5T5) | trivial |
5.3.19951.1 | $x^{5} - 2 x^{4} + x^{3} - 3 x^{2} + 3 x + 1$ | $-\,71\cdot 281$ | $S_5$ (as 5T5) | trivial |
5.3.21191.1 | $x^{5} - x^{4} - x^{2} - 3 x - 1$ | $-\,21191$ | $S_5$ (as 5T5) | trivial |
5.3.21227.1 | $x^{5} - x^{4} - 4 x^{2} + 3 x + 2$ | $-\,21227$ | $S_5$ (as 5T5) | trivial |
5.3.22331.1 | $x^{5} - 2 x^{4} + 4 x^{2} - x - 1$ | $-\,137\cdot 163$ | $S_5$ (as 5T5) | trivial |
5.3.22424.1 | $x^{5} - 2 x^{3} - x^{2} - x + 1$ | $-\,2^{3}\cdot 2803$ | $S_5$ (as 5T5) | trivial |
5.3.22448.1 | $x^{5} - x^{4} - 2 x^{3} + 2 x^{2} - x - 1$ | $-\,2^{4}\cdot 23\cdot 61$ | $S_5$ (as 5T5) | trivial |
5.3.22583.1 | $x^{5} - x^{2} - 2 x + 1$ | $-\,11\cdot 2053$ | $S_5$ (as 5T5) | trivial |
5.3.22687.1 | $x^{5} - x^{4} + x^{3} - x^{2} - 2 x + 1$ | $-\,7^{2}\cdot 463$ | $S_5$ (as 5T5) | trivial |
5.3.22935.1 | $x^{5} + x^{3} - 2 x^{2} - 4 x + 1$ | $-\,3\cdot 5\cdot 11\cdot 139$ | $S_5$ (as 5T5) | trivial |
5.3.23103.1 | $x^{5} - x^{4} + x^{2} - 3 x + 1$ | $-\,3^{2}\cdot 17\cdot 151$ | $S_5$ (as 5T5) | trivial |
5.3.23119.1 | $x^{5} - 3 x^{2} + 1$ | $-\,61\cdot 379$ | $S_5$ (as 5T5) | trivial |
5.3.23339.1 | $x^{5} - x^{4} + 2 x^{2} - 2 x - 1$ | $-\,23339$ | $S_5$ (as 5T5) | trivial |
5.3.23679.1 | $x^{5} - 2 x^{4} + x^{2} - 2 x + 3$ | $-\,3^{3}\cdot 877$ | $S_5$ (as 5T5) | trivial |
5.3.23831.1 | $x^{5} - 3 x^{3} - 2 x^{2} + 4 x - 1$ | $-\,23831$ | $S_5$ (as 5T5) | trivial |
5.3.23891.1 | $x^{5} - x^{4} - 3 x^{3} - x^{2} + 3 x + 2$ | $-\,7\cdot 3413$ | $S_5$ (as 5T5) | trivial |
5.3.24299.1 | $x^{5} - x^{4} - x^{3} + 3 x^{2} - x - 2$ | $-\,11\cdot 47^{2}$ | $S_5$ (as 5T5) | trivial |