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 |
---|---|---|---|---|
10.2.799905449.1 | $x^{10} - x^{9} + x^{7} + x^{6} - x^{5} - x^{4} + x^{3} - x - 1$ | $7^{2}\cdot 41\cdot 631^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.2.801214577.1 | $x^{10} - 3 x^{9} + 3 x^{8} - x^{7} + x^{5} - 3 x^{4} + 4 x^{3} - x^{2} - x + 1$ | $801214577$ | $S_{10}$ (as 10T45) | trivial |
10.2.801589013.1 | $x^{10} - 2 x^{8} - x^{7} - x^{6} + x^{5} + 3 x^{4} - 2 x^{3} - 2 x^{2} + x + 1$ | $53\cdot 3889^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.2.802448461.1 | $x^{10} - 2 x^{7} - x^{6} + 2 x^{5} + x^{4} - 2 x^{2} - x + 1$ | $53\cdot 71\cdot 213247$ | $S_{10}$ (as 10T45) | trivial |
10.2.803282693.1 | $x^{10} - 3 x^{9} + 7 x^{8} - 11 x^{7} + 12 x^{6} - 8 x^{5} + 2 x^{4} + 4 x^{3} - 6 x^{2} + 4 x - 1$ | $803282693$ | $S_{10}$ (as 10T45) | trivial |
10.2.809040437.1 | $x^{10} - 2 x^{9} + 4 x^{7} - 4 x^{6} + 3 x^{4} - x^{3} - x^{2} + 1$ | $809040437$ | $S_{10}$ (as 10T45) | trivial |
10.2.814270253.1 | $x^{10} - x^{9} - 2 x^{8} + 4 x^{7} - x^{6} - 5 x^{5} + 5 x^{4} + x^{3} - 3 x^{2} + x + 1$ | $47\cdot 1753\cdot 9883$ | $S_{10}$ (as 10T45) | trivial |
10.2.817298432.1 | $x^{10} + x^{8} - 2 x^{7} + x^{4} + 2 x^{3} - x^{2} - 1$ | $2^{10}\cdot 798143$ | $S_{10}$ (as 10T45) | trivial |
10.2.819649013.1 | $x^{10} - 2 x^{9} + 2 x^{7} - x^{6} + x^{2} - x - 1$ | $819649013$ | $S_{10}$ (as 10T45) | trivial |
10.2.820675277.1 | $x^{10} - 2 x^{9} + 2 x^{8} - 5 x^{7} + 7 x^{6} - 4 x^{5} + 4 x^{4} - 8 x^{3} + 5 x^{2} - 1$ | $317\cdot 1609^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.2.821009933.1 | $x^{10} - x^{9} - 3 x^{8} + x^{7} + 6 x^{6} - 6 x^{4} - x^{3} + 3 x^{2} - 1$ | $5059\cdot 162287$ | $S_{10}$ (as 10T45) | trivial |
10.2.823435181.1 | $x^{10} - x^{9} + 3 x^{8} - x^{7} + 3 x^{5} - 4 x^{4} + x^{3} - 2 x + 1$ | $113\cdot 7287037$ | $S_{10}$ (as 10T45) | trivial |
10.2.826110449.1 | $x^{10} - x^{8} - x^{7} - x^{5} + 2 x^{4} + 3 x^{3} - 3 x^{2} + 1$ | $1229\cdot 672181$ | $S_{10}$ (as 10T45) | trivial |
10.2.827119069.1 | $x^{10} - x^{9} + 4 x^{8} - 4 x^{7} + 7 x^{6} - 8 x^{5} + 7 x^{4} - 7 x^{3} + 4 x^{2} - 3 x + 1$ | $7^{2}\cdot 61\cdot 276721$ | $S_{10}$ (as 10T45) | trivial |
10.2.827363461.1 | $x^{10} - x^{9} - x^{8} + 5 x^{7} - 4 x^{6} - 2 x^{5} + 7 x^{4} - 4 x^{3} - 2 x^{2} + 3 x - 1$ | $827363461$ | $S_{10}$ (as 10T45) | trivial |
10.2.828364813.1 | $x^{10} - x^{9} + x^{8} + 2 x^{7} - 4 x^{6} + 3 x^{4} - 2 x^{3} - 2 x^{2} + 2 x + 1$ | $157\cdot 2297^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.2.830003621.1 | $x^{10} - 3 x^{9} + 7 x^{8} - 11 x^{7} + 13 x^{6} - 13 x^{5} + 9 x^{4} - 5 x^{3} + x^{2} + x - 1$ | $2399\cdot 345979$ | $S_{10}$ (as 10T45) | trivial |
10.2.830597309.1 | $x^{10} - x^{9} - 2 x^{8} + x^{7} + x^{6} + 2 x^{5} + x^{4} - 2 x^{3} + x - 1$ | $193\cdot 4303613$ | $S_{10}$ (as 10T45) | trivial |
10.2.830677609.1 | $x^{10} - 2 x^{9} + 3 x^{8} - 3 x^{7} + 3 x^{6} - 4 x^{5} + 5 x^{4} - 7 x^{3} + 5 x^{2} - 3 x + 1$ | $5569\cdot 149161$ | $S_{10}$ (as 10T45) | trivial |
10.2.831295013.1 | $x^{10} - x^{9} - 2 x^{8} + 2 x^{7} + 3 x^{6} - 4 x^{5} - 3 x^{4} + 4 x^{3} + 2 x^{2} - 2 x - 1$ | $831295013$ | $S_{10}$ (as 10T45) | trivial |
10.2.831888493.1 | $x^{10} - x^{9} - 2 x^{8} + 2 x^{7} + 3 x^{6} - 3 x^{5} - 3 x^{4} + 3 x^{3} + 3 x^{2} - x - 1$ | $8111\cdot 102563$ | $S_{10}$ (as 10T45) | trivial |
10.2.833906069.1 | $x^{10} - 3 x^{8} - 3 x^{7} + x^{6} + 5 x^{5} + 5 x^{4} - 3 x^{2} - 3 x - 1$ | $7193\cdot 115933$ | $S_{10}$ (as 10T45) | trivial |
10.2.834771989.1 | $x^{10} - 2 x^{9} + 4 x^{8} - 7 x^{7} + 8 x^{6} - 8 x^{5} + 6 x^{4} - 3 x^{3} + x - 1$ | $29\cdot 307\cdot 93763$ | $S_{10}$ (as 10T45) | trivial |
10.2.836077225.1 | $x^{10} - 2 x^{9} + 4 x^{8} - 5 x^{7} + 7 x^{6} - 8 x^{5} + 8 x^{4} - 6 x^{3} + 2 x^{2} - x - 1$ | $5^{2}\cdot 5783^{2}$ | $(C_2^4:A_5) : C_2$ (as 10T37) | trivial |
10.2.836169077.1 | $x^{10} - 2 x^{9} - 2 x^{8} + 5 x^{7} + 3 x^{6} - 7 x^{5} - 2 x^{4} + 5 x^{3} + x^{2} - 2 x - 1$ | $149\cdot 5611873$ | $S_{10}$ (as 10T45) | trivial |
10.2.838803593.1 | $x^{10} - x^{9} - 2 x^{8} + 3 x^{7} + x^{6} - x^{5} - x^{4} - x^{3} + 2 x^{2} + x - 1$ | $79\cdot 10617767$ | $S_{10}$ (as 10T45) | trivial |
10.2.840291328.1 | $x^{10} - 2 x^{9} + 2 x^{8} - 4 x^{7} + 7 x^{6} - 8 x^{5} + 6 x^{4} - 6 x^{3} + 6 x^{2} - 4 x + 1$ | $2^{10}\cdot 820597$ | $S_{10}$ (as 10T45) | trivial |
10.2.844599673.1 | $x^{10} - x^{9} + x^{7} + 2 x^{5} - 4 x^{4} + 2 x^{3} + 2 x^{2} - 3 x + 1$ | $101\cdot 307\cdot 27239$ | $S_{10}$ (as 10T45) | trivial |
10.2.846083941.1 | $x^{10} - x^{9} + x^{8} + x^{7} - 4 x^{6} + 8 x^{5} - 10 x^{4} + 9 x^{3} - 7 x^{2} + 4 x - 1$ | $499\cdot 1695559$ | $S_{10}$ (as 10T45) | trivial |
10.2.848429441.1 | $x^{10} - x^{7} - 3 x^{6} + 3 x^{5} + 3 x^{4} - x^{3} - 1$ | $41\cdot 4549^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.2.851109913.1 | $x^{10} - 2 x^{9} + x^{6} + 2 x^{5} - 4 x^{4} + 2 x^{3} + 2 x^{2} - 2 x - 1$ | $17^{2}\cdot 97^{2}\cdot 313$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.2.851332877.1 | $x^{10} - x^{9} - x^{8} + 2 x^{7} + 2 x^{6} - 6 x^{5} + 5 x^{4} + x^{3} - 5 x^{2} + 4 x - 1$ | $43\cdot 19798439$ | $S_{10}$ (as 10T45) | trivial |
10.2.851763637.1 | $x^{10} - x^{9} - 2 x^{8} + x^{7} + 2 x^{5} + 2 x^{4} - 4 x^{3} - x^{2} + 2 x - 1$ | $851763637$ | $S_{10}$ (as 10T45) | trivial |
10.2.853697693.1 | $x^{10} - 4 x^{9} + 8 x^{8} - 11 x^{7} + 11 x^{6} - 7 x^{5} + 3 x^{4} - 2 x^{2} + x - 1$ | $23\cdot 37117291$ | $S_{10}$ (as 10T45) | trivial |
10.2.856749056.1 | $x^{10} - x^{8} - 2 x^{7} + x^{6} + 2 x^{5} - x^{4} - 2 x^{3} + 2 x + 1$ | $2^{10}\cdot 103\cdot 8123$ | $S_{10}$ (as 10T45) | trivial |
10.2.856799533.1 | $x^{10} - 2 x^{9} + 2 x^{8} + x^{7} - 2 x^{6} + 2 x^{4} - 2 x^{3} - 2 x^{2} + 2 x - 1$ | $2837\cdot 302009$ | $S_{10}$ (as 10T45) | trivial |
10.2.857695393.1 | $x^{10} - 2 x^{9} + 5 x^{7} - 5 x^{6} - 2 x^{5} + 8 x^{4} - 4 x^{3} - 2 x^{2} + 3 x - 1$ | $311\cdot 2757863$ | $S_{10}$ (as 10T45) | trivial |
10.2.858063061.1 | $x^{10} - x^{9} - x^{8} + 3 x^{7} - 4 x^{5} + 2 x^{4} + 3 x^{3} - 3 x^{2} + 1$ | $17959\cdot 47779$ | $S_{10}$ (as 10T45) | trivial |
10.2.859848569.1 | $x^{10} - 2 x^{9} + 4 x^{8} - 5 x^{7} + 6 x^{6} - 7 x^{5} + 7 x^{4} - 8 x^{3} + 5 x^{2} - 3 x + 1$ | $859848569$ | $S_{10}$ (as 10T45) | trivial |
10.2.860443648.1 | $x^{10} + x^{8} - 2 x^{7} - x^{6} - 2 x^{5} + 2 x^{3} + x^{2} + 2 x - 1$ | $2^{10}\cdot 840277$ | $S_{10}$ (as 10T45) | trivial |
10.2.860714261.1 | $x^{10} - x^{9} + x^{7} - 3 x^{6} + 3 x^{5} - x^{4} - x^{3} + 3 x^{2} - 2 x + 1$ | $11^{2}\cdot 7113341$ | $S_{10}$ (as 10T45) | trivial |
10.2.860949101.1 | $x^{10} - 3 x^{9} + 6 x^{8} - 9 x^{7} + 8 x^{6} - 6 x^{5} + 2 x^{4} + x^{2} + 1$ | $860949101$ | $S_{10}$ (as 10T45) | trivial |
10.2.862175261.1 | $x^{10} - 3 x^{9} + 4 x^{8} - x^{7} - 3 x^{6} + 6 x^{5} - 8 x^{4} + 10 x^{3} - 8 x^{2} + 4 x - 1$ | $199\cdot 4332539$ | $S_{10}$ (as 10T45) | trivial |
10.2.862897933.1 | $x^{10} - 3 x^{9} + 6 x^{8} - 9 x^{7} + 11 x^{6} - 9 x^{5} + 5 x^{4} - 3 x^{2} + 3 x - 1$ | $6763\cdot 127591$ | $S_{10}$ (as 10T45) | trivial |
10.2.863165333.1 | $x^{10} - 2 x^{9} + 3 x^{8} - 3 x^{7} + 5 x^{5} - 10 x^{4} + 10 x^{3} - 8 x^{2} + 4 x - 1$ | $31\cdot 41\cdot 679123$ | $S_{10}$ (as 10T45) | trivial |
10.2.867798793.1 | $x^{10} - 2 x^{8} - 3 x^{7} + 5 x^{5} + 5 x^{4} - 3 x^{2} - 3 x - 1$ | $103\cdot 257\cdot 32783$ | $S_{10}$ (as 10T45) | trivial |
10.2.869334889.1 | $x^{10} - 2 x^{9} + 3 x^{8} - x^{7} - 2 x^{6} + 5 x^{5} - 4 x^{4} + x^{3} + x^{2} - 2 x + 1$ | $47\cdot 18496487$ | $S_{10}$ (as 10T45) | trivial |
10.2.869414653.1 | $x^{10} - x^{9} - x^{8} + 4 x^{7} - x^{6} - 6 x^{5} + 8 x^{4} - x^{3} - 5 x^{2} + 4 x - 1$ | $869414653$ | $S_{10}$ (as 10T45) | trivial |
10.2.869777173.1 | $x^{10} - 2 x^{9} + 4 x^{8} - 4 x^{7} + 5 x^{6} - 5 x^{5} + 6 x^{4} - 7 x^{3} + 5 x^{2} - 3 x + 1$ | $869777173$ | $S_{10}$ (as 10T45) | trivial |
10.2.872338141.1 | $x^{10} - x^{9} - x^{8} + x^{6} + 2 x^{5} - 2 x^{4} - 4 x^{3} + x^{2} + 3 x + 1$ | $173\cdot 1487\cdot 3391$ | $S_{10}$ (as 10T45) | trivial |