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 |
---|---|---|---|---|
10.10.443952558373.1 | $x^{10} - 11 x^{8} - 3 x^{7} + 37 x^{6} + 14 x^{5} - 48 x^{4} - 22 x^{3} + 20 x^{2} + 12 x + 1$ | $61^{2}\cdot 397^{2}\cdot 757$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.10.513087549389.1 | $x^{10} - 4 x^{9} - 2 x^{8} + 23 x^{7} - 11 x^{6} - 40 x^{5} + 30 x^{4} + 21 x^{3} - 18 x^{2} + 1$ | $460181\cdot 1114969$ | $S_{10}$ (as 10T45) | trivial |
10.10.572981288913.1 | $x^{10} - x^{9} - 10 x^{8} + 10 x^{7} + 34 x^{6} - 34 x^{5} - 43 x^{4} + 43 x^{3} + 12 x^{2} - 12 x + 1$ | $3^{5}\cdot 11^{9}$ | $C_{10}$ (as 10T1) | trivial |
10.10.617567936161.1 | $x^{10} - x^{9} - 12 x^{8} + 5 x^{7} + 39 x^{6} - 11 x^{5} - 47 x^{4} + 15 x^{3} + 18 x^{2} - 9 x + 1$ | $11^{8}\cdot 43\cdot 67$ | $C_2 \times (C_2^4 : C_5)$ (as 10T14) | trivial |
10.10.645863308453.1 | $x^{10} - 2 x^{9} - 9 x^{8} + 15 x^{7} + 29 x^{6} - 31 x^{5} - 43 x^{4} + 14 x^{3} + 23 x^{2} + 3 x - 1$ | $11^{8}\cdot 23\cdot 131$ | $C_2 \times (C_2^4 : C_5)$ (as 10T14) | trivial |
10.10.653113904957.1 | $x^{10} - x^{9} - 9 x^{8} + 9 x^{7} + 25 x^{6} - 23 x^{5} - 24 x^{4} + 17 x^{3} + 8 x^{2} - 3 x - 1$ | $37\cdot 47\cdot 239\cdot 1571417$ | $S_{10}$ (as 10T45) | trivial |
10.10.669871503125.1 | $x^{10} - x^{9} - 13 x^{8} + 8 x^{7} + 46 x^{6} - 11 x^{5} - 52 x^{4} + 7 x^{3} + 18 x^{2} - 3 x - 1$ | $5^{5}\cdot 11^{8}$ | $C_{10}$ (as 10T1) | trivial |
10.10.762939453125.1 | $x^{10} - 10 x^{8} + 35 x^{6} - x^{5} - 50 x^{4} + 5 x^{3} + 25 x^{2} - 5 x - 1$ | $5^{17}$ | $C_{10}$ (as 10T1) | trivial |
10.10.769611580061.1 | $x^{10} - 4 x^{9} - 3 x^{8} + 22 x^{7} + 3 x^{6} - 41 x^{5} - 8 x^{4} + 25 x^{3} + 8 x^{2} - 3 x - 1$ | $769611580061$ | $S_{10}$ (as 10T45) | trivial |
10.10.782566688557.1 | $x^{10} - 3 x^{9} - 6 x^{8} + 19 x^{7} + 15 x^{6} - 40 x^{5} - 20 x^{4} + 29 x^{3} + 11 x^{2} - 4 x - 1$ | $17^{2}\cdot 157\cdot 4153^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.10.805213821197.1 | $x^{10} - 2 x^{9} - 8 x^{8} + 13 x^{7} + 23 x^{6} - 28 x^{5} - 28 x^{4} + 22 x^{3} + 13 x^{2} - 4 x - 1$ | $61^{2}\cdot 397^{2}\cdot 1373$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.10.820298081773.1 | $x^{10} - 2 x^{9} - 8 x^{8} + 12 x^{7} + 22 x^{6} - 22 x^{5} - 24 x^{4} + 13 x^{3} + 10 x^{2} - 2 x - 1$ | $1523\cdot 538606751$ | $S_{10}$ (as 10T45) | trivial |
10.10.822624971833.1 | $x^{10} - 10 x^{8} - 3 x^{7} + 29 x^{6} + 10 x^{5} - 32 x^{4} - 10 x^{3} + 12 x^{2} + 3 x - 1$ | $7\cdot 79\cdot 38569^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.10.823301450757.1 | $x^{10} - 4 x^{9} - 3 x^{8} + 25 x^{7} - 8 x^{6} - 46 x^{5} + 27 x^{4} + 27 x^{3} - 18 x^{2} - x + 1$ | $3^{2}\cdot 19^{2}\cdot 37\cdot 2617^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.10.838055754181.1 | $x^{10} - 2 x^{9} - 8 x^{8} + 17 x^{7} + 17 x^{6} - 43 x^{5} - 3 x^{4} + 31 x^{3} - 9 x^{2} - 3 x + 1$ | $61^{2}\cdot 397^{2}\cdot 1429$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.10.841363028173.1 | $x^{10} - 10 x^{8} - 2 x^{7} + 33 x^{6} + 11 x^{5} - 40 x^{4} - 16 x^{3} + 12 x^{2} + 3 x - 1$ | $841363028173$ | $S_{10}$ (as 10T45) | trivial |
10.10.872351958893.1 | $x^{10} - 3 x^{9} - 7 x^{8} + 22 x^{7} + 19 x^{6} - 56 x^{5} - 25 x^{4} + 56 x^{3} + 13 x^{2} - 18 x - 1$ | $48413\cdot 18018961$ | $S_{10}$ (as 10T45) | trivial |
10.10.901040998181.1 | $x^{10} - 2 x^{9} - 8 x^{8} + 15 x^{7} + 22 x^{6} - 37 x^{5} - 24 x^{4} + 35 x^{3} + 7 x^{2} - 11 x + 1$ | $31\cdot 1877\cdot 1933\cdot 8011$ | $S_{10}$ (as 10T45) | trivial |
10.10.911025153125.1 | $x^{10} - 4 x^{9} - 3 x^{8} + 22 x^{7} + 2 x^{6} - 41 x^{5} - 3 x^{4} + 27 x^{3} + 5 x^{2} - 4 x - 1$ | $5^{5}\cdot 419\cdot 695771$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.10.913378895261.1 | $x^{10} - 4 x^{9} - 3 x^{8} + 27 x^{7} - 15 x^{6} - 40 x^{5} + 30 x^{4} + 20 x^{3} - 13 x^{2} - 3 x + 1$ | $7\cdot 31^{2}\cdot 135778043$ | $S_{10}$ (as 10T45) | trivial |
10.10.925108450304.1 | $x^{10} - 2 x^{9} - 8 x^{8} + 12 x^{7} + 24 x^{6} - 22 x^{5} - 29 x^{4} + 14 x^{3} + 12 x^{2} - 2 x - 1$ | $2^{10}\cdot 9649\cdot 93629$ | $S_{10}$ (as 10T45) | trivial |
10.10.928565973197.1 | $x^{10} - 2 x^{9} - 8 x^{8} + 13 x^{7} + 24 x^{6} - 26 x^{5} - 32 x^{4} + 16 x^{3} + 16 x^{2} - 1$ | $2729\cdot 5659\cdot 60127$ | $S_{10}$ (as 10T45) | trivial |
10.10.943765631693.1 | $x^{10} - 2 x^{9} - 8 x^{8} + 12 x^{7} + 23 x^{6} - 20 x^{5} - 25 x^{4} + 10 x^{3} + 10 x^{2} - x - 1$ | $943765631693$ | $S_{10}$ (as 10T45) | trivial |
10.10.944409985381.1 | $x^{10} - x^{9} - 11 x^{8} + 9 x^{7} + 38 x^{6} - 27 x^{5} - 51 x^{4} + 34 x^{3} + 22 x^{2} - 16 x + 1$ | $709\cdot 36497^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.10.950202516997.1 | $x^{10} - 10 x^{8} - x^{7} + 33 x^{6} + 3 x^{5} - 44 x^{4} - x^{3} + 21 x^{2} - 2 x - 1$ | $607\cdot 37649\cdot 41579$ | $S_{10}$ (as 10T45) | trivial |
10.10.958265834381.1 | $x^{10} - 4 x^{9} - 2 x^{8} + 22 x^{7} - 8 x^{6} - 39 x^{5} + 22 x^{4} + 23 x^{3} - 13 x^{2} - 2 x + 1$ | $17\cdot 56368578493$ | $S_{10}$ (as 10T45) | trivial |
10.10.967077633761.1 | $x^{10} - 5 x^{9} + 2 x^{8} + 22 x^{7} - 22 x^{6} - 32 x^{5} + 35 x^{4} + 19 x^{3} - 16 x^{2} - 4 x + 1$ | $17\cdot 61^{2}\cdot 97\cdot 397^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.10.968074628125.1 | $x^{10} - x^{9} - 10 x^{8} + 8 x^{7} + 34 x^{6} - 23 x^{5} - 46 x^{4} + 28 x^{3} + 20 x^{2} - 13 x + 1$ | $5^{5}\cdot 11\cdot 28162171$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.10.983282290021.1 | $x^{10} - 4 x^{9} - 3 x^{8} + 23 x^{7} - 2 x^{6} - 42 x^{5} + 8 x^{4} + 28 x^{3} - 5 x^{2} - 6 x + 1$ | $661\cdot 38569^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.10.983479472873.1 | $x^{10} - 2 x^{9} - 8 x^{8} + 15 x^{7} + 17 x^{6} - 28 x^{5} - 15 x^{4} + 17 x^{3} + 6 x^{2} - 3 x - 1$ | $1567\cdot 627619319$ | $S_{10}$ (as 10T45) | trivial |
10.10.993530403125.1 | $x^{10} - x^{9} - 10 x^{8} + 7 x^{7} + 34 x^{6} - 18 x^{5} - 46 x^{4} + 21 x^{3} + 20 x^{2} - 10 x + 1$ | $5^{5}\cdot 13^{2}\cdot 1881241$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.10.995293579409.1 | $x^{10} - 2 x^{9} - 8 x^{8} + 16 x^{7} + 17 x^{6} - 35 x^{5} - 11 x^{4} + 26 x^{3} - 6 x + 1$ | $17783\cdot 55968823$ | $S_{10}$ (as 10T45) | trivial |
10.10.1056719528125.1 | $x^{10} - x^{9} - 11 x^{8} + 13 x^{7} + 35 x^{6} - 43 x^{5} - 36 x^{4} + 41 x^{3} + 10 x^{2} - 7 x - 1$ | $5^{5}\cdot 89\cdot 1061\cdot 3581$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.10.1071443843101.1 | $x^{10} - 2 x^{9} - 8 x^{8} + 17 x^{7} + 17 x^{6} - 40 x^{5} - 12 x^{4} + 32 x^{3} + 3 x^{2} - 6 x - 1$ | $41\cdot 283\cdot 92341967$ | $S_{10}$ (as 10T45) | trivial |
10.10.1086015136753.1 | $x^{10} - 2 x^{9} - 8 x^{8} + 15 x^{7} + 19 x^{6} - 32 x^{5} - 18 x^{4} + 22 x^{3} + 8 x^{2} - 3 x - 1$ | $43^{2}\cdot 4583\cdot 128159$ | $S_{10}$ (as 10T45) | trivial |
10.10.1092599165069.1 | $x^{10} - x^{9} - 9 x^{8} + 8 x^{7} + 25 x^{6} - 18 x^{5} - 26 x^{4} + 13 x^{3} + 9 x^{2} - 2 x - 1$ | $1092599165069$ | $S_{10}$ (as 10T45) | trivial |
10.10.1102817328125.1 | $x^{10} - 2 x^{9} - 10 x^{8} + 23 x^{7} + 15 x^{6} - 47 x^{5} - 5 x^{4} + 32 x^{3} - 2 x^{2} - 7 x + 1$ | $5^{6}\cdot 1039\cdot 67931$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.10.1125421834861.1 | $x^{10} - 3 x^{9} - 6 x^{8} + 23 x^{7} + x^{6} - 40 x^{5} + 11 x^{4} + 22 x^{3} - 8 x^{2} - 3 x + 1$ | $1125421834861$ | $S_{10}$ (as 10T45) | trivial |
10.10.1129529628125.1 | $x^{10} - x^{9} - 10 x^{8} + 6 x^{7} + 36 x^{6} - 7 x^{5} - 53 x^{4} - 8 x^{3} + 25 x^{2} + 11 x + 1$ | $5^{5}\cdot 41\cdot 521\cdot 16921$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.10.1131659253125.1 | $x^{10} - 4 x^{9} - 4 x^{8} + 28 x^{7} - 6 x^{6} - 48 x^{5} + 10 x^{4} + 31 x^{3} - 6 x - 1$ | $5^{5}\cdot 5471\cdot 66191$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.10.1135185393317.1 | $x^{10} - 10 x^{8} - 2 x^{7} + 32 x^{6} + 12 x^{5} - 35 x^{4} - 17 x^{3} + 10 x^{2} + 7 x + 1$ | $1135185393317$ | $S_{10}$ (as 10T45) | trivial |
10.10.1136222450677.1 | $x^{10} - 12 x^{8} - 6 x^{7} + 39 x^{6} + 26 x^{5} - 37 x^{4} - 22 x^{3} + 10 x^{2} + 3 x - 1$ | $853\cdot 36497^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.10.1140241465757.1 | $x^{10} - 2 x^{9} - 8 x^{8} + 15 x^{7} + 22 x^{6} - 36 x^{5} - 25 x^{4} + 31 x^{3} + 10 x^{2} - 8 x - 1$ | $29\cdot 4217\cdot 9323849$ | $S_{10}$ (as 10T45) | trivial |
10.10.1142405128125.1 | $x^{10} - 3 x^{9} - 6 x^{8} + 23 x^{7} + 4 x^{6} - 49 x^{5} + 15 x^{4} + 27 x^{3} - 9 x^{2} - 3 x + 1$ | $3^{2}\cdot 5^{5}\cdot 151\cdot 268999$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.10.1148718338533.1 | $x^{10} - x^{9} - 11 x^{8} + 9 x^{7} + 35 x^{6} - 18 x^{5} - 44 x^{4} + 8 x^{3} + 19 x^{2} + 2 x - 1$ | $1148718338533$ | $S_{10}$ (as 10T45) | trivial |
10.10.1172459165509.1 | $x^{10} - 12 x^{8} - 6 x^{7} + 40 x^{6} + 29 x^{5} - 42 x^{4} - 38 x^{3} + 3 x^{2} + 7 x + 1$ | $4723\cdot 7639\cdot 32497$ | $S_{10}$ (as 10T45) | trivial |
10.10.1175858493445.1 | $x^{10} - 5 x^{9} + 28 x^{7} - 17 x^{6} - 55 x^{5} + 33 x^{4} + 43 x^{3} - 13 x^{2} - 9 x - 1$ | $5\cdot 61^{2}\cdot 397^{2}\cdot 401$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.10.1185241902869.1 | $x^{10} - 3 x^{9} - 8 x^{8} + 25 x^{7} + 20 x^{6} - 60 x^{5} - 30 x^{4} + 47 x^{3} + 26 x^{2} - 1$ | $43\cdot 47\cdot 61^{2}\cdot 397^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.10.1230634335821.1 | $x^{10} - x^{9} - 9 x^{8} + 7 x^{7} + 25 x^{6} - 13 x^{5} - 25 x^{4} + 7 x^{3} + 9 x^{2} - x - 1$ | $11^{8}\cdot 5741$ | $C_2 \times (C_2^4 : C_5)$ (as 10T14) | trivial |
10.10.1236714909341.1 | $x^{10} - 11 x^{8} - 3 x^{7} + 35 x^{6} + 11 x^{5} - 41 x^{4} - 7 x^{3} + 18 x^{2} - x - 1$ | $877\cdot 1410165233$ | $S_{10}$ (as 10T45) | trivial |