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 |
---|---|---|---|---|
10.4.3120654523.1 | $x^{10} - 2 x^{9} + 2 x^{8} - 7 x^{7} + 8 x^{6} - 3 x^{5} + 8 x^{4} - 7 x^{3} + 2 x^{2} - 2 x + 1$ | $-\,7^{2}\cdot 43\cdot 1217^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.4.3191230411.1 | $x^{10} - x^{9} - 4 x^{6} - x^{5} - x^{4} + 3 x^{2} + 3 x + 1$ | $-\,3191230411$ | $S_{10}$ (as 10T45) | trivial |
10.4.3196989667.1 | $x^{10} - x^{9} - x^{8} - 2 x^{7} + x^{6} - 2 x^{4} + x^{3} + x^{2} + 2 x - 1$ | $-\,29\cdot 73^{2}\cdot 137\cdot 151$ | $S_{10}$ (as 10T45) | trivial |
10.4.3202088651.1 | $x^{10} - 2 x^{9} - x^{8} + 2 x^{7} + 2 x^{6} - 5 x^{4} + 3 x^{3} + 4 x^{2} - 2 x - 1$ | $-\,53^{2}\cdot 59\cdot 139^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.4.3204506051.1 | $x^{10} - x^{9} - 2 x^{8} + 2 x^{7} + 3 x^{6} - 4 x^{5} - 2 x^{4} + 2 x^{3} + x + 1$ | $-\,3204506051$ | $S_{10}$ (as 10T45) | trivial |
10.4.3209183443.1 | $x^{10} - 3 x^{9} + 2 x^{8} + 2 x^{7} - 3 x^{6} + x^{4} + x^{3} - 2 x^{2} + x + 1$ | $-\,53\cdot 6091\cdot 9941$ | $S_{10}$ (as 10T45) | trivial |
10.4.3259151627.1 | $x^{10} - x^{9} - 2 x^{8} + x^{7} + x^{6} - 2 x^{5} + 4 x^{4} + x^{3} - 5 x^{2} + 1$ | $-\,107\cdot 5519^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.4.3295770139.1 | $x^{10} - 2 x^{9} - x^{8} + 7 x^{7} - 7 x^{6} - x^{5} + 9 x^{4} - 6 x^{3} - x^{2} + 3 x - 1$ | $-\,11287\cdot 291997$ | $S_{10}$ (as 10T45) | trivial |
10.4.3307392083.1 | $x^{10} - x^{9} - 4 x^{8} + 2 x^{7} + 4 x^{6} - x^{4} - 4 x^{3} + 3 x - 1$ | $-\,30091\cdot 109913$ | $S_{10}$ (as 10T45) | trivial |
10.4.3312142387.1 | $x^{10} - 2 x^{9} - 3 x^{8} + 8 x^{7} - 8 x^{5} + 2 x^{4} + 3 x^{3} + 2 x^{2} - x - 1$ | $-\,67\cdot 79^{2}\cdot 89^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.4.3316535227.1 | $x^{10} - x^{7} + x^{6} + 3 x^{5} - 2 x^{3} - 3 x^{2} + x + 1$ | $-\,1483\cdot 2236369$ | $S_{10}$ (as 10T45) | trivial |
10.4.3338068347.1 | $x^{10} - 2 x^{9} - 2 x^{8} + 5 x^{7} + x^{6} - 3 x^{5} - 2 x^{3} - x^{2} + 3 x + 1$ | $-\,3^{3}\cdot 11119^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.4.3342094627.1 | $x^{10} - 4 x^{9} + 8 x^{8} - 12 x^{7} + 12 x^{6} - 9 x^{5} + 5 x^{4} - x^{2} + 2 x - 1$ | $-\,151\cdot 22133077$ | $S_{10}$ (as 10T45) | trivial |
10.4.3343581827.1 | $x^{10} - 2 x^{9} + 6 x^{7} - 6 x^{6} - x^{5} + 8 x^{4} - 5 x^{3} - x^{2} + 2 x - 1$ | $-\,3343581827$ | $S_{10}$ (as 10T45) | trivial |
10.4.3351773171.1 | $x^{10} - x^{9} - 2 x^{8} + x^{6} + 3 x^{5} + x^{4} - 3 x^{3} - 2 x^{2} + 2 x + 1$ | $-\,3351773171$ | $S_{10}$ (as 10T45) | trivial |
10.4.3367690163.1 | $x^{10} - 2 x^{9} + 3 x^{8} - 3 x^{7} - x^{6} + 3 x^{5} - 5 x^{4} + 3 x^{3} - x + 1$ | $-\,29\cdot 103\cdot 181\cdot 6229$ | $S_{10}$ (as 10T45) | trivial |
10.4.3385346179.1 | $x^{10} - 2 x^{9} + x^{8} + 3 x^{7} - 6 x^{6} + 3 x^{5} + 2 x^{4} - 5 x^{3} + 2 x^{2} + x - 1$ | $-\,41\cdot 101\cdot 817519$ | $S_{10}$ (as 10T45) | trivial |
10.4.3385465123.1 | $x^{10} - 4 x^{9} + 6 x^{8} - 2 x^{7} - 7 x^{6} + 11 x^{5} - 4 x^{4} - 4 x^{3} + 5 x^{2} - 1$ | $-\,3385465123$ | $S_{10}$ (as 10T45) | trivial |
10.4.3393524187.1 | $x^{10} - 4 x^{9} + 7 x^{8} - 4 x^{7} - 6 x^{6} + 13 x^{5} - 9 x^{4} - x^{3} + 5 x^{2} - 4 x + 1$ | $-\,3^{3}\cdot 1367\cdot 91943$ | $S_{10}$ (as 10T45) | trivial |
10.4.3398303207.1 | $x^{10} - 3 x^{9} + 3 x^{8} + x^{7} - 5 x^{6} + 8 x^{5} - 15 x^{4} + 13 x^{3} - 5 x^{2} + 2 x + 1$ | $-\,13^{2}\cdot 167\cdot 347^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.4.3405971875.1 | $x^{10} - 3 x^{9} + 5 x^{8} - 4 x^{7} - 2 x^{6} + 8 x^{5} - 8 x^{4} + x^{3} + 3 x^{2} - 3 x + 1$ | $-\,5^{5}\cdot 1039\cdot 1049$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.4.3406095083.1 | $x^{10} - x^{9} - x^{8} + 2 x^{7} - 4 x^{6} - 2 x^{5} + 9 x^{4} - 6 x^{2} + 1$ | $-\,911\cdot 3738853$ | $S_{10}$ (as 10T45) | trivial |
10.4.3408425011.1 | $x^{10} - 3 x^{8} - x^{6} + 5 x^{4} - 4 x^{3} - x^{2} + 3 x - 1$ | $-\,1721\cdot 1980491$ | $S_{10}$ (as 10T45) | trivial |
10.4.3409004107.1 | $x^{10} - x^{8} - x^{7} - x^{6} - 3 x^{5} + 3 x^{4} + x^{3} + 3 x - 1$ | $-\,3409004107$ | $S_{10}$ (as 10T45) | trivial |
10.4.3410947967.1 | $x^{10} - 2 x^{9} - 2 x^{8} + 7 x^{7} - x^{6} - 8 x^{5} + 2 x^{4} + 6 x^{3} - 3 x - 1$ | $-\,7^{2}\cdot 47\cdot 1217^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.4.3410962979.1 | $x^{10} - 3 x^{9} + 5 x^{8} - 3 x^{7} - 3 x^{6} + 8 x^{5} - 5 x^{4} - x^{3} + 4 x^{2} - x - 1$ | $-\,41\cdot 619\cdot 134401$ | $S_{10}$ (as 10T45) | trivial |
10.4.3412809931.1 | $x^{10} - x^{9} - 2 x^{8} + 5 x^{7} + x^{6} - 8 x^{5} + x^{4} + 7 x^{3} - 3 x^{2} - 3 x + 1$ | $-\,89\cdot 103\cdot 372293$ | $S_{10}$ (as 10T45) | trivial |
10.4.3419621875.1 | $x^{10} - 3 x^{9} + x^{8} + 6 x^{7} - 9 x^{6} + 2 x^{5} + 6 x^{4} - 5 x^{3} + x^{2} + 1$ | $-\,5^{5}\cdot 61\cdot 17939$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.4.3428429131.1 | $x^{10} - x^{9} - 3 x^{8} + 3 x^{7} + 2 x^{6} - x^{5} - x^{4} - 2 x^{3} + 2 x + 1$ | $-\,20323\cdot 168697$ | $S_{10}$ (as 10T45) | trivial |
10.4.3434563283.1 | $x^{10} - x^{9} - x^{8} + 2 x^{7} + x^{5} - 3 x^{4} - 2 x^{3} + 3 x^{2} - 1$ | $-\,59\cdot 58212937$ | $S_{10}$ (as 10T45) | trivial |
10.4.3444638167.1 | $x^{10} - 2 x^{9} + x^{8} + 2 x^{7} - 5 x^{6} + 4 x^{4} - 4 x^{3} - x^{2} + 4 x - 1$ | $-\,103\cdot 5783^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.4.3445999883.1 | $x^{10} - 3 x^{8} + x^{6} - 3 x^{5} + 6 x^{4} + 4 x^{3} - 5 x^{2} - x + 1$ | $-\,211\cdot 16331753$ | $S_{10}$ (as 10T45) | trivial |
10.4.3451623299.1 | $x^{10} - x^{9} - 3 x^{8} + 2 x^{6} + 2 x^{5} - 3 x^{3} + x^{2} + 3 x - 1$ | $-\,811\cdot 4256009$ | $S_{10}$ (as 10T45) | trivial |
10.4.3476098739.1 | $x^{10} - x^{9} - 2 x^{8} + 4 x^{7} - x^{6} - 3 x^{5} + x^{4} + x^{3} - 2 x + 1$ | $-\,3476098739$ | $S_{10}$ (as 10T45) | trivial |
10.4.3479589887.1 | $x^{10} - x^{9} + x^{7} + x^{6} - 3 x^{5} - 3 x^{4} + x^{3} + 2 x^{2} + x - 1$ | $-\,109\cdot 31922843$ | $S_{10}$ (as 10T45) | trivial |
10.4.3485322811.1 | $x^{10} - x^{9} - x^{8} - x^{7} + x^{6} + 5 x^{5} - 5 x^{4} - 3 x^{3} + 4 x^{2} - 1$ | $-\,97\cdot 233\cdot 154211$ | $S_{10}$ (as 10T45) | trivial |
10.4.3505569499.1 | $x^{10} - x^{9} + x^{8} - x^{7} - x^{6} + 5 x^{5} - 4 x^{4} - x^{3} + 4 x^{2} - x - 1$ | $-\,3505569499$ | $S_{10}$ (as 10T45) | trivial |
10.4.3510827191.1 | $x^{10} - 3 x^{9} + 2 x^{8} + x^{7} - 2 x^{6} + 4 x^{5} - 2 x^{4} - 4 x^{3} + 3 x + 1$ | $-\,9043\cdot 388237$ | $S_{10}$ (as 10T45) | trivial |
10.4.3514218623.1 | $x^{10} - x^{9} + x^{8} - x^{7} - x^{6} - 5 x^{4} + x^{3} + 5 x^{2} - 1$ | $-\,47\cdot 8647^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.4.3521646451.1 | $x^{10} - 2 x^{9} - x^{8} + 3 x^{7} + x^{5} - 4 x^{4} - 3 x^{3} + 4 x^{2} + x - 1$ | $-\,3521646451$ | $S_{10}$ (as 10T45) | trivial |
10.4.3526725619.1 | $x^{10} - x^{9} - x^{8} - 3 x^{6} + 6 x^{5} + x^{4} - 8 x^{3} + 3 x^{2} + 2 x - 1$ | $-\,349\cdot 2707\cdot 3733$ | $S_{10}$ (as 10T45) | trivial |
10.4.3528835307.1 | $x^{10} - x^{9} + x^{8} - 2 x^{7} + x^{6} - 2 x^{5} + 2 x^{3} - 3 x^{2} + 3 x - 1$ | $-\,31\cdot 113833397$ | $S_{10}$ (as 10T45) | trivial |
10.4.3531636739.1 | $x^{10} - x^{9} + 5 x^{5} - x^{4} - x^{2} - 3 x + 1$ | $-\,7933\cdot 445183$ | $S_{10}$ (as 10T45) | trivial |
10.4.3540851199.1 | $x^{10} - x^{9} - 3 x^{8} + x^{7} + 4 x^{6} + x^{5} - 5 x^{4} + 3 x^{2} - x - 1$ | $-\,3^{3}\cdot 3779\cdot 34703$ | $S_{10}$ (as 10T45) | trivial |
10.4.3547219843.1 | $x^{10} - x^{9} - 2 x^{8} + 5 x^{5} + 2 x^{4} - 4 x^{3} - x - 1$ | $-\,79\cdot 499\cdot 89983$ | $S_{10}$ (as 10T45) | trivial |
10.4.3548877539.1 | $x^{10} - 2 x^{9} + x^{8} - x^{7} + 3 x^{6} - x^{5} - 3 x^{4} - x^{2} + 3 x - 1$ | $-\,173\cdot 4373\cdot 4691$ | $S_{10}$ (as 10T45) | trivial |
10.4.3550900883.1 | $x^{10} - x^{9} + 2 x^{8} - 2 x^{6} + 3 x^{5} - 4 x^{4} + x^{2} - 2 x + 1$ | $-\,3550900883$ | $S_{10}$ (as 10T45) | trivial |
10.4.3554861923.1 | $x^{10} - 2 x^{9} - 2 x^{8} + 7 x^{7} - 3 x^{6} - 9 x^{5} + 11 x^{4} - x^{3} - 7 x^{2} + 5 x - 1$ | $-\,59\cdot 6577\cdot 9161$ | $S_{10}$ (as 10T45) | trivial |
10.4.3574437551.1 | $x^{10} - 3 x^{8} - 2 x^{7} + 3 x^{6} + 3 x^{5} - x^{4} + 2 x^{2} - x - 1$ | $-\,647\cdot 5524633$ | $S_{10}$ (as 10T45) | trivial |
10.4.3576073931.1 | $x^{10} - x^{9} + 2 x^{8} + 2 x^{7} - x^{6} + 3 x^{5} - x^{4} - x^{3} - 2 x - 1$ | $-\,52121\cdot 68611$ | $S_{10}$ (as 10T45) | trivial |