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Results (1-50 of 108 matches)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Narrow class group	Unit group torsion	Unit group rank	Regulator
10.2.125000000000000000.6	$x^{10} - 30 x^{5} + 25$	$10$	[2,4]	$2^{15}\cdot 5^{18}$	$2$	$51.2496615053$	$74.20857674741244$			?	$(C_5^2 : C_4) : C_2$ (as 10T17)	trivial	trivial	$2$	$5$	$82564.8412283$
10.4.500000000000000000.2	$x^{10} - 100 x^{6} - 140 x^{5} - 625 x^{2} - 500 x - 100$	$10$	[4,3]	$-\,2^{17}\cdot 5^{18}$	$2$	$58.8704018652$	$171.474158552352$			?	$S_{10}$ (as 10T45)	trivial	$[2]$	$2$	$6$	$753999.034354$
10.2.949218750000000000.2	$x^{10} - 20 x^{5} + 25$	$10$	[2,4]	$2^{10}\cdot 3^{5}\cdot 5^{18}$	$3$	$62.7677600891$	$90.8865737846625$			?	$(C_5^2 : C_4) : C_2$ (as 10T17)	$[2]$	$[2, 2]$	$2$	$5$	$107224.766762$
10.0.120...000.6	$x^{10} - 25 x^{7} + 75 x^{6} + 75 x^{5} + 4375 x^{4} - 9375 x^{3} + 3000 x^{2} + 4500 x + 1575$	$10$	[0,5]	$-\,2^{4}\cdot 3^{9}\cdot 5^{18}$	$3$	$64.2639084583$	$189.05169186208974$				$(A_5^2 : C_2):C_2$ (as 10T41)	trivial	trivial	$6$	$4$	$636404.437222$
10.2.854...000.7	$x^{10} - 5 x^{9} - 30 x^{8} + 150 x^{7} + 255 x^{6} - 1251 x^{5} - 240 x^{4} + 2250 x^{3} - 4740 x^{2} + 520 x - 3248$	$10$	[2,4]	$2^{10}\cdot 3^{7}\cdot 5^{18}$	$3$	$78.1917407534$	$342.3263198329909$				$S_{10}$ (as 10T45)	trivial	trivial	$2$	$5$	$11069256.8533$
10.0.108...000.4	$x^{10} - 25 x^{8} + 625 x^{6} - 420 x^{5} - 11250 x^{4} - 8250 x^{3} + 67500 x^{2} + 162000 x + 141300$	$10$	[0,5]	$-\,2^{4}\cdot 3^{11}\cdot 5^{18}$	$3$	$80.0555390671$	$276.2514715692136$				$(A_5^2 : C_2):C_2$ (as 10T41)	trivial	trivial	$6$	$4$	$2812704.69139$
10.0.180...000.32	$x^{10} - 200 x^{6} - 80 x^{5} + 1250 x^{4} - 2500 x^{3} + 28250 x^{2} - 9000 x + 59400$	$10$	[0,5]	$-\,2^{19}\cdot 3^{2}\cdot 5^{18}$	$3$	$84.2417248614$	$192.58194139522587$				$(A_5^2 : C_2):C_2$ (as 10T41)	trivial	trivial	$2$	$4$	$3610154.49166$
10.6.320...000.11	$x^{10} - 50 x^{8} + 875 x^{6} - 100 x^{5} - 6250 x^{4} + 2500 x^{3} + 15625 x^{2} - 12500 x - 2500$	$10$	[6,2]	$2^{23}\cdot 5^{18}$	$2$	$89.2308433843$	$176.4987349244967$			?	$(D_5 \wr C_2):C_2$ (as 10T27)	trivial	trivial	$2$	$7$	$2919365.38818$
10.0.405...000.37	$x^{10} - 50 x^{8} + 625 x^{6} - 400 x^{5} + 10000 x^{3} + 60000$	$10$	[0,5]	$-\,2^{17}\cdot 3^{4}\cdot 5^{18}$	$3$	$91.3577725692$	$404.5377989174622$				$(A_5^2 : C_2):C_2$ (as 10T41)	trivial	trivial	$2$	$4$	$9998877.09284$
10.0.405...000.44	$x^{10} + 50 x^{8} - 150 x^{7} + 725 x^{6} - 4440 x^{5} + 8125 x^{4} - 24750 x^{3} + 74250 x^{2} - 130500 x + 234225$	$10$	[0,5]	$-\,2^{17}\cdot 3^{4}\cdot 5^{18}$	$3$	$91.3577725692$	$336.8518198843963$			?	$(A_5^2 : C_2):C_2$ (as 10T41)	trivial	trivial	$2$	$4$	$2918061.90553$
10.0.768...000.90	$x^{10} + 50 x^{8} - 100 x^{7} + 1075 x^{6} - 2900 x^{5} + 13750 x^{4} - 32500 x^{3} + 87500 x^{2} - 171000 x + 137200$	$10$	[0,5]	$-\,2^{10}\cdot 3^{9}\cdot 5^{18}$	$3$	$97.4058706789$	$449.6432341313983$				$(A_5^2 : C_2):C_2$ (as 10T41)	trivial	trivial	$6$	$4$	$4433441.52491$
10.0.768...000.96	$x^{10} - 75 x^{8} + 1875 x^{6} - 450 x^{5} + 202500$	$10$	[0,5]	$-\,2^{10}\cdot 3^{9}\cdot 5^{18}$	$3$	$97.4058706789$	$347.28999037331886$				$(A_5^2 : C_2):C_2$ (as 10T41)	trivial	trivial	$6$	$4$	$7321910.75029$
10.2.768...000.49	$x^{10} - 6750 x - 6075$	$10$	[2,4]	$2^{10}\cdot 3^{9}\cdot 5^{18}$	$3$	$97.4058706789$	$317.9457799689622$			?	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$5$	$4374170.6999$
10.2.136...000.41	$x^{10} - 15 x^{8} + 90 x^{6} - 840 x^{5} + 1530 x^{4} - 3600 x^{3} + 7605 x^{2} - 1800 x + 20277$	$10$	[2,4]	$2^{14}\cdot 3^{7}\cdot 5^{18}$	$3$	$103.174620481$	$254.97790184447035$			?	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$5$	$6493755.58396$
10.0.162...000.12	$x^{10} - 40 x^{5} + 600$	$10$	[0,5]	$-\,2^{19}\cdot 3^{4}\cdot 5^{18}$	$3$	$104.942523066$	$235.8104811034793$			?	$(C_5^2 : C_4) : C_2$ (as 10T17)	trivial	trivial	$2$	$4$	$3591802.56506$
10.2.162...000.100	$x^{10} + 50 x^{8} + 875 x^{6} - 520 x^{5} + 6250 x^{4} - 13000 x^{3} + 15625 x^{2} - 65000 x - 20600$	$10$	[2,4]	$2^{19}\cdot 3^{4}\cdot 5^{18}$	$3$	$104.94252306643652$	$181.773147569325$			?	$(C_5^2 : C_4) : C_2$ (as 10T17)	trivial	trivial	$2$	$5$	$4857415.68517165$
10.0.172...000.16	$x^{10} - 25 x^{8} - 100 x^{7} + 1150 x^{6} + 130 x^{5} - 6875 x^{4} + 7250 x^{3} + 129125 x^{2} - 352500 x + 516400$	$10$	[0,5]	$-\,2^{8}\cdot 3^{11}\cdot 5^{18}$	$3$	$105.6339171$	$492.22416381078955$				$(A_5^2 : C_2):C_2$ (as 10T41)	trivial	trivial	$6$	$4$	$6709466.38015$
10.2.243...000.62	$x^{10} - 50 x^{8} + 875 x^{6} - 800 x^{5} - 6250 x^{4} + 20000 x^{3} + 15625 x^{2} - 100000 x + 92500$	$10$	[2,4]	$2^{18}\cdot 3^{5}\cdot 5^{18}$	$3$	$109.285017805$	$181.773147569325$			?	$(C_5^2 : C_4) : C_2$ (as 10T17)	$[2]$	$[2, 2]$	$2$	$5$	$2329741.47915$
10.0.389...000.19	$x^{10} - 75 x^{8} - 100 x^{7} + 2850 x^{6} - 615 x^{5} - 20000 x^{4} - 54000 x^{3} + 28125 x^{2} + 538875 x + 733575$	$10$	[0,5]	$-\,2^{6}\cdot 3^{13}\cdot 5^{18}$	$3$	$114.557001176$	$731.9083743495286$			?	$(A_5^2 : C_2):C_2$ (as 10T41)	trivial	trivial	$6$	$4$	$8977145.44559$
10.0.432...000.17	$x^{10} - 100 x^{7} - 50 x^{6} + 420 x^{5} + 2500 x^{4} + 2500 x^{3} - 375 x^{2} + 13500 x + 51300$	$10$	[0,5]	$-\,2^{22}\cdot 3^{3}\cdot 5^{18}$	$3$	$115.757296328$	$756.206767448359$				$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$2$	$4$	$28681793.1304$
10.6.512...000.2	$x^{10} - 100 x^{8} + 3250 x^{6} - 640 x^{5} - 37500 x^{4} + 32000 x^{3} + 129375 x^{2} - 129000 x - 171400$	$10$	[6,2]	$2^{27}\cdot 5^{18}$	$2$	$117.74080373049493$	$239.0243907988439$			?	$(A_5^2 : C_2):C_2$ (as 10T41)	trivial	trivial	$2$	$7$	$14533027.287582077$
10.6.691...000.1	$x^{10} - 50 x^{8} + 625 x^{6} - 450 x^{5} + 11250 x^{3} - 16875$	$10$	[6,2]	$2^{10}\cdot 3^{11}\cdot 5^{18}$	$3$	$121.341506805$	$272.6597213539875$			?	$(A_5^2 : C_2):C_2$ (as 10T41)	trivial	$[2]$	$2$	$7$	$19938970.0459$
10.0.820...000.35	$x^{10} - 90 x^{5} + 6075$	$10$	[0,5]	$-\,2^{15}\cdot 3^{8}\cdot 5^{18}$	$3$	$123.420699949$	$178.71092638266538$			?	$(C_5^2 : C_4) : C_2$ (as 10T17)	trivial	trivial	$2$	$4$	$5954771.24335$
10.0.820...000.94	$x^{10} - 100 x^{7} + 450 x^{6} + 690 x^{5} + 2500 x^{4} - 22500 x^{3} + 27375 x^{2} + 65250 x + 299025$	$10$	[0,5]	$-\,2^{15}\cdot 3^{8}\cdot 5^{18}$	$3$	$123.420699949$	$556.1301014580166$				$(A_5^2 : C_2):C_2$ (as 10T41)	trivial	trivial	$2$	$4$	$21029009.8103$
10.0.115...000.12	$x^{10} + 750 x^{6} - 10000 x^{3} + 62500 x^{2} + 20000$	$10$	[0,5]	$-\,2^{25}\cdot 3^{2}\cdot 5^{18}$	$3$	$127.686577964$	$305.7047763608597$			?	$(D_5 \wr C_2):C_2$ (as 10T27)	trivial	trivial	$2$	$4$	$9759547.3046$
10.2.123...000.127	$x^{10} - 150 x^{5} - 450$	$10$	[2,4]	$2^{14}\cdot 3^{9}\cdot 5^{18}$	$3$	$128.527816917$	$186.10593876502662$			?	$(C_5^2 : C_4) : C_2$ (as 10T17)	trivial	$[2]$	$2$	$5$	$6436084.56975$
10.2.123...000.131	$x^{10} - 180 x^{5} + 600$	$10$	[2,4]	$2^{14}\cdot 3^{9}\cdot 5^{18}$	$3$	$128.527816917$	$186.10593876502662$			?	$(C_5^2 : C_4) : C_2$ (as 10T17)	trivial	$[2]$	$2$	$5$	$13127614.1504$
10.2.123...000.194	$x^{10} - 360 x^{5} + 8100$	$10$	[2,4]	$2^{14}\cdot 3^{9}\cdot 5^{18}$	$3$	$128.527816917$	$186.10593876502662$			?	$(C_5^2 : C_4) : C_2$ (as 10T17)	trivial	$[2]$	$2$	$5$	$6981425.97885$
10.2.123...000.198	$x^{10} - 300 x^{5} + 15000$	$10$	[2,4]	$2^{14}\cdot 3^{9}\cdot 5^{18}$	$3$	$128.527816917$	$186.10593876502662$			?	$(C_5^2 : C_4) : C_2$ (as 10T17)	trivial	$[2]$	$2$	$5$	$11423095.7903$
10.0.145...000.79	$x^{10} - 50 x^{8} - 100 x^{7} + 625 x^{6} + 3020 x^{5} + 7500 x^{4} + 17000 x^{3} + 18000 x^{2} - 3000 x + 67650$	$10$	[0,5]	$-\,2^{19}\cdot 3^{6}\cdot 5^{18}$	$3$	$130.730147865$	$465.09571089526173$				$(A_5^2 : C_2):C_2$ (as 10T41)	trivial	trivial	$2$	$4$	$68904996.1066$
10.0.145...000.86	$x^{10} - 50 x^{8} - 300 x^{7} - 125 x^{6} + 7020 x^{5} + 41250 x^{4} + 124500 x^{3} + 223875 x^{2} + 211500 x + 79650$	$10$	[0,5]	$-\,2^{19}\cdot 3^{6}\cdot 5^{18}$	$3$	$130.730147865$	$935.2956174614613$				$(A_5^2 : C_2):C_2$ (as 10T41)	trivial	trivial	$2$	$4$	$90689457.6672$
10.0.145...000.110	$x^{10} - 300 x^{7} - 150 x^{6} + 900 x^{5} + 23750 x^{4} - 22500 x^{3} + 292125 x^{2} - 364500 x + 256950$	$10$	[0,5]	$-\,2^{19}\cdot 3^{6}\cdot 5^{18}$	$3$	$130.730147865$	$449.6432341313983$				$(A_5^2 : C_2):C_2$ (as 10T41)	$[2]$	$[2]$	$2$	$4$	$21110544.1592$
10.0.155...000.16	$x^{10} - 150 x^{7} + 225 x^{6} - 90 x^{5} + 7500 x^{4} - 11250 x^{3} + 16875 x^{2} - 20250 x + 8100$	$10$	[0,5]	$-\,2^{8}\cdot 3^{13}\cdot 5^{18}$	$3$	$131.591438804$	$633.4934573060877$				$(A_5^2 : C_2):C_2$ (as 10T41)	trivial	trivial	$6$	$4$	$37172084.844$
10.0.155...000.38	$x^{10} - 50 x^{7} - 150 x^{6} + 150 x^{5} + 17500 x^{4} + 71250 x^{3} + 197625 x^{2} + 245250 x + 249300$	$10$	[0,5]	$-\,2^{8}\cdot 3^{13}\cdot 5^{18}$	$3$	$131.591438804$	$636.6100478516211$				$(A_5^2 : C_2):C_2$ (as 10T41)	trivial	trivial	$6$	$4$	$17814644.7218$
10.0.155...000.44	$x^{10} - 100 x^{7} - 300 x^{6} + 360 x^{5} + 10000 x^{4} - 30000 x^{3} - 54000 x^{2} + 324000 x + 561600$	$10$	[0,5]	$-\,2^{8}\cdot 3^{13}\cdot 5^{18}$	$3$	$131.591438804$	$633.4934573060877$				$(A_5^2 : C_2):C_2$ (as 10T41)	trivial	trivial	$6$	$4$	$30988961.4749$
10.0.204...000.6	$x^{10} - 100 x^{8} + 2850 x^{6} - 80 x^{5} - 12500 x^{4} - 1000 x^{3} + 33875 x^{2} - 15000 x + 1800$	$10$	[0,5]	$-\,2^{29}\cdot 5^{18}$	$2$	$135.248667561$	$301.1518614057619$			?	$(A_5^2 : C_2):C_2$ (as 10T41)	trivial	trivial	$2$	$4$	$25253888.85275605$
10.6.204...000.5	$x^{10} - 100 x^{8} - 200 x^{7} + 2850 x^{6} + 12200 x^{5} - 12500 x^{4} - 190000 x^{3} - 448625 x^{2} - 326000 x - 38200$	$10$	[6,2]	$2^{29}\cdot 5^{18}$	$2$	$135.24866756124828$	$301.1518614057619$			?	$(A_5^2 : C_2):C_2$ (as 10T41)	trivial	trivial	$2$	$7$	$38233520.14786721$
10.2.204...000.26	$x^{10} - 100 x^{8} - 200 x^{7} + 4550 x^{6} + 18920 x^{5} - 92500 x^{4} - 651000 x^{3} + 78625 x^{2} + 7927000 x + 15270800$	$10$	[2,4]	$2^{29}\cdot 5^{18}$	$2$	$135.24866756124828$	$284.2495061971761$			?	$(A_5^2 : C_2):C_2$ (as 10T41)	trivial	trivial	$2$	$5$	$14492543.076974966$
10.0.259...000.31	$x^{10} - 100 x^{6} + 22500 x^{2} - 72000 x + 64800$	$10$	[0,5]	$-\,2^{23}\cdot 3^{4}\cdot 5^{18}$	$3$	$138.472489363$	$378.67526212238977$				$(A_5^2 : C_2):C_2$ (as 10T41)	trivial	trivial	$2$	$4$	$41279150.9298$
10.0.276...000.47	$x^{10} - 200 x^{7} + 300 x^{6} + 17500 x^{4} - 52500 x^{3} - 41625 x^{2} + 121500 x + 218700$	$10$	[0,5]	$-\,2^{12}\cdot 3^{11}\cdot 5^{18}$	$3$	$139.38478926$	$638.33576538485$				$(A_5^2 : C_2):C_2$ (as 10T41)	trivial	trivial	$6$	$4$	$63903394.9509$
10.0.276...000.62	$x^{10} - 100 x^{7} + 150 x^{6} + 660 x^{5} + 10000 x^{4} - 30000 x^{3} - 127500 x^{2} + 225000 x + 565200$	$10$	[0,5]	$-\,2^{12}\cdot 3^{11}\cdot 5^{18}$	$3$	$139.38478926$	$385.59907585167815$				$(A_5^2 : C_2):C_2$ (as 10T41)	trivial	trivial	$6$	$4$	$35823512.2476$
10.2.328...000.4	$x^{10} - 200 x^{7} - 1350 x^{6} - 2160 x^{5} - 21250 x^{4} + 22500 x^{3} - 44625 x^{2} + 351000 x - 1859400$	$10$	[2,4]	$2^{17}\cdot 3^{8}\cdot 5^{18}$	$3$	$141.773155004$	$429.99741377626566$				$(A_5^2 : C_2):C_2$ (as 10T41)	trivial	trivial	$2$	$5$	$69420217.7651$
10.0.388...000.33	$x^{10} + 400 x^{6} - 240 x^{5} - 3000 x^{3} + 10375 x^{2} + 3000 x + 11700$	$10$	[0,5]	$-\,2^{22}\cdot 3^{5}\cdot 5^{18}$	$3$	$144.202445522$	$492.3345867598735$			?	$S_{10}$ (as 10T45)	$[2]$	$[2]$	$2$	$4$	$33920888.4858$
10.0.388...000.76	$x^{10} - 100 x^{7} - 300 x^{6} + 1080 x^{5} + 7500 x^{4} - 45000 x^{3} + 58500 x^{2} + 378000 x + 696600$	$10$	[0,5]	$-\,2^{22}\cdot 3^{5}\cdot 5^{18}$	$3$	$144.202445522$	$756.206767448359$				$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$2$	$4$	$279210594.529$
10.2.627...000.2	$x^{10} - 50 x^{8} + 125 x^{6} - 2220 x^{5} + 6250 x^{4} - 20500 x^{3} + 15625 x^{2} - 72500 x + 76900$	$10$	[2,4]	$2^{25}\cdot 5^{18}\cdot 7^{2}$	$3$	$151.265749981$	$555.3261386978734$			?	$(D_5 \wr C_2):C_2$ (as 10T27)	trivial	trivial	$2$	$5$	$19258085.5213$
10.4.819...000.30	$x^{10} + 100 x^{8} - 200 x^{7} + 2400 x^{6} - 10640 x^{5} + 5000 x^{4} - 22000 x^{3} - 144750 x^{2} + 32000 x + 102400$	$10$	[4,3]	$-\,2^{31}\cdot 5^{18}$	$2$	$155.35992194314676$	$323.700107092546$			?	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$2$	$6$	$44278565.206738956$
10.2.874...000.65	$x^{10} + 50 x^{8} + 875 x^{6} - 1720 x^{5} + 6250 x^{4} - 43000 x^{3} + 15625 x^{2} - 215000 x - 103100$	$10$	[2,4]	$2^{20}\cdot 3^{7}\cdot 5^{18}$	$3$	$156.383481507$	$402.3301118039809$			?	$(D_5 \wr C_2):C_2$ (as 10T27)	trivial	$[2]$	$2$	$5$	$30649897.3953$
10.2.874...000.130	$x^{10} + 50 x^{8} + 875 x^{6} - 400 x^{5} + 6250 x^{4} - 10000 x^{3} + 15625 x^{2} - 50000 x + 32500$	$10$	[2,4]	$2^{20}\cdot 3^{7}\cdot 5^{18}$	$3$	$156.383481507$	$402.3301118039809$			?	$(D_5 \wr C_2):C_2$ (as 10T27)	trivial	$[2]$	$2$	$5$	$29943582.8504$
10.0.124...375.4	$x^{10} + 2625 x^{6} - 2275 x^{5} + 30625 x^{3} + 765625 x^{2} + 1990625 x + 1347500$	$10$	[0,5]	$-\,3^{4}\cdot 5^{18}\cdot 7^{9}$	$3$	$162.0252669663216$	$261.85325219708193$			?	$(C_5^2 : C_4) : C_2$ (as 10T17)	$[2]$	$[2]$	$2$	$4$	$20695090.898274314$
10.4.131...000.21	$x^{10} - 50 x^{7} + 300 x^{5} - 625 x^{4} + 3000 x^{2} + 450$	$10$	[4,3]	$-\,2^{19}\cdot 3^{8}\cdot 5^{18}$	$3$	$162.854589936$	$811.727026765957$			?	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$2$	$6$	$107277081.975$

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