Number field search results

Results (1-50 of 1020 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
10.2.11103890625.1	$x^{10} - 3 x^{9} + 5 x^{8} - 9 x^{7} + 11 x^{6} - 14 x^{5} + 18 x^{4} - 16 x^{3} + 12 x^{2} - 5 x + 1$	$10$	[2,4]	$3^{2}\cdot 5^{6}\cdot 281^{2}$	$3$	$10.1052605932$	$97.08257580617448$			?	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$10.3877480129$
10.2.64262250000.1	$x^{10} - 2 x^{9} + 2 x^{8} - 5 x^{7} + 11 x^{6} - 14 x^{5} + 12 x^{4} - 18 x^{3} + 24 x^{2} - 16 x + 4$	$10$	[2,4]	$2^{4}\cdot 3^{2}\cdot 5^{6}\cdot 13^{4}$	$4$	$12.0446890543$	$50.828078961274464$			?	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$29.1533130368$
10.6.85629390625.1	$x^{10} - 2 x^{8} - 4 x^{7} + x^{6} + 2 x^{5} - 6 x^{4} + 7 x^{3} + 4 x^{2} - 5 x + 1$	$10$	[6,2]	$5^{6}\cdot 2341^{2}$	$2$	$12.3954496426$	$589.5153425318138$			?	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$7$	$50.4878389565$
10.2.88729515625.1	$x^{10} - 2 x^{9} - 2 x^{8} + 11 x^{7} - 6 x^{6} - 14 x^{5} + 23 x^{4} - 2 x^{3} - 15 x^{2} + 12 x - 1$	$10$	[2,4]	$5^{6}\cdot 2383^{2}$	$2$	$12.4396113254$	$163.22607007432973$			✓	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$38.2266964409$
10.2.92112250000.1	$x^{10} - 4 x^{9} + 3 x^{8} + 5 x^{7} - 4 x^{6} - 10 x^{5} + 12 x^{4} + 2 x^{3} - 4 x^{2} - 5 x + 5$	$10$	[2,4]	$2^{4}\cdot 5^{6}\cdot 607^{2}$	$3$	$12.486241747$	$130.77011707976862$			?	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$40.2776580972$
10.2.106194515625.1	$x^{10} - 3 x^{9} + 4 x^{8} - 5 x^{7} + 2 x^{6} - x^{5} + 4 x^{4} + 7 x^{3} + 6 x^{2} + 4 x + 1$	$10$	[2,4]	$3^{2}\cdot 5^{6}\cdot 11^{2}\cdot 79^{2}$	$4$	$12.665146241$	$254.6029705124389$			?	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$42.272771079$
10.2.111556000000.1	$x^{10} - x^{9} - 4 x^{8} + 3 x^{7} - x^{6} + 2 x^{5} + 10 x^{4} - 12 x^{3} + 11 x^{2} - 5 x + 1$	$10$	[2,4]	$2^{8}\cdot 5^{6}\cdot 167^{2}$	$3$	$12.7276813376$	$86.42029301529415$			?	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$39.9513656639$
10.2.113498914816.1	$x^{10} - 4 x^{9} + 4 x^{8} + 2 x^{7} - 5 x^{6} + 2 x^{5} + 3 x^{4} - 4 x^{3} - 2 x^{2} + 4 x - 2$	$10$	[2,4]	$2^{20}\cdot 7^{2}\cdot 47^{2}$	$3$	$12.7496766599$	$231.79999025711257$			✓	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$60.3380279306$
10.2.142223265625.1	$x^{10} - x^{9} + x^{8} - 4 x^{7} + 2 x^{6} - 7 x^{5} + 2 x^{4} - 6 x^{3} + 3 x^{2} - 3 x + 1$	$10$	[2,4]	$5^{6}\cdot 7^{2}\cdot 431^{2}$	$3$	$13.040584711$	$183.6602445838084$			✓	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$38.29422592380403$
10.2.369056250000.1	$x^{10} - 4 x^{9} + 9 x^{8} - 15 x^{7} + 20 x^{6} - 30 x^{5} + 40 x^{4} - 40 x^{3} + 30 x^{2} - 15 x + 5$	$10$	[2,4]	$2^{4}\cdot 3^{10}\cdot 5^{8}$	$3$	$14.3452874969$	$62.09185911106938$			?	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$89.6293713522$
10.2.419904000000.1	$x^{10} - x^{9} + 5 x^{7} + 3 x^{6} + 12 x^{5} + 14 x^{4} + 8 x^{3} + 9 x^{2} + 3 x + 1$	$10$	[2,4]	$2^{12}\cdot 3^{8}\cdot 5^{6}$	$3$	$14.531652409$	$68.8187320105403$			?	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$93.8195092416$
10.2.477757440000.1	$x^{10} - 4 x^{9} + 10 x^{8} - 14 x^{7} + 14 x^{6} - 6 x^{5} + x^{4} + 2 x^{3} + 7 x^{2} - 2 x - 1$	$10$	[2,4]	$2^{20}\cdot 3^{6}\cdot 5^{4}$	$3$	$14.7204384564$	$69.18085093139564$			?	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$139.933108442$
10.2.490000000000.1	$x^{10} + 5 x^{8} + 5 x^{6} - 2 x^{5} + 25 x^{4} + 10 x^{3} + 25 x^{2} + 10 x + 1$	$10$	[2,4]	$2^{10}\cdot 5^{10}\cdot 7^{2}$	$3$	$14.7577316159$	$75.7213006392564$				$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$125.722279847$
10.2.519691042816.1	$x^{10} - 2 x^{9} + 3 x^{8} - 8 x^{5} + 12 x^{4} - 10 x^{2} + 4 x + 2$	$10$	[2,4]	$2^{32}\cdot 11^{2}$	$2$	$14.844805890064675$	$64.48831232840281$			?	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$213.02523314632333$
10.2.576650390625.1	$x^{10} + 5 x^{6} - 18 x^{5} + 25 x^{4} - 25 x^{3} + 15 x^{2} - 5 x + 1$	$10$	[2,4]	$3^{10}\cdot 5^{10}$	$2$	$15.0$	$57.557351363759764$			?	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$106.084902385$
10.6.625878765625.1	$x^{10} - 2 x^{9} - 5 x^{8} + 3 x^{7} + 19 x^{6} + 4 x^{5} - 17 x^{4} - 19 x^{3} - 7 x^{2} + 2 x + 1$	$10$	[6,2]	$5^{6}\cdot 6329^{2}$	$2$	$15.1233854697$	$1144.0655289413864$			?	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$7$	$183.407507693$
10.6.655897515625.1	$x^{10} - x^{9} - 6 x^{8} + 10 x^{7} + 7 x^{6} - 23 x^{5} + 6 x^{4} + 15 x^{3} - 9 x^{2} - 2 x + 1$	$10$	[6,2]	$5^{6}\cdot 11^{2}\cdot 19^{2}\cdot 31^{2}$	$4$	$15.194401516926348$	$655.6507176534141$			✓	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$7$	$171.0150342492628$
10.2.1166400000000.2	$x^{10} - 3 x^{9} + 7 x^{8} - 8 x^{7} - 8 x^{6} + 12 x^{5} - 8 x^{4} + 12 x^{3} + 7 x^{2} + 7 x + 1$	$10$	[2,4]	$2^{12}\cdot 3^{6}\cdot 5^{8}$	$3$	$16.09476912$	$73.76021181154222$				$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$202.946633188$
10.2.1476225000000.1	$x^{10} - x^{9} + x^{7} - 2 x^{6} + 4 x^{4} - 5 x^{3} - 9 x^{2} + 3 x - 1$	$10$	[2,4]	$2^{6}\cdot 3^{10}\cdot 5^{8}$	$3$	$16.4784081496$	$86.66945140649595$			?	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$167.740226014$
10.2.1665712890625.1	$x^{10} - 5 x^{8} - 5 x^{7} + 5 x^{6} + 18 x^{5} + 5 x^{4} - 25 x^{3} - 15 x^{2} + 1$	$10$	[2,4]	$5^{10}\cdot 7^{2}\cdot 59^{2}$	$3$	$16.6786161861$	$241.25070025561354$			?	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$147.4861422968398$
10.2.1822500000000.2	$x^{10} + 5 x^{8} + 10 x^{6} - 12 x^{5} + 15 x^{4} - 30 x^{3} - 9$	$10$	[2,4]	$2^{8}\cdot 3^{6}\cdot 5^{10}$	$3$	$16.8293271817$	$78.26452569923332$			?	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$200.290640655$
10.2.2078764171264.1	$x^{10} - 2 x^{9} - 3 x^{8} + 8 x^{7} + 10 x^{6} - 12 x^{5} - 14 x^{4} - 8 x^{3} + 3 x^{2} + 2 x - 1$	$10$	[2,4]	$2^{34}\cdot 11^{2}$	$2$	$17.052204106167586$	$60.43095387214439$			?	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$478.17642826709766$
10.2.2250000000000.1	$x^{10} - 5 x^{8} - 10 x^{7} - 10 x^{6} + 6 x^{5} + 25 x^{4} + 30 x^{3} + 25 x^{2} + 10 x + 4$	$10$	[2,4]	$2^{10}\cdot 3^{2}\cdot 5^{12}$	$3$	$17.1877192759$	$72.942807263824$				$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$277.393798734$
10.2.2624400000000.2	$x^{10} - 3 x^{9} + 5 x^{8} - 18 x^{7} + 43 x^{6} - 45 x^{5} + 31 x^{4} - 30 x^{3} + 11 x^{2} + 9 x + 1$	$10$	[2,4]	$2^{10}\cdot 3^{8}\cdot 5^{8}$	$3$	$17.4543227746$	$52.49628164006941$				$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$342.732564309$
10.2.2985984000000.1	$x^{10} - 3 x^{9} + x^{8} - 8 x^{7} + 10 x^{6} - 6 x^{5} + 22 x^{4} - 12 x^{3} - 8 x^{2} + 4 x + 4$	$10$	[2,4]	$2^{18}\cdot 3^{6}\cdot 5^{6}$	$3$	$17.6810783088$	$140.0970607251795$				$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$321.797219002$
10.2.2985984000000.2	$x^{10} - 2 x^{9} - 7 x^{6} - 18 x^{5} - 2 x^{4} + 15 x^{2} - 2 x - 4$	$10$	[2,4]	$2^{18}\cdot 3^{6}\cdot 5^{6}$	$3$	$17.6810783088$	$109.74938070275512$				$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$337.413266136$
10.2.3779136000000.2	$x^{10} - x^{9} - 7 x^{8} + 4 x^{7} + 16 x^{6} - 18 x^{5} - 26 x^{4} + 20 x^{3} + 20 x^{2} - 20 x - 20$	$10$	[2,4]	$2^{12}\cdot 3^{10}\cdot 5^{6}$	$3$	$18.1025290096$	$63.72951702730302$				$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$342.301669964$
10.2.3779136000000.4	$x^{10} - 3 x^{9} + 5 x^{8} + 2 x^{7} - 20 x^{6} + 22 x^{5} - 10 x^{4} + 8 x^{3} - 32 x^{2} + 12 x - 4$	$10$	[2,4]	$2^{12}\cdot 3^{10}\cdot 5^{6}$	$3$	$18.1025290096$	$91.91386854852644$				$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$347.574141122$
10.6.5438807015625.1	$x^{10} - x^{9} - 9 x^{8} + 8 x^{7} + 39 x^{6} - 3 x^{5} - 75 x^{4} - 22 x^{3} + 51 x^{2} + 20 x - 4$	$10$	[6,2]	$3^{6}\cdot 5^{6}\cdot 691^{2}$	$3$	$18.7737212363$	$1201.9358181230848$			?	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$7$	$616.428296157$
10.2.5760000000000.2	$x^{10} + 5 x^{6} - 12 x^{5} - 5 x^{2} + 16$	$10$	[2,4]	$2^{16}\cdot 3^{2}\cdot 5^{10}$	$3$	$18.8817502259$	$54.05780681297108$				$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$402.990066408$
10.2.5904900000000.1	$x^{10} - x^{9} - x^{8} + 14 x^{7} - 6 x^{6} + 26 x^{5} - 3 x^{4} + 47 x^{3} - 38 x^{2} + 17 x - 1$	$10$	[2,4]	$2^{8}\cdot 3^{10}\cdot 5^{8}$	$3$	$18.9287203344$	$92.68080510525321$			?	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$443.896423484$
10.2.6191736422400.1	$x^{10} - 2 x^{9} - 3 x^{8} + 4 x^{7} + 9 x^{6} - 6 x^{5} - 25 x^{4} + 16 x^{3} + 24 x^{2} - 24 x - 2$	$10$	[2,4]	$2^{22}\cdot 3^{10}\cdot 5^{2}$	$3$	$19.0187183095$	$134.0594056050095$				$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$1381.74676427$
10.2.6718464000000.2	$x^{10} - 3 x^{9} + 3 x^{8} - 2 x^{7} + 11 x^{6} - 15 x^{5} - 7 x^{4} - 8 x^{3} + 9 x^{2} + 5 x + 5$	$10$	[2,4]	$2^{16}\cdot 3^{8}\cdot 5^{6}$	$3$	$19.1746303103$	$133.3576876204138$				$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$546.50821615$
10.2.7290000000000.1	$x^{10} + 5 x^{6} - 6 x^{5} - 5 x^{4} + 20 x^{3} - 30 x^{2} + 10 x - 11$	$10$	[2,4]	$2^{10}\cdot 3^{6}\cdot 5^{10}$	$3$	$19.3318204493$	$131.62471820403502$				$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$571.627197163$
10.2.9226406250000.1	$x^{10} - 5 x^{9} + 5 x^{8} + 5 x^{7} + 10 x^{6} - 39 x^{5} - 20 x^{4} + 85 x^{3} - 25 x^{2} - 10 x - 11$	$10$	[2,4]	$2^{4}\cdot 3^{10}\cdot 5^{10}$	$3$	$19.7926186616$	$71.57486193038407$			?	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$482.308886002$
10.2.10497600000000.2	$x^{10} - 2 x^{9} - 2 x^{8} + 6 x^{7} - 5 x^{6} + 6 x^{5} - 2 x^{4} - 2 x^{3} + x^{2} - 5$	$10$	[2,4]	$2^{12}\cdot 3^{8}\cdot 5^{8}$	$3$	$20.0497518587$	$137.12978906894952$			?	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$550.197799236$
10.6.11943936000000.1	$x^{10} - 3 x^{9} + x^{8} - 8 x^{6} - 4 x^{5} + 4 x^{4} + 20 x^{3} + 11 x^{2} - x - 1$	$10$	[6,2]	$2^{20}\cdot 3^{6}\cdot 5^{6}$	$3$	$20.3102255679$	$123.0228827802729$				$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$7$	$1300.87442037$
10.2.13286025000000.1	$x^{10} - 4 x^{9} + 11 x^{8} - 24 x^{7} + 41 x^{6} - 35 x^{5} - 5 x^{4} + 45 x^{3} - 35 x^{2} + 5 x + 5$	$10$	[2,4]	$2^{6}\cdot 3^{12}\cdot 5^{8}$	$3$	$20.5276628676$	$118.30871662096978$			?	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$592.463625348$
10.6.16000000000000.1	$x^{10} - 5 x^{9} + 5 x^{8} + 5 x^{6} - x^{5} + 55 x^{4} - 50 x^{3} + 5 x^{2} + 5 x - 1$	$10$	[6,2]	$2^{16}\cdot 5^{12}$	$2$	$20.9127910518$	$45.92515128073019$				$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$7$	$1439.52072902$
10.2.16402500000000.1	$x^{10} - 10 x^{8} + 40 x^{6} - 95 x^{4} - 90 x^{3} - 85 x^{2} - 90 x - 20$	$10$	[2,4]	$2^{8}\cdot 3^{8}\cdot 5^{10}$	$3$	$20.9648135631$	$142.6821389377603$			?	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$802.593178052$
10.2.16402500000000.2	$x^{10} + 5 x^{8} - 10 x^{7} + 25 x^{6} - 20 x^{5} - 5 x^{4} + 50 x^{3} - 70 x^{2} + 60 x - 20$	$10$	[2,4]	$2^{8}\cdot 3^{8}\cdot 5^{10}$	$3$	$20.9648135631$	$69.7257656213086$				$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$657.157528256$
10.2.16402500000000.3	$x^{10} + 5 x^{8} - 10 x^{7} - 5 x^{6} - 32 x^{5} - 25 x^{4} + 20 x^{3} - 65 x^{2} + 30 x - 19$	$10$	[2,4]	$2^{8}\cdot 3^{8}\cdot 5^{10}$	$3$	$20.9648135631$	$78.26452569923332$				$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$955.287374573$
10.2.18662400000000.1	$x^{10} - 3 x^{9} + 9 x^{8} - 20 x^{7} + 26 x^{6} - 30 x^{5} + 42 x^{4} - 36 x^{3} + 36 x - 36$	$10$	[2,4]	$2^{16}\cdot 3^{6}\cdot 5^{8}$	$3$	$21.2371751759$	$76.41637945674692$				$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$991.471518871$
10.2.18662400000000.2	$x^{10} - 2 x^{9} + 4 x^{8} - 4 x^{6} - 8 x^{4} + 16 x^{3} - 20 x^{2} + 24 x - 16$	$10$	[2,4]	$2^{16}\cdot 3^{6}\cdot 5^{8}$	$3$	$21.2371751759$	$89.45088740322718$				$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$983.73750343$
10.2.18662400000000.3	$x^{10} - 2 x^{9} + 6 x^{8} - 8 x^{7} - x^{6} + 42 x^{5} + 88 x^{4} + 136 x^{3} + 117 x^{2} + 34 x - 4$	$10$	[2,4]	$2^{16}\cdot 3^{6}\cdot 5^{8}$	$3$	$21.2371751759$	$104.31269190739516$				$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$987.647103002$
10.2.19518724000000.1	$x^{10} - 2 x^{8} - 6 x^{7} + x^{6} - 2 x^{5} + 4 x^{4} - 32 x^{3} - 56 x^{2} + 16$	$10$	[2,4]	$2^{8}\cdot 5^{6}\cdot 47^{4}$	$3$	$21.332666419$	$109.73185882835593$				$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$816.5374346295982$
10.2.23040000000000.1	$x^{10} - 5 x^{8} + 10 x^{6} - 56 x^{5} - 30 x^{4} - 40 x^{3} + 4$	$10$	[2,4]	$2^{18}\cdot 3^{2}\cdot 5^{10}$	$3$	$21.689435424$	$94.93914000032292$				$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$883.093446961$
10.2.23040000000000.2	$x^{10} + 5 x^{8} - 24 x^{5} - 10 x^{4} + 60 x^{2} - 36$	$10$	[2,4]	$2^{18}\cdot 3^{2}\cdot 5^{10}$	$3$	$21.689435424$	$94.93914000032292$				$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$5$	$987.741841846$
10.6.25628906250000.1	$x^{10} - 10 x^{8} - 15 x^{7} - 10 x^{6} - 7 x^{5} - 5 x^{4} + 35 x^{3} - 5 x^{2} - 5 x + 1$	$10$	[6,2]	$2^{4}\cdot 3^{8}\cdot 5^{12}$	$3$	$21.9216382743$	$124.8388948829259$				$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$7$	$2089.92661385$
10.6.25628906250000.2	$x^{10} - 10 x^{8} - 5 x^{7} + 25 x^{6} - x^{5} - 35 x^{4} + 115 x^{3} + 290 x^{2} + 210 x + 49$	$10$	[6,2]	$2^{4}\cdot 3^{8}\cdot 5^{12}$	$3$	$21.9216382743$	$64.63376114723813$			?	$A_5^2 : C_4$ (as 10T42)	trivial	$2$	$7$	$1660.17397174$