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 |
---|---|---|---|---|
10.0.209352647.1 | $x^{10} - 3 x^{9} + 7 x^{8} - 11 x^{7} + 13 x^{6} - 12 x^{5} + 9 x^{4} - 5 x^{3} + 3 x^{2} - 2 x + 1$ | $-\,7^{2}\cdot 23\cdot 431^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.0.212309359.1 | $x^{10} - 3 x^{9} + 5 x^{8} - 7 x^{7} + 9 x^{6} - 10 x^{5} + 9 x^{4} - 7 x^{3} + 5 x^{2} - 2 x + 1$ | $-\,31\cdot 2617^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.0.214816879.1 | $x^{10} - 2 x^{9} + 4 x^{8} - 7 x^{7} + 9 x^{6} - 10 x^{5} + 10 x^{4} - 8 x^{3} + 6 x^{2} - 3 x + 1$ | $-\,17^{2}\cdot 79\cdot 97^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.0.215067767.1 | $x^{10} - x^{9} - x^{8} + 2 x^{7} + x^{6} - 3 x^{5} + 3 x^{3} - x^{2} - x + 1$ | $-\,215067767$ | $S_{10}$ (as 10T45) | trivial |
10.0.216670707.1 | $x^{10} - 3 x^{9} + 5 x^{8} - 6 x^{7} + 6 x^{6} - 4 x^{5} + 2 x^{4} - x^{3} + x^{2} - x + 1$ | $-\,3^{5}\cdot 11^{2}\cdot 7369$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.0.220168975.1 | $x^{10} - x^{9} - x^{8} + 2 x^{7} - x^{6} - x^{5} + 4 x^{4} - x^{3} - 3 x^{2} + x + 1$ | $-\,5^{2}\cdot 13^{2}\cdot 31\cdot 41^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.0.220506347.1 | $x^{10} - 3 x^{9} + 5 x^{8} - 5 x^{7} + 3 x^{6} - x^{4} + x^{3} - x + 1$ | $-\,37\cdot 677\cdot 8803$ | $S_{10}$ (as 10T45) | trivial |
10.0.224198759.1 | $x^{10} - x^{9} - 2 x^{8} + 4 x^{7} - 4 x^{5} + 3 x^{4} + x^{3} - 2 x^{2} + 1$ | $-\,71\cdot 1777^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.0.224415603.1 | $x^{10} + 2 x^{8} - 3 x^{7} + 3 x^{6} - 7 x^{5} + 8 x^{4} - 7 x^{3} + 7 x^{2} - 4 x + 1$ | $-\,3^{5}\cdot 31^{4}$ | $D_5\times C_5$ (as 10T6) | trivial |
10.0.226173952.1 | $x^{10} - x^{8} - 2 x^{7} - x^{6} + 2 x^{5} + 2 x^{4} - x^{2} + 1$ | $-\,2^{10}\cdot 220873$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.0.226876987.1 | $x^{10} - 2 x^{9} + 3 x^{8} - 3 x^{7} + 2 x^{6} + x^{5} - x^{4} - 3 x^{3} + 6 x^{2} - 4 x + 1$ | $-\,43\cdot 2297^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.0.227991979.1 | $x^{10} - x^{9} - x^{8} + 3 x^{7} - x^{6} - 3 x^{5} + 3 x^{4} + x^{3} - 2 x^{2} + 1$ | $-\,599\cdot 380621$ | $S_{10}$ (as 10T45) | trivial |
10.0.229203619.1 | $x^{10} - x^{9} + 2 x^{8} - 3 x^{7} + 4 x^{6} - 4 x^{5} + 4 x^{4} - 4 x^{3} + 3 x^{2} - 2 x + 1$ | $-\,229203619$ | $S_{10}$ (as 10T45) | trivial |
10.0.229345007.1 | $x^{10} - x^{9} + 6 x^{8} - 3 x^{7} + 11 x^{6} - 3 x^{5} + 11 x^{4} - 3 x^{3} + 6 x^{2} - x + 1$ | $-\,47^{5}$ | $D_5$ (as 10T2) | trivial |
10.0.233043179.1 | $x^{10} - x^{9} + 2 x^{8} - 4 x^{7} + 4 x^{6} - 5 x^{5} + 5 x^{4} - 4 x^{3} + 3 x^{2} - x + 1$ | $-\,97\cdot 463\cdot 5189$ | $S_{10}$ (as 10T45) | trivial |
10.0.236184579.1 | $x^{10} - 3 x^{9} + 5 x^{8} - 7 x^{7} + 7 x^{6} - 6 x^{5} + 4 x^{4} - 2 x^{3} + x^{2} + 1$ | $-\,3^{5}\cdot 37\cdot 109\cdot 241$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.0.236438047.1 | $x^{10} - 2 x^{9} + x^{8} + 2 x^{7} - 3 x^{6} + x^{5} + x^{4} - x + 1$ | $-\,236438047$ | $S_{10}$ (as 10T45) | trivial |
10.0.240232739.1 | $x^{10} - 2 x^{9} + 2 x^{8} - 2 x^{6} + 4 x^{5} - 4 x^{4} + x^{3} + 3 x^{2} - 3 x + 1$ | $-\,467\cdot 514417$ | $S_{10}$ (as 10T45) | trivial |
10.0.243226747.1 | $x^{10} - 3 x^{9} + 4 x^{8} - 3 x^{7} + 2 x^{6} - x^{5} + x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 1$ | $-\,243226747$ | $S_{10}$ (as 10T45) | trivial |
10.0.243415027.1 | $x^{10} - x^{7} + x^{6} + 2 x^{5} - x^{3} - 2 x^{2} + 1$ | $-\,17\cdot 14318531$ | $S_{10}$ (as 10T45) | trivial |
10.0.244175707.1 | $x^{10} - x^{9} + x^{7} - x^{6} - x^{4} + x^{3} + x^{2} - x + 1$ | $-\,19^{2}\cdot 676387$ | $S_{10}$ (as 10T45) | trivial |
10.0.246071287.1 | $x^{10} - 3 x^{9} + 7 x^{8} - 12 x^{7} + 15 x^{6} - 15 x^{5} + 12 x^{4} - 7 x^{3} + 4 x^{2} - 2 x + 1$ | $-\,7^{5}\cdot 11^{4}$ | $D_5\times C_5$ (as 10T6) | trivial |
10.0.246944619.1 | $x^{10} - x^{9} + x^{6} - x^{5} - x^{4} + 3 x^{3} - x^{2} - x + 1$ | $-\,3^{5}\cdot 73\cdot 13921$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.0.250679267.1 | $x^{10} - x^{9} - 2 x^{8} + x^{7} + 3 x^{6} - 2 x^{4} - 2 x^{3} + 2 x + 1$ | $-\,250679267$ | $S_{10}$ (as 10T45) | trivial |
10.0.252486127.1 | $x^{10} - x^{9} + 2 x^{8} - 4 x^{7} + 4 x^{6} - 4 x^{5} + 5 x^{4} - 3 x^{3} + 2 x^{2} - 2 x + 1$ | $-\,787\cdot 320821$ | $S_{10}$ (as 10T45) | trivial |
10.0.254121139.1 | $x^{10} - 2 x^{8} - x^{7} + 2 x^{6} + 3 x^{5} - 3 x^{3} - x^{2} + x + 1$ | $-\,149\cdot 991\cdot 1721$ | $S_{10}$ (as 10T45) | trivial |
10.0.260270739.1 | $x^{10} - x^{8} - 2 x^{7} + x^{6} + 3 x^{5} - 2 x^{4} - 4 x^{3} + x^{2} + 3 x + 1$ | $-\,3^{5}\cdot 163\cdot 6571$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.0.262091507.1 | $x^{10} - x^{9} - 2 x^{6} + 3 x^{5} + 3 x^{4} - 4 x^{3} - 2 x^{2} + 2 x + 1$ | $-\,83\cdot 1777^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.0.262477979.1 | $x^{10} - x^{9} + x^{8} - 2 x^{6} + x^{5} - x^{4} + x^{2} + 1$ | $-\,251\cdot 1045729$ | $S_{10}$ (as 10T45) | trivial |
10.0.262864627.1 | $x^{10} - 2 x^{8} - x^{7} + x^{6} + 2 x^{5} - x^{4} - 2 x^{3} + x^{2} + x + 1$ | $-\,353\cdot 744659$ | $S_{10}$ (as 10T45) | trivial |
10.0.262909719.1 | $x^{10} - x^{8} - x^{7} - 2 x^{6} + 4 x^{4} + x^{3} - 2 x^{2} + 1$ | $-\,3^{5}\cdot 73\cdot 14821$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.0.263786699.1 | $x^{10} - 2 x^{9} + 2 x^{8} - 2 x^{7} + 4 x^{6} - 5 x^{5} + 4 x^{4} - 2 x^{3} + 3 x^{2} - 3 x + 1$ | $-\,11\cdot 59^{2}\cdot 83^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.0.268043264.1 | $x^{10} - 2 x^{9} + 3 x^{8} - 6 x^{7} + 6 x^{6} - 6 x^{5} + 7 x^{4} - 4 x^{3} + 3 x^{2} - 2 x + 1$ | $-\,2^{10}\cdot 261761$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.0.274127275.1 | $x^{10} - x^{9} + x^{8} - 3 x^{7} + 3 x^{6} - x^{5} + 3 x^{4} - 3 x^{3} + 1$ | $-\,5^{2}\cdot 59\cdot 185849$ | $S_{10}$ (as 10T45) | trivial |
10.0.274550779.1 | $x^{10} - x^{9} + 2 x^{8} - 2 x^{7} + 3 x^{6} - 3 x^{5} + 3 x^{4} - 3 x^{3} + 2 x^{2} - 2 x + 1$ | $-\,19\cdot 14450041$ | $S_{10}$ (as 10T45) | trivial |
10.0.277010267.1 | $x^{10} - 2 x^{9} + x^{8} + 2 x^{7} - 3 x^{6} + 3 x^{5} - 2 x^{4} + 3 x^{2} - 3 x + 1$ | $-\,107\cdot 1609^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.0.278005859.1 | $x^{10} - x^{9} - x^{8} + 4 x^{7} - 2 x^{6} - 3 x^{5} + 4 x^{4} - 2 x^{2} + 1$ | $-\,278005859$ | $S_{10}$ (as 10T45) | trivial |
10.0.278645219.1 | $x^{10} + 3 x^{8} - x^{7} + 4 x^{6} - x^{5} + 4 x^{4} + 2 x^{2} + 1$ | $-\,317\cdot 879007$ | $S_{10}$ (as 10T45) | trivial |
10.0.281268947.1 | $x^{10} + 3 x^{8} - x^{7} + 4 x^{6} - x^{5} + 4 x^{4} - x^{3} + 2 x^{2} - x + 1$ | $-\,281268947$ | $S_{10}$ (as 10T45) | trivial |
10.0.282748447.1 | $x^{10} - x^{9} - 2 x^{8} + 3 x^{7} + 2 x^{6} - 5 x^{5} + x^{4} + 4 x^{3} - 2 x^{2} - x + 1$ | $-\,282748447$ | $S_{10}$ (as 10T45) | trivial |
10.0.283885691.1 | $x^{10} - x^{9} + 2 x^{8} - 4 x^{7} + 3 x^{6} - 4 x^{5} + 3 x^{4} - 2 x^{3} + 2 x^{2} + 1$ | $-\,8941\cdot 31751$ | $S_{10}$ (as 10T45) | trivial |
10.0.284152779.1 | $x^{10} - x^{9} - 2 x^{8} + 3 x^{7} + 2 x^{6} - 3 x^{5} - 2 x^{4} + 3 x^{3} + x^{2} - 2 x + 1$ | $-\,3^{5}\cdot 1169353$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.0.285267739.1 | $x^{10} - x^{9} + x^{8} - x^{7} - x^{5} + 3 x^{4} - 4 x^{3} + 4 x^{2} - 2 x + 1$ | $-\,285267739$ | $S_{10}$ (as 10T45) | trivial |
10.0.288806267.1 | $x^{10} - x^{9} - x^{8} + 2 x^{7} - x^{5} + x^{3} - x + 1$ | $-\,1321\cdot 218627$ | $S_{10}$ (as 10T45) | trivial |
10.0.290432899.1 | $x^{10} - 3 x^{8} - x^{7} + 4 x^{6} + 3 x^{5} - 2 x^{4} - 4 x^{3} + 2 x + 1$ | $-\,89\cdot 3263291$ | $S_{10}$ (as 10T45) | trivial |
10.0.290491759.1 | $x^{10} - 3 x^{9} + 5 x^{8} - 5 x^{7} + 5 x^{6} - 6 x^{5} + 6 x^{4} - 3 x^{3} + x^{2} - x + 1$ | $-\,290491759$ | $S_{10}$ (as 10T45) | trivial |
10.0.290954507.1 | $x^{10} - x^{9} + 2 x^{8} + 2 x^{7} - x^{6} + 4 x^{5} + 4 x^{4} + 2 x^{2} + 3 x + 1$ | $-\,17^{2}\cdot 97^{2}\cdot 107$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.0.291458939.1 | $x^{10} - x^{9} + 2 x^{8} - 2 x^{6} + 3 x^{5} - 3 x^{4} + 2 x^{2} - 2 x + 1$ | $-\,197\cdot 1479487$ | $S_{10}$ (as 10T45) | trivial |
10.0.292693979.1 | $x^{10} - 3 x^{9} + 4 x^{8} - 3 x^{7} + 3 x^{6} - 4 x^{5} + 3 x^{4} - x + 1$ | $-\,127\cdot 239\cdot 9643$ | $S_{10}$ (as 10T45) | trivial |
10.0.293025059.1 | $x^{10} - 2 x^{9} + 3 x^{8} - 4 x^{7} + 5 x^{6} - 6 x^{5} + 8 x^{4} - 8 x^{3} + 6 x^{2} - 3 x + 1$ | $-\,293025059$ | $S_{10}$ (as 10T45) | trivial |