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 |
---|---|---|---|---|
7.1.184607.1 | $x^{7} - x^{6} - x^{5} + x^{4} - x^{2} + x + 1$ | $-\,184607$ | $S_7$ (as 7T7) | trivial |
7.1.193327.1 | $x^{7} - x^{6} + 2 x^{4} - 2 x^{3} + 2 x - 1$ | $-\,193327$ | $S_7$ (as 7T7) | trivial |
7.1.193607.1 | $x^{7} - x^{4} - x^{3} + x^{2} + 1$ | $-\,193607$ | $S_7$ (as 7T7) | trivial |
7.1.196127.1 | $x^{7} - 2 x^{6} + 2 x^{5} - x^{4} + 2 x^{2} - 2 x + 1$ | $-\,29\cdot 6763$ | $S_7$ (as 7T7) | trivial |
7.1.199559.1 | $x^{7} - x^{6} + x^{3} - x + 1$ | $-\,199559$ | $S_7$ (as 7T7) | trivial |
7.1.201671.1 | $x^{7} - x^{6} + 2 x^{5} - 2 x^{4} + 2 x^{3} - 2 x^{2} + 2 x - 1$ | $-\,17\cdot 11863$ | $S_7$ (as 7T7) | trivial |
7.1.202471.1 | $x^{7} - x^{6} - x^{5} + 2 x^{4} - x^{2} + 1$ | $-\,202471$ | $S_7$ (as 7T7) | trivial |
7.1.207911.1 | $x^{7} - x^{5} - x^{4} - x^{3} + x^{2} + x + 1$ | $-\,11\cdot 41\cdot 461$ | $S_7$ (as 7T7) | trivial |
7.1.211831.1 | $x^{7} - x^{6} + 2 x^{5} - x^{4} + x^{2} - 2 x + 1$ | $-\,19\cdot 11149$ | $S_7$ (as 7T7) | trivial |
7.1.214607.1 | $x^{7} - x^{6} + 2 x^{5} - 2 x^{4} + 2 x^{3} - 2 x^{2} - 1$ | $-\,214607$ | $S_7$ (as 7T7) | trivial |
7.1.224647.1 | $x^{7} - 2 x^{5} - x^{4} + 2 x^{3} + 2 x^{2} - 1$ | $-\,277\cdot 811$ | $S_7$ (as 7T7) | trivial |
7.1.227287.1 | $x^{7} - 2 x^{6} + 3 x^{5} - 3 x^{4} + 3 x^{3} - 2 x^{2} + 2 x - 1$ | $-\,167\cdot 1361$ | $S_7$ (as 7T7) | trivial |
7.1.237751.1 | $x^{7} - x^{6} + x^{5} - x^{4} + x^{3} + x^{2} - 2 x + 1$ | $-\,23\cdot 10337$ | $S_7$ (as 7T7) | trivial |
7.1.242147.1 | $x^{7} - 2 x^{6} + 2 x^{5} - x^{4} - x^{3} + 2 x^{2} - x + 1$ | $-\,242147$ | $S_7$ (as 7T7) | trivial |
7.1.242971.1 | $x^{7} - x^{6} - x^{5} + 2 x^{4} - 2 x^{2} + x + 1$ | $-\,242971$ | $S_7$ (as 7T7) | trivial |
7.1.250367.1 | $x^{7} - 2 x^{6} + 4 x^{5} - 4 x^{4} + 3 x^{3} - x^{2} - x + 1$ | $-\,13\cdot 19259$ | $S_7$ (as 7T7) | trivial |
7.1.252071.1 | $x^{7} - x^{6} + 2 x^{4} - x^{3} - 2 x^{2} + x + 1$ | $-\,83\cdot 3037$ | $S_7$ (as 7T7) | trivial |
7.1.261871.1 | $x^{7} - x^{6} - x^{5} + 2 x^{4} - x^{3} - x^{2} + x - 1$ | $-\,307\cdot 853$ | $S_7$ (as 7T7) | trivial |
7.1.267347.1 | $x^{7} - x^{4} - 2 x^{3} + x^{2} + x - 1$ | $-\,101\cdot 2647$ | $S_7$ (as 7T7) | trivial |
7.1.270607.1 | $x^{7} - x^{6} + x^{5} - 3 x^{4} + 2 x^{3} - 2 x^{2} + 2 x - 1$ | $-\,461\cdot 587$ | $S_7$ (as 7T7) | trivial |
7.1.272671.1 | $x^{7} - 2 x^{6} + 3 x^{5} - 4 x^{4} + 4 x^{3} - 3 x^{2} + x - 1$ | $-\,7\cdot 38953$ | $S_7$ (as 7T7) | trivial |
7.1.283223.1 | $x^{7} + x^{3} - 2 x - 1$ | $-\,61\cdot 4643$ | $S_7$ (as 7T7) | trivial |
7.1.286711.1 | $x^{7} - x^{5} - 2 x^{4} + x^{3} + 2 x^{2} - x - 1$ | $-\,286711$ | $S_7$ (as 7T7) | trivial |
7.1.289831.1 | $x^{7} + x^{5} - x^{4} + x^{3} - x^{2} + x - 1$ | $-\,109\cdot 2659$ | $S_7$ (as 7T7) | trivial |
7.1.289987.1 | $x^{7} - x^{6} + 2 x^{5} - 2 x^{4} + 2 x^{3} - x^{2} + x - 1$ | $-\,289987$ | $S_7$ (as 7T7) | trivial |
7.1.300527.1 | $x^{7} - 2 x^{6} + 2 x^{5} - 2 x^{3} + 4 x^{2} - 3 x + 1$ | $-\,29\cdot 43\cdot 241$ | $S_7$ (as 7T7) | trivial |
7.1.311071.1 | $x^{7} - x^{6} + 3 x^{5} - 3 x^{4} + 4 x^{3} - 4 x^{2} + 2 x - 1$ | $-\,277\cdot 1123$ | $S_7$ (as 7T7) | trivial |
7.1.315631.1 | $x^{7} - x^{5} - 2 x^{4} + x^{2} + x + 1$ | $-\,315631$ | $S_7$ (as 7T7) | trivial |
7.1.317159.1 | $x^{7} - 3 x^{6} + 4 x^{5} - 4 x^{4} + 4 x^{3} - 4 x^{2} + 2 x - 1$ | $-\,317159$ | $S_7$ (as 7T7) | trivial |
7.1.319831.1 | $x^{7} - x^{6} + 2 x^{4} - 3 x^{3} + 4 x^{2} - 3 x + 1$ | $-\,319831$ | $S_7$ (as 7T7) | trivial |
7.1.320975.1 | $x^{7} - x^{6} + x^{5} - x^{4} + 2 x^{2} - 2 x + 1$ | $-\,5^{2}\cdot 37\cdot 347$ | $S_7$ (as 7T7) | trivial |
7.1.330487.1 | $x^{7} + x^{5} - x^{3} - x - 1$ | $-\,23\cdot 14369$ | $S_7$ (as 7T7) | trivial |
7.1.332447.1 | $x^{7} - x^{5} - x^{4} + x^{3} + x^{2} - x - 1$ | $-\,332447$ | $S_7$ (as 7T7) | trivial |
7.1.334727.1 | $x^{7} - x^{5} - 2 x^{4} - x^{3} + 2 x^{2} + x + 1$ | $-\,334727$ | $S_7$ (as 7T7) | trivial |
7.1.338191.1 | $x^{7} - x^{4} - 2 x^{3} + 2 x + 1$ | $-\,7\cdot 48313$ | $S_7$ (as 7T7) | trivial |
7.1.349847.1 | $x^{7} - x^{6} + x^{5} - x^{4} + x^{2} - x + 1$ | $-\,19\cdot 18413$ | $S_7$ (as 7T7) | trivial |
7.1.351587.1 | $x^{7} - 2 x^{5} - 2 x^{4} + 2 x^{3} + 3 x^{2} - 1$ | $-\,351587$ | $S_7$ (as 7T7) | trivial |
7.1.351655.1 | $x^{7} - x^{6} - 2 x^{4} + x^{3} + x + 1$ | $-\,5\cdot 53\cdot 1327$ | $S_7$ (as 7T7) | trivial |
7.1.357911.1 | $x^{7} - x^{6} - x^{5} + x^{4} - x^{3} - x^{2} + 2 x + 1$ | $-\,71^{3}$ | $D_{7}$ (as 7T2) | trivial |
7.1.364871.1 | $x^{7} - x^{6} + 2 x^{4} + 2 x + 1$ | $-\,13^{2}\cdot 17\cdot 127$ | $S_7$ (as 7T7) | trivial |
7.1.371131.1 | $x^{7} - x^{4} - 2 x^{2} - x - 1$ | $-\,371131$ | $S_7$ (as 7T7) | trivial |
7.1.373607.1 | $x^{7} - x^{6} + x^{5} - 2 x^{3} + 3 x^{2} - 2 x + 1$ | $-\,13\cdot 29\cdot 991$ | $S_7$ (as 7T7) | trivial |
7.1.376163.1 | $x^{7} - x^{6} - x^{4} - x^{3} + x^{2} + x + 1$ | $-\,389\cdot 967$ | $S_7$ (as 7T7) | trivial |
7.1.380831.1 | $x^{7} - x^{5} - x^{4} - x^{3} + 2 x + 1$ | $-\,11\cdot 89\cdot 389$ | $S_7$ (as 7T7) | trivial |
7.1.382631.1 | $x^{7} - x^{5} + x^{3} - x - 1$ | $-\,382631$ | $S_7$ (as 7T7) | trivial |
7.1.383687.1 | $x^{7} - x^{6} + 2 x^{5} - 2 x^{4} + x^{3} - x + 1$ | $-\,31\cdot 12377$ | $S_7$ (as 7T7) | trivial |
7.1.396259.1 | $x^{7} - x^{4} - x^{3} + x + 1$ | $-\,396259$ | $S_7$ (as 7T7) | trivial |
7.1.397703.1 | $x^{7} + x^{5} + x^{3} - 2 x^{2} + x - 1$ | $-\,499\cdot 797$ | $S_7$ (as 7T7) | trivial |
7.1.397991.1 | $x^{7} - 2 x^{5} + 3 x^{3} - x^{2} - x + 1$ | $-\,11\cdot 97\cdot 373$ | $S_7$ (as 7T7) | trivial |
7.1.402011.1 | $x^{7} - x^{6} + 2 x^{5} - 4 x^{4} + 3 x^{3} - 3 x^{2} + 2 x - 1$ | $-\,73\cdot 5507$ | $S_7$ (as 7T7) | trivial |