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 |
---|---|---|---|---|
10.8.70952789611.1 | $x^{10} - x^{9} - 6 x^{8} + 9 x^{7} + 5 x^{6} - 18 x^{5} + 9 x^{4} + 12 x^{3} - 10 x^{2} - 3 x + 1$ | $-\,11^{8}\cdot 331$ | $C_2 \times (C_2^4 : C_5)$ (as 10T14) | trivial |
10.8.73401286963.1 | $x^{10} - x^{9} - 6 x^{8} + 2 x^{7} + 15 x^{6} + 6 x^{5} - 21 x^{4} - 13 x^{3} + 10 x^{2} + 7 x + 1$ | $-\,149\cdot 492626087$ | $S_{10}$ (as 10T45) | trivial |
10.8.74596123648.1 | $x^{10} - 2 x^{9} - 4 x^{8} + 12 x^{7} - x^{6} - 22 x^{5} + 16 x^{4} + 12 x^{3} - 12 x^{2} + 1$ | $-\,2^{10}\cdot 2389\cdot 30493$ | $S_{10}$ (as 10T45) | trivial |
10.8.76575120067.1 | $x^{10} - 3 x^{9} - 2 x^{8} + 13 x^{7} - 7 x^{6} - 14 x^{5} + 16 x^{4} + 4 x^{3} - 8 x^{2} + 1$ | $-\,76575120067$ | $S_{10}$ (as 10T45) | trivial |
10.8.80706729619.1 | $x^{10} - x^{9} - 6 x^{8} + 7 x^{7} + 9 x^{6} - 15 x^{5} - x^{4} + 12 x^{3} - 3 x^{2} - 3 x + 1$ | $-\,80706729619$ | $S_{10}$ (as 10T45) | trivial |
10.8.81895986176.1 | $x^{10} - 5 x^{8} - 2 x^{7} + 5 x^{6} + 8 x^{5} + 6 x^{4} - 8 x^{3} - 7 x^{2} + 2 x + 1$ | $-\,2^{10}\cdot 79976549$ | $S_{10}$ (as 10T45) | trivial |
10.8.82252830707.1 | $x^{10} - 6 x^{8} - 2 x^{7} + 11 x^{6} + 10 x^{5} - 6 x^{4} - 14 x^{3} + x^{2} + 5 x - 1$ | $-\,19\cdot 4329096353$ | $S_{10}$ (as 10T45) | trivial |
10.8.85583036411.1 | $x^{10} - x^{9} - 7 x^{8} + 4 x^{7} + 18 x^{6} - 2 x^{5} - 20 x^{4} - 5 x^{3} + 9 x^{2} + 3 x - 1$ | $-\,2377\cdot 36004643$ | $S_{10}$ (as 10T45) | trivial |
10.8.85992371875.1 | $x^{10} - 2 x^{9} - x^{8} - x^{6} + 12 x^{5} - x^{4} - 12 x^{3} + 3 x^{2} + 3 x - 1$ | $-\,5^{5}\cdot 27517559$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.8.88118370211.1 | $x^{10} - 4 x^{8} - 4 x^{7} + x^{6} + 13 x^{5} + 6 x^{4} - 10 x^{3} - 5 x^{2} + 2 x + 1$ | $-\,101\cdot 953\cdot 915487$ | $S_{10}$ (as 10T45) | trivial |
10.8.88642871875.1 | $x^{10} - x^{9} - 2 x^{8} - 3 x^{7} - x^{6} + 20 x^{5} + 4 x^{4} - 25 x^{3} - 3 x^{2} + 8 x + 1$ | $-\,5^{5}\cdot 3169\cdot 8951$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.8.88849549891.1 | $x^{10} - 3 x^{9} - 2 x^{8} + 11 x^{7} - 3 x^{6} - 8 x^{5} + 8 x^{4} - 7 x^{3} - 5 x^{2} + 6 x + 1$ | $-\,6133\cdot 14487127$ | $S_{10}$ (as 10T45) | trivial |
10.8.90213934375.1 | $x^{10} - 3 x^{9} - 2 x^{8} + 12 x^{7} - 9 x^{6} - 9 x^{5} + 26 x^{4} - 9 x^{3} - 15 x^{2} + 10 x - 1$ | $-\,5^{5}\cdot 28868459$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.8.90614121875.1 | $x^{10} - x^{9} - 7 x^{8} + 9 x^{7} + 9 x^{6} - 15 x^{5} + 4 x^{4} + 3 x^{3} - 8 x^{2} + 3 x + 1$ | $-\,5^{5}\cdot 28996519$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.8.91588346875.1 | $x^{10} - x^{9} - 7 x^{8} + 5 x^{7} + 14 x^{6} - x^{5} - 11 x^{4} - 8 x^{3} + 2 x^{2} + 4 x + 1$ | $-\,5^{5}\cdot 29308271$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.8.92090628691.1 | $x^{10} - 2 x^{9} - 3 x^{8} + 11 x^{7} - 4 x^{6} - 17 x^{5} + 14 x^{4} + 9 x^{3} - 8 x^{2} - x + 1$ | $-\,293\cdot 2957\cdot 106291$ | $S_{10}$ (as 10T45) | trivial |
10.8.94136471875.1 | $x^{10} - 5 x^{8} - 2 x^{7} + 8 x^{5} + 11 x^{4} - 5 x^{3} - 8 x^{2} + 1$ | $-\,5^{5}\cdot 30123671$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.8.94459871875.1 | $x^{10} - 3 x^{9} + 5 x^{7} - 5 x^{6} + 9 x^{5} + x^{4} - 16 x^{3} + x^{2} + 5 x + 1$ | $-\,5^{5}\cdot 89\cdot 339631$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.8.94747154563.1 | $x^{10} - 2 x^{9} - 4 x^{8} + 8 x^{7} + 3 x^{6} - 5 x^{5} - 5 x^{3} + x^{2} + 3 x - 1$ | $-\,221047\cdot 428629$ | $S_{10}$ (as 10T45) | trivial |
10.8.94822656283.1 | $x^{10} - x^{9} - 4 x^{8} + 3 x^{7} + 6 x^{5} + 4 x^{4} - 11 x^{3} + 4 x - 1$ | $-\,111847\cdot 847789$ | $S_{10}$ (as 10T45) | trivial |
10.8.96433540579.1 | $x^{10} - x^{9} - 6 x^{8} + 9 x^{7} + 13 x^{6} - 24 x^{5} - 13 x^{4} + 22 x^{3} + 6 x^{2} - 5 x - 1$ | $-\,347\cdot 277906457$ | $S_{10}$ (as 10T45) | trivial |
10.8.97939335863.1 | $x^{10} - 3 x^{9} - x^{8} + 5 x^{7} + 7 x^{5} - 3 x^{4} - 16 x^{3} + x^{2} + 7 x + 1$ | $-\,61^{2}\cdot 167\cdot 397^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.8.98289657019.1 | $x^{10} - 4 x^{8} - 3 x^{5} + 11 x^{4} + 8 x^{3} - 7 x^{2} - 6 x - 1$ | $-\,98289657019$ | $S_{10}$ (as 10T45) | trivial |
10.8.99136309375.1 | $x^{10} - 3 x^{9} - 4 x^{8} + 17 x^{7} + 3 x^{6} - 32 x^{5} + 3 x^{4} + 21 x^{3} - 4 x^{2} - 4 x + 1$ | $-\,5^{5}\cdot 31723619$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.8.99667039987.1 | $x^{10} - x^{9} - 7 x^{8} + 7 x^{7} + 15 x^{6} - 17 x^{5} - 11 x^{4} + 15 x^{3} + 4 x^{2} - 4 x - 1$ | $-\,67\cdot 38569^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.8.100564499456.1 | $x^{10} - 4 x^{9} + 2 x^{8} + 8 x^{7} - 9 x^{6} + 4 x^{5} - 2 x^{4} - 8 x^{3} + 8 x^{2} - 1$ | $-\,2^{10}\cdot 751\cdot 130769$ | $S_{10}$ (as 10T45) | trivial |
10.8.103196621875.1 | $x^{10} - 4 x^{9} + 2 x^{8} + 7 x^{7} - 9 x^{6} + 6 x^{5} + 3 x^{4} - 12 x^{3} + 3 x^{2} + 3 x - 1$ | $-\,5^{5}\cdot 2129\cdot 15511$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.8.103545471875.1 | $x^{10} - 2 x^{9} - x^{8} + 3 x^{7} - 6 x^{6} + 8 x^{5} + 12 x^{4} - 16 x^{3} - 7 x^{2} + 6 x + 1$ | $-\,5^{5}\cdot 1009\cdot 32839$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.8.103764024667.1 | $x^{10} - x^{9} - 7 x^{8} + 3 x^{7} + 17 x^{6} + 2 x^{5} - 16 x^{4} - 6 x^{3} + 7 x^{2} + 2 x - 1$ | $-\,103764024667$ | $S_{10}$ (as 10T45) | trivial |
10.8.104621536619.1 | $x^{10} - x^{9} - 4 x^{8} + 2 x^{7} + 2 x^{6} + 7 x^{5} + 2 x^{4} - 12 x^{3} + x^{2} + 4 x - 1$ | $-\,104621536619$ | $S_{10}$ (as 10T45) | trivial |
10.8.104644780979.1 | $x^{10} - 8 x^{8} - 3 x^{7} + 20 x^{6} + 12 x^{5} - 19 x^{4} - 11 x^{3} + 8 x^{2} + 2 x - 1$ | $-\,10657\cdot 9819347$ | $S_{10}$ (as 10T45) | trivial |
10.8.107012672267.1 | $x^{10} - x^{9} - 6 x^{8} + x^{7} + 13 x^{6} + 8 x^{5} - 13 x^{4} - 10 x^{3} + 6 x^{2} + 3 x - 1$ | $-\,139187\cdot 768841$ | $S_{10}$ (as 10T45) | trivial |
10.8.107711957323.1 | $x^{10} - 3 x^{9} - 2 x^{8} + 9 x^{7} + 4 x^{6} - 8 x^{5} - 12 x^{4} + 3 x^{3} + 10 x^{2} - 1$ | $-\,101\cdot 1066455023$ | $S_{10}$ (as 10T45) | trivial |
10.8.108076720883.1 | $x^{10} - 7 x^{8} - x^{7} + 16 x^{6} + 6 x^{5} - 16 x^{4} - 8 x^{3} + 7 x^{2} + 2 x - 1$ | $-\,521\cdot 12119\cdot 17117$ | $S_{10}$ (as 10T45) | trivial |
10.8.108727098211.1 | $x^{10} - x^{9} - 8 x^{8} + 6 x^{7} + 22 x^{6} - 12 x^{5} - 25 x^{4} + 8 x^{3} + 10 x^{2} - x - 1$ | $-\,223319\cdot 486869$ | $S_{10}$ (as 10T45) | trivial |
10.8.110978730539.1 | $x^{10} - x^{9} - 5 x^{8} + 6 x^{7} + 4 x^{6} - 9 x^{5} + 7 x^{4} + 3 x^{3} - 8 x^{2} + 1$ | $-\,401\cdot 276754939$ | $S_{10}$ (as 10T45) | trivial |
10.8.111511052371.1 | $x^{10} - x^{9} - 3 x^{8} + 6 x^{7} - 7 x^{6} - 4 x^{5} + 19 x^{4} - 2 x^{3} - 11 x^{2} + 1$ | $-\,1171\cdot 95227201$ | $S_{10}$ (as 10T45) | trivial |
10.8.111579297443.1 | $x^{10} - 4 x^{9} + 2 x^{8} + 6 x^{7} - 3 x^{6} + 4 x^{5} - 9 x^{4} - 12 x^{3} + 8 x^{2} + 7 x + 1$ | $-\,113\cdot 987427411$ | $S_{10}$ (as 10T45) | trivial |
10.8.112791868547.1 | $x^{10} - 8 x^{8} - 2 x^{7} + 20 x^{6} + 8 x^{5} - 19 x^{4} - 9 x^{3} + 7 x^{2} + 2 x - 1$ | $-\,271\cdot 1723\cdot 241559$ | $S_{10}$ (as 10T45) | trivial |
10.8.113109434387.1 | $x^{10} - x^{9} - 2 x^{8} + 5 x^{7} - 8 x^{6} - 9 x^{5} + 23 x^{4} + 6 x^{3} - 15 x^{2} + 1$ | $-\,113109434387$ | $S_{10}$ (as 10T45) | trivial |
10.8.113379547139.1 | $x^{10} - x^{9} - 6 x^{8} + 4 x^{7} + 12 x^{6} - x^{5} - 13 x^{4} - 4 x^{3} + 7 x^{2} + x - 1$ | $-\,79\cdot 4799\cdot 299059$ | $S_{10}$ (as 10T45) | trivial |
10.8.113709931627.1 | $x^{10} - 3 x^{9} - x^{8} + 8 x^{7} - 4 x^{6} - x^{5} + 6 x^{4} - 7 x^{3} - 4 x^{2} + 3 x + 1$ | $-\,349\cdot 325816423$ | $S_{10}$ (as 10T45) | trivial |
10.8.113849658368.1 | $x^{10} - 2 x^{9} - 4 x^{8} + 4 x^{7} + 13 x^{6} - 2 x^{5} - 18 x^{4} + 8 x^{2} - 1$ | $-\,2^{10}\cdot 111181307$ | $S_{10}$ (as 10T45) | trivial |
10.8.114095358976.1 | $x^{10} - 5 x^{8} + 2 x^{6} - 6 x^{5} + 7 x^{4} + 8 x^{3} - 5 x^{2} - 2 x + 1$ | $-\,2^{10}\cdot 5081\cdot 21929$ | $S_{10}$ (as 10T45) | trivial |
10.8.114458329088.1 | $x^{10} - 2 x^{9} - 5 x^{8} + 12 x^{7} + x^{6} - 20 x^{5} + 13 x^{4} + 10 x^{3} - 10 x^{2} + 1$ | $-\,2^{15}\cdot 3492991$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.8.115079251267.1 | $x^{10} - 4 x^{9} + 2 x^{8} + 10 x^{7} - 15 x^{6} + 2 x^{5} + 16 x^{4} - 16 x^{3} - 3 x^{2} + 7 x - 1$ | $-\,98041\cdot 1173787$ | $S_{10}$ (as 10T45) | trivial |
10.8.117161033728.1 | $x^{10} - 6 x^{8} - 2 x^{7} + 10 x^{6} + 10 x^{5} - 5 x^{4} - 12 x^{3} + 2 x^{2} + 4 x - 1$ | $-\,2^{15}\cdot 3575471$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.8.117333345203.1 | $x^{10} - 2 x^{9} - 2 x^{8} + 11 x^{7} - 7 x^{6} - 19 x^{5} + 14 x^{4} + 11 x^{3} - 7 x^{2} - 2 x + 1$ | $-\,1973\cdot 59469511$ | $S_{10}$ (as 10T45) | trivial |
10.8.120062096875.1 | $x^{10} - 5 x^{8} - 2 x^{7} + 5 x^{6} + 8 x^{5} + 6 x^{4} - 10 x^{3} - 8 x^{2} + 5 x + 1$ | $-\,5^{5}\cdot 7^{2}\cdot 739\cdot 1061$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.8.121442676499.1 | $x^{10} - 2 x^{9} - 5 x^{8} + 8 x^{7} + 11 x^{6} - 9 x^{5} - 14 x^{4} + 3 x^{3} + 8 x^{2} - x - 1$ | $-\,121442676499$ | $S_{10}$ (as 10T45) | trivial |