Number field search results

Results (1-50 of 280367 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
10.10.443952558373.1	$x^{10} - 11 x^{8} - 3 x^{7} + 37 x^{6} + 14 x^{5} - 48 x^{4} - 22 x^{3} + 20 x^{2} + 12 x + 1$	$10$	[10,0]	$61^{2}\cdot 397^{2}\cdot 757$	$3$	$14.6128072678$	$4281.619903728027$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$9$	$207.94659148$
10.10.513087549389.1	$x^{10} - 4 x^{9} - 2 x^{8} + 23 x^{7} - 11 x^{6} - 40 x^{5} + 30 x^{4} + 21 x^{3} - 18 x^{2} + 1$	$10$	[10,0]	$460181\cdot 1114969$	$2$	$14.8258344935$	$716301.2979110117$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$9$	$224.18969507$
10.10.572981288913.1	$x^{10} - x^{9} - 10 x^{8} + 10 x^{7} + 34 x^{6} - 34 x^{5} - 43 x^{4} + 43 x^{3} + 12 x^{2} - 12 x + 1$	$10$	[10,0]	$3^{5}\cdot 11^{9}$	$2$	$14.9904283864$	$14.990428386414978$		✓	✓	$C_{10}$ (as 10T1)	trivial	$2$	$9$	$245.278866244$
10.10.617567936161.1	$x^{10} - x^{9} - 12 x^{8} + 5 x^{7} + 39 x^{6} - 11 x^{5} - 47 x^{4} + 15 x^{3} + 18 x^{2} - 9 x + 1$	$10$	[10,0]	$11^{8}\cdot 43\cdot 67$	$3$	$15.103182629$	$365.49865006155005$			✓	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	trivial	$2$	$9$	$250.927290416$
10.10.645863308453.1	$x^{10} - 2 x^{9} - 9 x^{8} + 15 x^{7} + 29 x^{6} - 31 x^{5} - 43 x^{4} + 14 x^{3} + 23 x^{2} + 3 x - 1$	$10$	[10,0]	$11^{8}\cdot 23\cdot 131$	$3$	$15.1709948629$	$373.7779811305969$			✓	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	trivial	$2$	$9$	$258.616788218$
10.10.653113904957.1	$x^{10} - x^{9} - 9 x^{8} + 9 x^{7} + 25 x^{6} - 23 x^{5} - 24 x^{4} + 17 x^{3} + 8 x^{2} - 3 x - 1$	$10$	[10,0]	$37\cdot 47\cdot 239\cdot 1571417$	$4$	$15.1879407071$	$808154.6293606194$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$9$	$264.663215216$
10.10.669871503125.1	$x^{10} - x^{9} - 13 x^{8} + 8 x^{7} + 46 x^{6} - 11 x^{5} - 52 x^{4} + 7 x^{3} + 18 x^{2} - 3 x - 1$	$10$	[10,0]	$5^{5}\cdot 11^{8}$	$2$	$15.2264671648$	$15.226467164777734$		✓	?	$C_{10}$ (as 10T1)	trivial	$2$	$9$	$274.696482776$
10.10.762939453125.1	$x^{10} - 10 x^{8} + 35 x^{6} - x^{5} - 50 x^{4} + 5 x^{3} + 25 x^{2} - 5 x - 1$	$10$	[10,0]	$5^{17}$	$1$	$15.425846568$	$15.42584656800024$		✓	✓	$C_{10}$ (as 10T1)	trivial	$2$	$9$	$315.247729768$
10.10.769611580061.1	$x^{10} - 4 x^{9} - 3 x^{8} + 22 x^{7} + 3 x^{6} - 41 x^{5} - 8 x^{4} + 25 x^{3} + 8 x^{2} - 3 x - 1$	$10$	[10,0]	$769611580061$	$1$	$15.439284121$	$877275.0880202857$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$9$	$284.870071711$
10.10.782566688557.1	$x^{10} - 3 x^{9} - 6 x^{8} + 19 x^{7} + 15 x^{6} - 40 x^{5} - 20 x^{4} + 29 x^{3} + 11 x^{2} - 4 x - 1$	$10$	[10,0]	$17^{2}\cdot 157\cdot 4153^{2}$	$3$	$15.465078747$	$3329.31779798805$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$9$	$301.03717021$
10.10.805213821197.1	$x^{10} - 2 x^{9} - 8 x^{8} + 13 x^{7} + 23 x^{6} - 28 x^{5} - 28 x^{4} + 22 x^{3} + 13 x^{2} - 4 x - 1$	$10$	[10,0]	$61^{2}\cdot 397^{2}\cdot 1373$	$3$	$15.5092616231$	$5766.276181384308$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$9$	$291.274557272$
10.10.820298081773.1	$x^{10} - 2 x^{9} - 8 x^{8} + 12 x^{7} + 22 x^{6} - 22 x^{5} - 24 x^{4} + 13 x^{3} + 10 x^{2} - 2 x - 1$	$10$	[10,0]	$1523\cdot 538606751$	$2$	$15.5380734331$	$905703.0869843605$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$9$	$305.86034405$
10.10.822624971833.1	$x^{10} - 10 x^{8} - 3 x^{7} + 29 x^{6} + 10 x^{5} - 32 x^{4} - 10 x^{3} + 12 x^{2} + 3 x - 1$	$10$	[10,0]	$7\cdot 79\cdot 38569^{2}$	$3$	$15.5424754085$	$4618.295897839375$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$9$	$313.286716031$
10.10.823301450757.1	$x^{10} - 4 x^{9} - 3 x^{8} + 25 x^{7} - 8 x^{6} - 46 x^{5} + 27 x^{4} + 27 x^{3} - 18 x^{2} - x + 1$	$10$	[10,0]	$3^{2}\cdot 19^{2}\cdot 37\cdot 2617^{2}$	$4$	$15.5437530585$	$2349.309047358393$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$9$	$307.940302196$
10.10.838055754181.1	$x^{10} - 2 x^{9} - 8 x^{8} + 17 x^{7} + 17 x^{6} - 43 x^{5} - 3 x^{4} + 31 x^{3} - 9 x^{2} - 3 x + 1$	$10$	[10,0]	$61^{2}\cdot 397^{2}\cdot 1429$	$3$	$15.5713867403$	$5882.694365679727$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$9$	$295.76092578$
10.10.841363028173.1	$x^{10} - 10 x^{8} - 2 x^{7} + 33 x^{6} + 11 x^{5} - 40 x^{4} - 16 x^{3} + 12 x^{2} + 3 x - 1$	$10$	[10,0]	$841363028173$	$1$	$15.5775208924$	$917258.4304180583$			?	$S_{10}$ (as 10T45)	trivial	$2$	$9$	$313.1247297756671$
10.10.872351958893.1	$x^{10} - 3 x^{9} - 7 x^{8} + 22 x^{7} + 19 x^{6} - 56 x^{5} - 25 x^{4} + 56 x^{3} + 13 x^{2} - 18 x - 1$	$10$	[10,0]	$48413\cdot 18018961$	$2$	$15.6339663932$	$933997.8366639828$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$9$	$306.6984491932094$
10.10.901040998181.1	$x^{10} - 2 x^{9} - 8 x^{8} + 15 x^{7} + 22 x^{6} - 37 x^{5} - 24 x^{4} + 35 x^{3} + 7 x^{2} - 11 x + 1$	$10$	[10,0]	$31\cdot 1877\cdot 1933\cdot 8011$	$4$	$15.6846363947$	$949231.7937053099$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$9$	$312.8479439581071$
10.10.911025153125.1	$x^{10} - 4 x^{9} - 3 x^{8} + 22 x^{7} + 2 x^{6} - 41 x^{5} - 3 x^{4} + 27 x^{3} + 5 x^{2} - 4 x - 1$	$10$	[10,0]	$5^{5}\cdot 419\cdot 695771$	$3$	$15.7019299952$	$38179.05505640495$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$2$	$9$	$314.60686502$
10.10.913378895261.1	$x^{10} - 4 x^{9} - 3 x^{8} + 27 x^{7} - 15 x^{6} - 40 x^{5} + 30 x^{4} + 20 x^{3} - 13 x^{2} - 3 x + 1$	$10$	[10,0]	$7\cdot 31^{2}\cdot 135778043$	$3$	$15.7059820672$	$171650.32866557525$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$9$	$333.856456137$
10.10.925108450304.1	$x^{10} - 2 x^{9} - 8 x^{8} + 12 x^{7} + 24 x^{6} - 22 x^{5} - 29 x^{4} + 14 x^{3} + 12 x^{2} - 2 x - 1$	$10$	[10,0]	$2^{10}\cdot 9649\cdot 93629$	$3$	$15.726035974$	$110249.74345077526$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$9$	$324.421089039$
10.10.928565973197.1	$x^{10} - 2 x^{9} - 8 x^{8} + 13 x^{7} + 24 x^{6} - 26 x^{5} - 32 x^{4} + 16 x^{3} + 16 x^{2} - 1$	$10$	[10,0]	$2729\cdot 5659\cdot 60127$	$3$	$15.7319035994$	$963621.2810004769$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$9$	$321.811607365$
10.10.943765631693.1	$x^{10} - 2 x^{9} - 8 x^{8} + 12 x^{7} + 23 x^{6} - 20 x^{5} - 25 x^{4} + 10 x^{3} + 10 x^{2} - x - 1$	$10$	[10,0]	$943765631693$	$1$	$15.7574673453$	$971476.0067510675$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$9$	$320.4622197789755$
10.10.944409985381.1	$x^{10} - x^{9} - 11 x^{8} + 9 x^{7} + 38 x^{6} - 27 x^{5} - 51 x^{4} + 34 x^{3} + 22 x^{2} - 16 x + 1$	$10$	[10,0]	$709\cdot 36497^{2}$	$2$	$15.7585428522$	$5086.882444090879$			?	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$9$	$332.184947708$
10.10.950202516997.1	$x^{10} - 10 x^{8} - x^{7} + 33 x^{6} + 3 x^{5} - 44 x^{4} - x^{3} + 21 x^{2} - 2 x - 1$	$10$	[10,0]	$607\cdot 37649\cdot 41579$	$3$	$15.7681817684$	$974783.3179722559$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$9$	$322.962603475$
10.10.958265834381.1	$x^{10} - 4 x^{9} - 2 x^{8} + 22 x^{7} - 8 x^{6} - 39 x^{5} + 22 x^{4} + 23 x^{3} - 13 x^{2} - 2 x + 1$	$10$	[10,0]	$17\cdot 56368578493$	$2$	$15.7815116562$	$978910.534411087$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$9$	$326.0121722313577$
10.10.967077633761.1	$x^{10} - 5 x^{9} + 2 x^{8} + 22 x^{7} - 22 x^{6} - 32 x^{5} + 35 x^{4} + 19 x^{3} - 16 x^{2} - 4 x + 1$	$10$	[10,0]	$17\cdot 61^{2}\cdot 97\cdot 397^{2}$	$4$	$15.7959639505$	$6319.322194666133$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$9$	$325.386330707$
10.10.968074628125.1	$x^{10} - x^{9} - 10 x^{8} + 8 x^{7} + 34 x^{6} - 23 x^{5} - 46 x^{4} + 28 x^{3} + 20 x^{2} - 13 x + 1$	$10$	[10,0]	$5^{5}\cdot 11\cdot 28162171$	$3$	$15.797591657$	$39356.313407126945$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$2$	$9$	$332.660098136$
10.10.983282290021.1	$x^{10} - 4 x^{9} - 3 x^{8} + 23 x^{7} - 2 x^{6} - 42 x^{5} + 8 x^{4} + 28 x^{3} - 5 x^{2} - 6 x + 1$	$10$	[10,0]	$661\cdot 38569^{2}$	$2$	$15.8222346765$	$5049.169139571381$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$9$	$342.690572371$
10.10.983479472873.1	$x^{10} - 2 x^{9} - 8 x^{8} + 15 x^{7} + 17 x^{6} - 28 x^{5} - 15 x^{4} + 17 x^{3} + 6 x^{2} - 3 x - 1$	$10$	[10,0]	$1567\cdot 627619319$	$2$	$15.8225519396$	$991705.3357086469$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$9$	$334.297503967$
10.10.993530403125.1	$x^{10} - x^{9} - 10 x^{8} + 7 x^{7} + 34 x^{6} - 18 x^{5} - 46 x^{4} + 21 x^{3} + 20 x^{2} - 10 x + 1$	$10$	[10,0]	$5^{5}\cdot 13^{2}\cdot 1881241$	$3$	$15.8386483301$	$11058.058826032713$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$2$	$9$	$336.806371297$
10.10.995293579409.1	$x^{10} - 2 x^{9} - 8 x^{8} + 16 x^{7} + 17 x^{6} - 35 x^{5} - 11 x^{4} + 26 x^{3} - 6 x + 1$	$10$	[10,0]	$17783\cdot 55968823$	$2$	$15.8414569057$	$997644.0143703565$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$9$	$339.076281671$
10.10.1056719528125.1	$x^{10} - x^{9} - 11 x^{8} + 13 x^{7} + 35 x^{6} - 43 x^{5} - 36 x^{4} + 41 x^{3} + 10 x^{2} - 7 x - 1$	$10$	[10,0]	$5^{5}\cdot 89\cdot 1061\cdot 3581$	$4$	$15.9366110491$	$41118.745664234455$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$2$	$9$	$380.770505294$
10.10.1071443843101.1	$x^{10} - 2 x^{9} - 8 x^{8} + 17 x^{7} + 17 x^{6} - 40 x^{5} - 12 x^{4} + 32 x^{3} + 3 x^{2} - 6 x - 1$	$10$	[10,0]	$41\cdot 283\cdot 92341967$	$3$	$15.9586790784$	$1035105.7159058682$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$9$	$343.451747061$
10.10.1086015136753.1	$x^{10} - 2 x^{9} - 8 x^{8} + 15 x^{7} + 19 x^{6} - 32 x^{5} - 18 x^{4} + 22 x^{3} + 8 x^{2} - 3 x - 1$	$10$	[10,0]	$43^{2}\cdot 4583\cdot 128159$	$3$	$15.9802506835$	$297459.91809924005$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$9$	$355.053110684$
10.10.1092599165069.1	$x^{10} - x^{9} - 9 x^{8} + 8 x^{7} + 25 x^{6} - 18 x^{5} - 26 x^{4} + 13 x^{3} + 9 x^{2} - 2 x - 1$	$10$	[10,0]	$1092599165069$	$1$	$15.9899124714$	$1045274.6840276005$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$9$	$388.8541204130411$
10.10.1102817328125.1	$x^{10} - 2 x^{9} - 10 x^{8} + 23 x^{7} + 15 x^{6} - 47 x^{5} - 5 x^{4} + 32 x^{3} - 2 x^{2} - 7 x + 1$	$10$	[10,0]	$5^{6}\cdot 1039\cdot 67931$	$3$	$16.0048039313$	$28091.134615474344$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$2$	$9$	$391.26161615$
10.10.1125421834861.1	$x^{10} - 3 x^{9} - 6 x^{8} + 23 x^{7} + x^{6} - 40 x^{5} + 11 x^{4} + 22 x^{3} - 8 x^{2} - 3 x + 1$	$10$	[10,0]	$1125421834861$	$1$	$16.0373103516$	$1060859.0080029485$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$9$	$399.398906814$
10.10.1129529628125.1	$x^{10} - x^{9} - 10 x^{8} + 6 x^{7} + 36 x^{6} - 7 x^{5} - 53 x^{4} - 8 x^{3} + 25 x^{2} + 11 x + 1$	$10$	[10,0]	$5^{5}\cdot 41\cdot 521\cdot 16921$	$4$	$16.0431543825$	$42511.73255702477$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$2$	$9$	$364.774343099$
10.10.1131659253125.1	$x^{10} - 4 x^{9} - 4 x^{8} + 28 x^{7} - 6 x^{6} - 48 x^{5} + 10 x^{4} + 31 x^{3} - 6 x - 1$	$10$	[10,0]	$5^{5}\cdot 5471\cdot 66191$	$3$	$16.0461766096$	$42551.789680341295$			?	$S_5^2 \wr C_2$ (as 10T43)	trivial	$2$	$9$	$364.21895888$
10.10.1135185393317.1	$x^{10} - 10 x^{8} - 2 x^{7} + 32 x^{6} + 12 x^{5} - 35 x^{4} - 17 x^{3} + 10 x^{2} + 7 x + 1$	$10$	[10,0]	$1135185393317$	$1$	$16.0511694454$	$1065450.7934752314$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$9$	$361.67462315589364$
10.10.1136222450677.1	$x^{10} - 12 x^{8} - 6 x^{7} + 39 x^{6} + 26 x^{5} - 37 x^{4} - 22 x^{3} + 10 x^{2} + 3 x - 1$	$10$	[10,0]	$853\cdot 36497^{2}$	$2$	$16.0526352099$	$5579.6004337228305$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$9$	$366.678419825$
10.10.1140241465757.1	$x^{10} - 2 x^{9} - 8 x^{8} + 15 x^{7} + 22 x^{6} - 36 x^{5} - 25 x^{4} + 31 x^{3} + 10 x^{2} - 8 x - 1$	$10$	[10,0]	$29\cdot 4217\cdot 9323849$	$3$	$16.0583042865$	$1067820.8959170072$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$9$	$379.179313365$
10.10.1142405128125.1	$x^{10} - 3 x^{9} - 6 x^{8} + 23 x^{7} + 4 x^{6} - 49 x^{5} + 15 x^{4} + 27 x^{3} - 9 x^{2} - 3 x + 1$	$10$	[10,0]	$3^{2}\cdot 5^{5}\cdot 151\cdot 268999$	$4$	$16.0613488272$	$24683.653193966245$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$2$	$9$	$379.778230292$
10.10.1148718338533.1	$x^{10} - x^{9} - 11 x^{8} + 9 x^{7} + 35 x^{6} - 18 x^{5} - 44 x^{4} + 8 x^{3} + 19 x^{2} + 2 x - 1$	$10$	[10,0]	$1148718338533$	$1$	$16.0702027261$	$1071782.7851449193$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$9$	$382.589857342$
10.10.1172459165509.1	$x^{10} - 12 x^{8} - 6 x^{7} + 40 x^{6} + 29 x^{5} - 42 x^{4} - 38 x^{3} + 3 x^{2} + 7 x + 1$	$10$	[10,0]	$4723\cdot 7639\cdot 32497$	$3$	$16.1031104822$	$1082801.5356052096$			?	$S_{10}$ (as 10T45)	trivial	$2$	$9$	$373.861679191$
10.10.1175858493445.1	$x^{10} - 5 x^{9} + 28 x^{7} - 17 x^{6} - 55 x^{5} + 33 x^{4} + 43 x^{3} - 13 x^{2} - 9 x - 1$	$10$	[10,0]	$5\cdot 61^{2}\cdot 397^{2}\cdot 401$	$4$	$16.1077732003$	$6968.147888786518$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$9$	$405.753874634$
10.10.1185241902869.1	$x^{10} - 3 x^{9} - 8 x^{8} + 25 x^{7} + 20 x^{6} - 60 x^{5} - 30 x^{4} + 47 x^{3} + 26 x^{2} - 1$	$10$	[10,0]	$43\cdot 47\cdot 61^{2}\cdot 397^{2}$	$4$	$16.1205813563$	$6995.895725352116$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$9$	$366.770868267$
10.10.1230634335821.1	$x^{10} - x^{9} - 9 x^{8} + 7 x^{7} + 25 x^{6} - 13 x^{5} - 25 x^{4} + 7 x^{3} + 9 x^{2} - x - 1$	$10$	[10,0]	$11^{8}\cdot 5741$	$2$	$16.1812811123$	$515.9503620736074$			✓	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	trivial	$2$	$9$	$373.411226053$
10.10.1236714909341.1	$x^{10} - 11 x^{8} - 3 x^{7} + 35 x^{6} + 11 x^{5} - 41 x^{4} - 7 x^{3} + 18 x^{2} - x - 1$	$10$	[10,0]	$877\cdot 1410165233$	$2$	$16.189258574$	$1112076.84507007$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$9$	$391.1283759495338$