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 |
---|---|---|---|---|
7.5.2306599.1 | $x^{7} - 3 x^{5} - x^{4} + x^{3} + 3 x^{2} + x - 1$ | $-\,107\cdot 21557$ | $S_7$ (as 7T7) | trivial |
7.5.2369207.1 | $x^{7} - 4 x^{5} + 3 x^{3} - x^{2} + x + 1$ | $-\,23\cdot 239\cdot 431$ | $S_7$ (as 7T7) | trivial |
7.5.2616839.1 | $x^{7} - x^{6} - 3 x^{5} + 4 x^{4} + x^{3} - 5 x^{2} + x + 1$ | $-\,61\cdot 42899$ | $S_7$ (as 7T7) | trivial |
7.5.2790047.1 | $x^{7} - x^{6} - 2 x^{5} + 3 x^{4} - 2 x^{3} - 3 x^{2} + 4 x + 1$ | $-\,13\cdot 157\cdot 1367$ | $S_7$ (as 7T7) | trivial |
7.5.2790551.1 | $x^{7} - 2 x^{5} - 3 x^{3} - x^{2} + 3 x + 1$ | $-\,317\cdot 8803$ | $S_7$ (as 7T7) | trivial |
7.5.2894039.1 | $x^{7} - x^{6} - x^{5} - 2 x^{3} + 3 x^{2} + 2 x - 1$ | $-\,829\cdot 3491$ | $S_7$ (as 7T7) | trivial |
7.5.2932823.1 | $x^{7} - x^{6} - 4 x^{3} + 2 x^{2} + 2 x - 1$ | $-\,17\cdot 172519$ | $S_7$ (as 7T7) | trivial |
7.5.3063719.1 | $x^{7} - 3 x^{6} + x^{5} + 4 x^{4} - 5 x^{3} + x^{2} + 3 x - 1$ | $-\,1423\cdot 2153$ | $S_7$ (as 7T7) | trivial |
7.5.3373751.1 | $x^{7} - 2 x^{5} - 2 x^{4} - x^{3} + 3 x^{2} + x - 1$ | $-\,1567\cdot 2153$ | $S_7$ (as 7T7) | trivial |
7.5.3394343.1 | $x^{7} - 2 x^{6} - 2 x^{5} + 6 x^{4} - x^{3} - 5 x^{2} + x + 1$ | $-\,37\cdot 199\cdot 461$ | $S_7$ (as 7T7) | trivial |
7.5.3394511.1 | $x^{7} - 2 x^{6} + x^{5} - x^{4} - 3 x^{3} + 4 x^{2} + 2 x - 1$ | $-\,269\cdot 12619$ | $S_7$ (as 7T7) | trivial |
7.5.3404423.1 | $x^{7} - 2 x^{5} - 3 x^{4} + x^{3} + 5 x^{2} - 1$ | $-\,11\cdot 309493$ | $S_7$ (as 7T7) | trivial |
7.5.3444743.1 | $x^{7} - x^{6} - 4 x^{5} + 4 x^{4} + 3 x^{3} - 4 x^{2} + x + 1$ | $-\,3444743$ | $S_7$ (as 7T7) | trivial |
7.5.3455831.1 | $x^{7} - x^{6} - 4 x^{5} + 4 x^{4} + 2 x^{3} - 2 x^{2} + 2 x - 1$ | $-\,223\cdot 15497$ | $S_7$ (as 7T7) | trivial |
7.5.3685907.1 | $x^{7} - x^{6} - x^{5} + 4 x^{4} - 2 x^{3} - 4 x^{2} + x + 1$ | $-\,59\cdot 62473$ | $S_7$ (as 7T7) | trivial |
7.5.3689911.1 | $x^{7} - 2 x^{6} - x^{5} + 4 x^{4} - 5 x^{3} + 4 x^{2} + x - 1$ | $-\,3689911$ | $S_7$ (as 7T7) | trivial |
7.5.3872527.1 | $x^{7} - x^{6} - x^{5} - 3 x^{3} + 3 x^{2} + 3 x - 1$ | $-\,3872527$ | $S_7$ (as 7T7) | trivial |
7.5.3929623.1 | $x^{7} - x^{6} - 4 x^{5} + x^{4} + 6 x^{3} + 2 x^{2} - 3 x - 1$ | $-\,47\cdot 83609$ | $S_7$ (as 7T7) | trivial |
7.5.3953927.1 | $x^{7} - 5 x^{5} + 6 x^{3} - x^{2} - x + 1$ | $-\,3953927$ | $S_7$ (as 7T7) | trivial |
7.5.3998639.1 | $x^{7} - x^{6} - 2 x^{5} + 5 x^{4} - 6 x^{2} + x + 1$ | $-\,3998639$ | $S_7$ (as 7T7) | trivial |
7.5.4010959.1 | $x^{7} - 2 x^{6} - 2 x^{5} + 5 x^{4} - 3 x^{3} - 3 x^{2} + 4 x - 1$ | $-\,283\cdot 14173$ | $S_7$ (as 7T7) | trivial |
7.5.4071943.1 | $x^{7} - x^{6} - 3 x^{5} + 2 x^{4} + x^{3} + x^{2} + x - 1$ | $-\,23\cdot 31\cdot 5711$ | $S_7$ (as 7T7) | trivial |
7.5.4080391.1 | $x^{7} - 2 x^{6} - 2 x^{5} + 6 x^{4} - 3 x^{3} - 2 x^{2} + 4 x - 1$ | $-\,7\cdot 17^{2}\cdot 2017$ | $S_7$ (as 7T7) | trivial |
7.5.4297259.1 | $x^{7} - 3 x^{5} - 3 x^{4} + 4 x^{3} + 5 x^{2} - 2 x - 1$ | $-\,4297259$ | $S_7$ (as 7T7) | trivial |
7.5.4375127.1 | $x^{7} - 2 x^{6} - 2 x^{5} + 5 x^{4} - x^{3} - 3 x^{2} + 2 x + 1$ | $-\,4375127$ | $S_7$ (as 7T7) | trivial |
7.5.4438087.1 | $x^{7} - 4 x^{5} + 2 x^{3} - 4 x^{2} - x + 1$ | $-\,4438087$ | $S_7$ (as 7T7) | trivial |
7.5.4486007.1 | $x^{7} - 2 x^{6} - x^{5} + 6 x^{4} - 2 x^{3} - 5 x^{2} + x + 1$ | $-\,463\cdot 9689$ | $S_7$ (as 7T7) | trivial |
7.5.4520279.1 | $x^{7} - x^{6} - x^{5} + 3 x^{4} - 4 x^{3} - 2 x^{2} + 4 x - 1$ | $-\,4520279$ | $S_7$ (as 7T7) | trivial |
7.5.4582807.1 | $x^{7} - 3 x^{5} - x^{4} - x^{3} + 4 x + 1$ | $-\,4582807$ | $S_7$ (as 7T7) | trivial |
7.5.4734119.1 | $x^{7} - x^{6} - 3 x^{5} + 3 x^{4} - x^{2} + 3 x - 1$ | $-\,13\cdot 53\cdot 6871$ | $S_7$ (as 7T7) | trivial |
7.5.4795631.1 | $x^{7} - 2 x^{5} - 3 x^{4} - 3 x^{3} + 3 x^{2} + 4 x + 1$ | $-\,4795631$ | $S_7$ (as 7T7) | trivial |
7.5.4850543.1 | $x^{7} - x^{6} - 2 x^{5} + 4 x^{4} - x^{3} - 4 x^{2} + x + 1$ | $-\,4850543$ | $S_7$ (as 7T7) | trivial |
7.5.4934959.1 | $x^{7} - x^{6} - 3 x^{5} + 4 x^{3} + 3 x^{2} - 2 x - 1$ | $-\,29\cdot 379\cdot 449$ | $S_7$ (as 7T7) | trivial |
7.5.5025907.1 | $x^{7} - x^{6} - 4 x^{5} + 3 x^{4} + 3 x^{3} - 3 x^{2} + x + 1$ | $-\,5025907$ | $S_7$ (as 7T7) | trivial |
7.5.5044607.1 | $x^{7} - 2 x^{6} - 3 x^{5} + 6 x^{4} + x^{3} - 4 x^{2} + x + 1$ | $-\,5044607$ | $S_7$ (as 7T7) | trivial |
7.5.5280527.1 | $x^{7} - x^{5} - 3 x^{4} - 3 x^{3} + 5 x^{2} + 3 x - 1$ | $-\,7\cdot 353\cdot 2137$ | $S_7$ (as 7T7) | trivial |
7.5.5307751.1 | $x^{7} - x^{6} - x^{5} - 6 x^{3} - 3 x^{2} + 2 x + 1$ | $-\,541\cdot 9811$ | $S_7$ (as 7T7) | trivial |
7.5.5334959.1 | $x^{7} - 3 x^{5} - 3 x^{4} + x^{3} + 4 x^{2} - 1$ | $-\,7\cdot 139\cdot 5483$ | $S_7$ (as 7T7) | trivial |
7.5.5560327.1 | $x^{7} - 2 x^{6} - 3 x^{5} + 7 x^{4} + x^{3} - 7 x^{2} + x + 1$ | $-\,5560327$ | $S_7$ (as 7T7) | trivial |
7.5.5615543.1 | $x^{7} - x^{6} - 3 x^{5} + 5 x^{4} + 2 x^{3} - 6 x^{2} + 1$ | $-\,1097\cdot 5119$ | $S_7$ (as 7T7) | trivial |
7.5.5663239.1 | $x^{7} - x^{6} - 3 x^{5} + 3 x^{3} + 3 x^{2} - x - 1$ | $-\,5663239$ | $S_7$ (as 7T7) | trivial |
7.5.5671079.1 | $x^{7} - 2 x^{6} - x^{5} + x^{3} + 6 x^{2} + x - 1$ | $-\,41\cdot 138319$ | $S_7$ (as 7T7) | trivial |
7.5.5679431.1 | $x^{7} - 2 x^{6} - 2 x^{5} + 7 x^{4} - 6 x^{2} + 1$ | $-\,5679431$ | $S_7$ (as 7T7) | trivial |
7.5.5839319.1 | $x^{7} - 2 x^{6} + 5 x^{4} - 6 x^{3} - 2 x^{2} + 4 x - 1$ | $-\,5839319$ | $S_7$ (as 7T7) | trivial |
7.5.5983559.1 | $x^{7} - x^{5} - x^{4} - 3 x^{3} + 2 x^{2} + 2 x - 1$ | $-\,89\cdot 67231$ | $S_7$ (as 7T7) | trivial |
7.5.6099227.1 | $x^{7} - 2 x^{6} - 3 x^{5} + 8 x^{4} + x^{3} - 7 x^{2} + 1$ | $-\,6099227$ | $S_7$ (as 7T7) | trivial |
7.5.6132103.1 | $x^{7} - x^{6} - 3 x^{5} - x^{4} + 5 x^{3} + 3 x^{2} - 2 x - 1$ | $-\,6132103$ | $S_7$ (as 7T7) | trivial |
7.5.6155647.1 | $x^{7} - 2 x^{5} - 2 x^{3} + 3 x - 1$ | $-\,59\cdot 101\cdot 1033$ | $S_7$ (as 7T7) | trivial |
7.5.6202855.1 | $x^{7} - 2 x^{6} + x^{5} + 4 x^{4} - 8 x^{3} + x^{2} + 3 x - 1$ | $-\,5\cdot 53\cdot 89\cdot 263$ | $S_7$ (as 7T7) | trivial |
7.5.6365719.1 | $x^{7} - x^{6} - 2 x^{5} + 5 x^{4} - 5 x^{2} + 1$ | $-\,193\cdot 32983$ | $S_7$ (as 7T7) | trivial |