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Label | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
2.0.3.1 | $x^{2} - x + 1$ | $-\,3$ | $C_2$ (as 2T1) | trivial |
2.0.4.1 | $x^{2} + 1$ | $-\,2^{2}$ | $C_2$ (as 2T1) | trivial |
2.2.5.1 | $x^{2} - x - 1$ | $5$ | $C_2$ (as 2T1) | trivial |
2.0.7.1 | $x^{2} - x + 2$ | $-\,7$ | $C_2$ (as 2T1) | trivial |
2.0.8.1 | $x^{2} + 2$ | $-\,2^{3}$ | $C_2$ (as 2T1) | trivial |
2.2.8.1 | $x^{2} - 2$ | $2^{3}$ | $C_2$ (as 2T1) | trivial |
2.0.11.1 | $x^{2} - x + 3$ | $-\,11$ | $C_2$ (as 2T1) | trivial |
2.2.12.1 | $x^{2} - 3$ | $2^{2}\cdot 3$ | $C_2$ (as 2T1) | trivial |
2.2.13.1 | $x^{2} - x - 3$ | $13$ | $C_2$ (as 2T1) | trivial |
2.0.15.1 | $x^{2} - x + 4$ | $-\,3\cdot 5$ | $C_2$ (as 2T1) | $[2]$ |
2.2.17.1 | $x^{2} - x - 4$ | $17$ | $C_2$ (as 2T1) | trivial |
2.0.19.1 | $x^{2} - x + 5$ | $-\,19$ | $C_2$ (as 2T1) | trivial |
2.0.20.1 | $x^{2} + 5$ | $-\,2^{2}\cdot 5$ | $C_2$ (as 2T1) | $[2]$ |
2.2.21.1 | $x^{2} - x - 5$ | $3\cdot 7$ | $C_2$ (as 2T1) | trivial |
2.0.23.1 | $x^{2} - x + 6$ | $-\,23$ | $C_2$ (as 2T1) | $[3]$ |
2.0.24.1 | $x^{2} + 6$ | $-\,2^{3}\cdot 3$ | $C_2$ (as 2T1) | $[2]$ |
2.2.24.1 | $x^{2} - 6$ | $2^{3}\cdot 3$ | $C_2$ (as 2T1) | trivial |
2.2.28.1 | $x^{2} - 7$ | $2^{2}\cdot 7$ | $C_2$ (as 2T1) | trivial |
2.2.29.1 | $x^{2} - x - 7$ | $29$ | $C_2$ (as 2T1) | trivial |
2.0.31.1 | $x^{2} - x + 8$ | $-\,31$ | $C_2$ (as 2T1) | $[3]$ |
2.2.33.1 | $x^{2} - x - 8$ | $3\cdot 11$ | $C_2$ (as 2T1) | trivial |
2.0.35.1 | $x^{2} - x + 9$ | $-\,5\cdot 7$ | $C_2$ (as 2T1) | $[2]$ |
2.2.37.1 | $x^{2} - x - 9$ | $37$ | $C_2$ (as 2T1) | trivial |
2.0.39.1 | $x^{2} - x + 10$ | $-\,3\cdot 13$ | $C_2$ (as 2T1) | $[4]$ |
2.0.40.1 | $x^{2} + 10$ | $-\,2^{3}\cdot 5$ | $C_2$ (as 2T1) | $[2]$ |
2.2.40.1 | $x^{2} - 10$ | $2^{3}\cdot 5$ | $C_2$ (as 2T1) | $[2]$ |
2.2.41.1 | $x^{2} - x - 10$ | $41$ | $C_2$ (as 2T1) | trivial |
2.0.43.1 | $x^{2} - x + 11$ | $-\,43$ | $C_2$ (as 2T1) | trivial |
2.2.44.1 | $x^{2} - 11$ | $2^{2}\cdot 11$ | $C_2$ (as 2T1) | trivial |
2.0.47.1 | $x^{2} - x + 12$ | $-\,47$ | $C_2$ (as 2T1) | $[5]$ |
2.0.51.1 | $x^{2} - x + 13$ | $-\,3\cdot 17$ | $C_2$ (as 2T1) | $[2]$ |
2.0.52.1 | $x^{2} + 13$ | $-\,2^{2}\cdot 13$ | $C_2$ (as 2T1) | $[2]$ |
2.2.53.1 | $x^{2} - x - 13$ | $53$ | $C_2$ (as 2T1) | trivial |
2.0.55.1 | $x^{2} - x + 14$ | $-\,5\cdot 11$ | $C_2$ (as 2T1) | $[4]$ |
2.0.56.1 | $x^{2} + 14$ | $-\,2^{3}\cdot 7$ | $C_2$ (as 2T1) | $[4]$ |
2.2.56.1 | $x^{2} - 14$ | $2^{3}\cdot 7$ | $C_2$ (as 2T1) | trivial |
2.2.57.1 | $x^{2} - x - 14$ | $3\cdot 19$ | $C_2$ (as 2T1) | trivial |
2.0.59.1 | $x^{2} - x + 15$ | $-\,59$ | $C_2$ (as 2T1) | $[3]$ |
2.2.60.1 | $x^{2} - 15$ | $2^{2}\cdot 3\cdot 5$ | $C_2$ (as 2T1) | $[2]$ |
2.2.61.1 | $x^{2} - x - 15$ | $61$ | $C_2$ (as 2T1) | trivial |
2.2.65.1 | $x^{2} - x - 16$ | $5\cdot 13$ | $C_2$ (as 2T1) | $[2]$ |
2.0.67.1 | $x^{2} - x + 17$ | $-\,67$ | $C_2$ (as 2T1) | trivial |
2.0.68.1 | $x^{2} + 17$ | $-\,2^{2}\cdot 17$ | $C_2$ (as 2T1) | $[4]$ |
2.2.69.1 | $x^{2} - x - 17$ | $3\cdot 23$ | $C_2$ (as 2T1) | trivial |
2.0.71.1 | $x^{2} - x + 18$ | $-\,71$ | $C_2$ (as 2T1) | $[7]$ |
2.2.73.1 | $x^{2} - x - 18$ | $73$ | $C_2$ (as 2T1) | trivial |
2.2.76.1 | $x^{2} - 19$ | $2^{2}\cdot 19$ | $C_2$ (as 2T1) | trivial |
2.2.77.1 | $x^{2} - x - 19$ | $7\cdot 11$ | $C_2$ (as 2T1) | trivial |
2.0.79.1 | $x^{2} - x + 20$ | $-\,79$ | $C_2$ (as 2T1) | $[5]$ |
2.0.83.1 | $x^{2} - x + 21$ | $-\,83$ | $C_2$ (as 2T1) | $[3]$ |