Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

Results (1-50 of 576764 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
8.0.22959825625.2	$x^{8} - 4 x^{7} + 16 x^{6} - 34 x^{5} + 109 x^{4} - 166 x^{3} + 343 x^{2} - 265 x + 671$	$8$	[0,4]	$5^{4}\cdot 11^{2}\cdot 19^{2}\cdot 29^{2}$	$4$	$19.729726873$	$174.0833133875846$	✓		?	$C_2^2 \wr C_2$ (as 8T18)	$[12]$	$2$	$3$	$6.600550783478059$
8.0.27328057344.2	$x^{8} - 2 x^{7} + 15 x^{6} - 20 x^{5} + 61 x^{4} + 6 x^{3} + 69 x^{2} + 126$	$8$	[0,4]	$2^{12}\cdot 3^{4}\cdot 7^{2}\cdot 41^{2}$	$4$	$20.1639724337$	$82.99397568498571$				$C_2^2 \wr C_2$ (as 8T18)	$[12]$	$2$	$3$	$76.9761569426$
8.0.27328057344.5	$x^{8} + 22 x^{6} + 179 x^{4} + 566 x^{2} + 289$	$8$	[0,4]	$2^{12}\cdot 3^{4}\cdot 7^{2}\cdot 41^{2}$	$4$	$20.1639724337$	$82.99397568498571$				$C_2^2 \wr C_2$ (as 8T18)	$[2, 6]$	$2$	$3$	$11.5645215419$
8.0.28288548864.31	$x^{8} + 10 x^{6} + 45 x^{4} + 28 x^{2} + 100$	$8$	[0,4]	$2^{16}\cdot 3^{4}\cdot 73^{2}$	$3$	$20.251226624$	$59.19459434779497$	✓		?	$D_4\times C_2$ (as 8T9)	$[12]$	$2$	$3$	$21.2871886415$
8.0.28288548864.32	$x^{8} - 12 x^{5} + 5 x^{4} + 60 x^{3} + 72 x^{2} + 120 x + 100$	$8$	[0,4]	$2^{16}\cdot 3^{4}\cdot 73^{2}$	$3$	$20.251226624$	$59.19459434779497$	✓		?	$D_4\times C_2$ (as 8T9)	$[12]$	$4$	$3$	$76.2177947492$
8.0.32319410176.2	$x^{8} - 2 x^{7} + 12 x^{6} - 28 x^{5} + 66 x^{4} - 152 x^{3} + 288 x^{2} - 272 x + 468$	$8$	[0,4]	$2^{12}\cdot 53^{4}$	$2$	$20.591260282$	$20.591260281974$			?	$S_4$ (as 8T14)	$[12]$	$2$	$3$	$16.1878519065$
8.0.33890333801.1	$x^{8} - x^{7} + 7 x^{6} - 11 x^{5} + 44 x^{4} - 71 x^{3} + 153 x^{2} - 112 x + 131$	$8$	[0,4]	$19^{2}\cdot 103^{2}\cdot 8849$	$3$	$20.7137857943$	$4161.429201608505$	✓		?	$C_2 \wr S_4$ (as 8T44)	$[11]$	$2$	$3$	$15.3469041871$
8.0.35296583633.1	$x^{8} - x^{7} + 7 x^{6} - 18 x^{5} + 23 x^{4} - 72 x^{3} + 112 x^{2} - 64 x + 256$	$8$	[0,4]	$23\cdot 199\cdot 2777^{2}$	$3$	$20.8193220852$	$3565.154835347267$	✓		?	$C_2 \wr S_4$ (as 8T44)	$[12]$	$2$	$3$	$24.3101872304$
8.0.35806100625.3	$x^{8} - 4 x^{7} + 18 x^{6} - 40 x^{5} + 132 x^{4} - 202 x^{3} + 449 x^{2} - 354 x + 979$	$8$	[0,4]	$3^{4}\cdot 5^{4}\cdot 29^{4}$	$3$	$20.8566536146$	$20.85665361461421$	✓		?	$D_4\times C_2$ (as 8T9)	$[12]$	$2$	$3$	$6.60055078348$
8.0.35806100625.4	$x^{8} + 17 x^{6} + 253 x^{4} + 612 x^{2} + 1296$	$8$	[0,4]	$3^{4}\cdot 5^{4}\cdot 29^{4}$	$3$	$20.8566536146$	$20.85665361461421$	✓	✓		$C_2^3$ (as 8T3)	$[12]$	$6$	$3$	$40.3281811419$
8.0.36457875625.1	$x^{8} - 3 x^{7} + 19 x^{6} - 32 x^{5} + 119 x^{4} - 112 x^{3} + 342 x^{2} - 140 x + 431$	$8$	[0,4]	$5^{4}\cdot 29^{2}\cdot 139\cdot 499$	$4$	$20.9037363835$	$3171.3317391909663$	✓		?	$C_2 \wr C_2\wr C_2$ (as 8T35)	$[12]$	$2$	$3$	$6.60055078348$
8.0.37036232704.2	$x^{8} + 10 x^{6} - 4 x^{5} + 79 x^{4} - 136 x^{3} + 338 x^{2} - 392 x + 136$	$8$	[0,4]	$2^{12}\cdot 31^{2}\cdot 97^{2}$	$3$	$20.9449028613$	$155.09996776273036$				$C_2^2 \wr C_2$ (as 8T18)	$[15]$	$2$	$3$	$58.3399156294$
8.0.37480572801.2	$x^{8} - 3 x^{7} - 14 x^{6} + 65 x^{5} - 58 x^{4} - 275 x^{3} + 1281 x^{2} - 2048 x + 1492$	$8$	[0,4]	$3^{4}\cdot 7^{4}\cdot 439^{2}$	$3$	$20.9761498763$	$96.01562372864116$				$D_4\times C_2$ (as 8T9)	$[15]$	$6$	$3$	$58.0109234015$
8.0.37480960000.9	$x^{8} - 2 x^{6} + 53 x^{4} + 388 x^{2} + 676$	$8$	[0,4]	$2^{12}\cdot 5^{4}\cdot 11^{4}$	$3$	$20.9761769634$	$20.97617696340303$	✓	✓		$C_2^3$ (as 8T3)	$[12]$	$2$	$3$	$12.3400472787$
8.0.37480960000.10	$x^{8} - 2 x^{7} - 9 x^{6} - 4 x^{5} + 73 x^{4} + 36 x^{3} - 11 x^{2} - 678 x + 729$	$8$	[0,4]	$2^{12}\cdot 5^{4}\cdot 11^{4}$	$3$	$20.9761769634$	$20.97617696340303$				$D_4\times C_2$ (as 8T9)	$[12]$	$2$	$3$	$36.2373917271$
8.0.37480960000.12	$x^{8} + 16 x^{6} + 152 x^{4} + 1144 x^{2} + 1936$	$8$	[0,4]	$2^{12}\cdot 5^{4}\cdot 11^{4}$	$3$	$20.9761769634$	$20.97617696340303$				$D_4\times C_2$ (as 8T9)	$[12]$	$2$	$3$	$9.58942800866$
8.0.39464206336.13	$x^{8} + 12 x^{6} + 66 x^{4} + 192 x^{2} + 256$	$8$	[0,4]	$2^{22}\cdot 97^{2}$	$2$	$21.111807712$	$66.25495375899139$	✓		?	$C_2^2:C_4$ (as 8T10)	$[12]$	$2$	$3$	$19.534360053$
8.0.39649172641.2	$x^{8} - 2 x^{6} + 85 x^{4} - 84 x^{2} + 64$	$8$	[0,4]	$13^{2}\cdot 17^{4}\cdot 53^{2}$	$3$	$21.1241511414$	$108.2266141020775$	✓			$C_2^2 \wr C_2$ (as 8T18)	$[11]$	$2$	$3$	$121.31279804$
8.0.40804000000.1	$x^{8} + 9 x^{6} + 36 x^{4} + 69 x^{2} + 121$	$8$	[0,4]	$2^{8}\cdot 5^{6}\cdot 101^{2}$	$3$	$21.2000967235$	$67.20756887843493$	✓			$C_2^2:C_4$ (as 8T10)	$[12]$	$2$	$3$	$14.8224845118$
8.0.40804000000.9	$x^{8} - x^{6} + 181 x^{4} - 2121 x^{2} + 10201$	$8$	[0,4]	$2^{8}\cdot 5^{6}\cdot 101^{2}$	$3$	$21.2000967235$	$67.20756887843493$	✓		?	$C_2^2:C_4$ (as 8T10)	$[2, 6]$	$10$	$3$	$53.3577685556$
8.0.41463140625.9	$x^{8} - 3 x^{7} + 17 x^{6} - 30 x^{5} + 91 x^{4} - 90 x^{3} + 228 x^{2} - 54 x + 261$	$8$	[0,4]	$3^{4}\cdot 5^{6}\cdot 181^{2}$	$3$	$21.2426050355$	$77.91613798765907$	✓		?	$C_2^3: C_4$ (as 8T20)	$[2, 6]$	$2$	$3$	$9.32364155459$
8.0.43057910016.1	$x^{8} - 46 x^{6} + 721 x^{4} - 4224 x^{2} + 9216$	$8$	[0,4]	$2^{8}\cdot 3^{4}\cdot 11^{2}\cdot 131^{2}$	$4$	$21.3430567049$	$131.4990494262221$	✓			$D_4\times C_2$ (as 8T9)	$[11]$	$12$	$3$	$86.2600668707$
8.0.43177515264.1	$x^{8} - 2 x^{7} + 9 x^{6} - 32 x^{5} + 28 x^{4} - 120 x^{3} + 228 x^{2} - 96 x + 384$	$8$	[0,4]	$2^{8}\cdot 3^{6}\cdot 13^{2}\cdot 37^{2}$	$4$	$21.3504584943$	$99.98698545954649$				$C_2^2 \wr C_2$ (as 8T18)	$[12]$	$2$	$3$	$149.925471216$
8.0.43177515264.22	$x^{8} + 11 x^{6} - 24 x^{5} + 48 x^{4} - 30 x^{3} + 23 x^{2} + 6 x + 1$	$8$	[0,4]	$2^{8}\cdot 3^{6}\cdot 13^{2}\cdot 37^{2}$	$4$	$21.3504584943$	$99.98698545954649$				$C_2^2 \wr C_2$ (as 8T18)	$[12]$	$2$	$3$	$27.6250897684$
8.0.44083201600.1	$x^{8} - 2 x^{7} - 2 x^{6} + 4 x^{5} + 14 x^{4} - 12 x^{3} - 18 x^{2} + 54 x + 81$	$8$	[0,4]	$2^{6}\cdot 5^{2}\cdot 29^{2}\cdot 181^{2}$	$4$	$21.405931977820384$	$363.68463236431063$			?	$C_2^3:S_4$ (as 8T39)	$[11]$	$2$	$3$	$45.55920560414165$
8.0.46128300625.1	$x^{8} - 4 x^{7} + 36 x^{6} - 94 x^{5} + 402 x^{4} - 652 x^{3} + 1821 x^{2} - 1510 x + 2729$	$8$	[0,4]	$5^{4}\cdot 11^{4}\cdot 71^{2}$	$3$	$21.5276156953$	$62.489999199871974$				$C_2^2 \wr C_2$ (as 8T18)	$[12]$	$2$	$3$	$11.468735918$
8.0.46128300625.2	$x^{8} + 14 x^{6} + 47 x^{4} + 206 x^{2} + 1$	$8$	[0,4]	$5^{4}\cdot 11^{4}\cdot 71^{2}$	$3$	$21.5276156953$	$62.489999199871974$				$D_4\times C_2$ (as 8T9)	$[2, 6]$	$2$	$3$	$23.4804848961$
8.0.46352367616.7	$x^{8} - 4 x^{7} + 10 x^{6} - 16 x^{5} + 54 x^{4} - 28 x^{3} + 86 x^{2} - 16 x + 45$	$8$	[0,4]	$2^{16}\cdot 29^{4}$	$2$	$21.5406592285$	$21.540659228538015$			?	$S_4$ (as 8T14)	$[12]$	$2$	$3$	$25.8379961692$
8.0.47436840000.4	$x^{8} + x^{6} - 53 x^{4} + 159 x^{2} + 36$	$8$	[0,4]	$2^{6}\cdot 3^{4}\cdot 5^{4}\cdot 11^{4}$	$4$	$21.603020057$	$36.3318042491699$				$D_4\times C_2$ (as 8T9)	$[2, 6]$	$6$	$3$	$148.840836458$
8.0.47436840000.5	$x^{8} - 3 x^{7} + 8 x^{6} - 12 x^{5} + 43 x^{4} + 27 x^{3} + 180 x^{2} + 108 x + 144$	$8$	[0,4]	$2^{6}\cdot 3^{4}\cdot 5^{4}\cdot 11^{4}$	$4$	$21.603020057$	$36.3318042491699$				$D_4\times C_2$ (as 8T9)	$[12]$	$2$	$3$	$282.191927439$
8.0.48180689001.3	$x^{8} - x^{7} + 8 x^{6} + 6 x^{5} + 8 x^{4} + 6 x^{3} + 8 x^{2} - x + 1$	$8$	[0,4]	$3^{4}\cdot 29^{6}$	$2$	$21.6450765353$	$21.645076535339435$			?	$S_4$ (as 8T14)	$[12]$	$2$	$3$	$46.5404636582$
8.0.48297515625.1	$x^{8} - x^{7} + 13 x^{6} - 10 x^{5} + 81 x^{4} - 50 x^{3} + 232 x^{2} - 62 x + 241$	$8$	[0,4]	$3^{4}\cdot 5^{6}\cdot 31\cdot 1231$	$4$	$21.6516301017$	$1131.352664442234$	✓		?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[12]$	$2$	$3$	$9.32364155459$
8.0.48576160000.4	$x^{8} + 27 x^{6} + 258 x^{4} + 957 x^{2} + 961$	$8$	[0,4]	$2^{8}\cdot 5^{4}\cdot 19^{2}\cdot 29^{2}$	$4$	$21.6672052598$	$148.45874847916508$				$C_2^2 \wr C_2$ (as 8T18)	$[4, 4]$	$2$	$3$	$10.3610327765$
8.0.48576160000.5	$x^{8} - 2 x^{7} + 13 x^{6} - 14 x^{5} + 112 x^{4} - 36 x^{3} + 500 x^{2} - 134 x + 1199$	$8$	[0,4]	$2^{8}\cdot 5^{4}\cdot 19^{2}\cdot 29^{2}$	$4$	$21.6672052598$	$148.45874847916508$	✓		?	$C_2^2 \wr C_2$ (as 8T18)	$[2, 8]$	$2$	$3$	$6.60055078348$
8.0.48576160000.9	$x^{8} - 4 x^{7} + 2 x^{6} + 8 x^{5} + 8 x^{4} - 34 x^{3} + 209 x^{2} - 190 x + 1805$	$8$	[0,4]	$2^{8}\cdot 5^{4}\cdot 19^{2}\cdot 29^{2}$	$4$	$21.6672052598$	$148.45874847916508$			?	$C_2^2 \wr C_2$ (as 8T18)	$[2, 8]$	$2$	$3$	$11.0119598915$
8.0.49630015625.1	$x^{8} - 2 x^{7} + 18 x^{6} - 24 x^{5} + 100 x^{4} - 74 x^{3} + 123 x^{2} + 18 x + 76$	$8$	[0,4]	$5^{6}\cdot 89^{2}\cdot 401$	$3$	$21.725413518030276$	$631.6764601003824$	✓			$C_2 \wr C_2\wr C_2$ (as 8T35)	$[12]$	$2$	$3$	$16.516095225064227$
8.0.49798971392.1	$x^{8} - 4 x^{7} + 14 x^{6} - 28 x^{5} + 63 x^{4} - 56 x^{3} + 140 x^{2} - 32 x + 158$	$8$	[0,4]	$2^{22}\cdot 31\cdot 383$	$3$	$21.7346447727$	$733.0147638579896$	✓		?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[16]$	$2$	$3$	$19.534360053$
8.0.49946886144.4	$x^{8} + 6 x^{6} + 53 x^{4} + 132 x^{2} + 100$	$8$	[0,4]	$2^{16}\cdot 3^{4}\cdot 97^{2}$	$3$	$21.7427039369$	$68.23488843692792$	✓		?	$D_4\times C_2$ (as 8T9)	$[2, 8]$	$2$	$3$	$21.2871886415$
8.0.49946886144.36	$x^{8} - 4 x^{7} + 14 x^{6} - 28 x^{5} + 79 x^{4} - 116 x^{3} + 98 x^{2} - 44 x + 334$	$8$	[0,4]	$2^{16}\cdot 3^{4}\cdot 97^{2}$	$3$	$21.7427039369$	$68.23488843692792$	✓		?	$D_4\times C_2$ (as 8T9)	$[2, 6]$	$2$	$3$	$21.2871886415$
8.0.50269227264.1	$x^{8} + 11 x^{6} + 33 x^{4} + 17 x^{2} + 1$	$8$	[0,4]	$2^{8}\cdot 3^{8}\cdot 173^{2}$	$3$	$21.7601946629$	$191.419958146375$	✓			$C_2^3:S_4$ (as 8T39)	$[12]$	$2$	$3$	$33.522860912176355$
8.0.50651578125.1	$x^{8} - 3 x^{7} + 17 x^{6} - 30 x^{5} + 106 x^{4} - 105 x^{3} + 273 x^{2} - 99 x + 261$	$8$	[0,4]	$3^{4}\cdot 5^{6}\cdot 31\cdot 1291$	$4$	$21.7808148175$	$1158.596197090594$	✓		?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[12]$	$2$	$3$	$9.32364155459$
8.0.50712825625.1	$x^{8} - 3 x^{7} + 20 x^{6} - 41 x^{5} + 149 x^{4} - 205 x^{3} + 500 x^{2} - 375 x + 625$	$8$	[0,4]	$5^{4}\cdot 7^{2}\cdot 11\cdot 29^{2}\cdot 179$	$5$	$21.7841052265$	$1413.6955117704802$	✓		?	$C_2 \wr C_2\wr C_2$ (as 8T35)	$[2, 6]$	$2$	$3$	$6.60055078348$
8.0.53075650625.1	$x^{8} + 7 x^{6} - 10 x^{5} + 23 x^{4} - 40 x^{3} + 112 x^{2} + 256$	$8$	[0,4]	$5^{4}\cdot 71\cdot 89^{2}\cdot 151$	$4$	$21.9084632706$	$2184.2264076784713$	✓			$C_2 \wr C_2\wr C_2$ (as 8T35)	$[12]$	$2$	$3$	$16.5160952251$
8.0.53553365056.1	$x^{8} + 12 x^{6} - 2 x^{5} + 45 x^{4} - 2 x^{3} + 56 x^{2} + 76 x + 70$	$8$	[0,4]	$2^{6}\cdot 28927^{2}$	$2$	$21.93301550539182$	$481.05716915975796$				$C_2^3:S_4$ (as 8T39)	$[13]$	$2$	$3$	$90.78004346407998$
8.0.53557067776.15	$x^{8} - 4 x^{7} + 30 x^{6} - 76 x^{5} + 205 x^{4} - 288 x^{3} + 356 x^{2} - 224 x + 98$	$8$	[0,4]	$2^{22}\cdot 113^{2}$	$2$	$21.9332050578$	$71.51081206042281$	✓		?	$C_2^3: C_4$ (as 8T20)	$[14]$	$2$	$3$	$19.534360053$
8.0.53824000000.4	$x^{8} - 2 x^{7} + 5 x^{6} - 2 x^{5} + 54 x^{4} - 18 x^{3} + 185 x^{2} - 138 x + 711$	$8$	[0,4]	$2^{12}\cdot 5^{6}\cdot 29^{2}$	$3$	$21.9468399354$	$50.92974429446663$	✓			$D_4\times C_2$ (as 8T9)	$[12]$	$2$	$3$	$12.3400472787$
8.0.53824000000.6	$x^{8} - 2 x^{7} + 15 x^{6} - 12 x^{5} + 129 x^{4} + 12 x^{3} + 525 x^{2} - 118 x + 1321$	$8$	[0,4]	$2^{12}\cdot 5^{6}\cdot 29^{2}$	$3$	$21.9468399354$	$50.92974429446663$	✓		?	$C_2^2:C_4$ (as 8T10)	$[12]$	$2$	$3$	$6.60055078348$
8.0.53824000000.12	$x^{8} + 6 x^{6} + 136 x^{4} + 1856 x^{2} + 13456$	$8$	[0,4]	$2^{12}\cdot 5^{6}\cdot 29^{2}$	$3$	$21.9468399354$	$50.92974429446663$	✓		?	$C_2^2:C_4$ (as 8T10)	$[12]$	$10$	$3$	$52.2683814915$
8.0.54414344192.14	$x^{8} + 14 x^{6} - 8 x^{5} + 47 x^{4} - 68 x^{3} + 34 x^{2} - 68 x + 102$	$8$	[0,4]	$2^{16}\cdot 13^{2}\cdot 17^{3}$	$3$	$21.9767857816$	$120.74477832264238$			?	$(C_4^2 : C_2):C_2$ (as 8T26)	$[12]$	$2$	$3$	$60.8252809907$
8.0.54539063296.2	$x^{8} + 2 x^{6} - 4 x^{5} + 51 x^{4} - 104 x^{3} + 190 x^{2} - 64 x + 284$	$8$	[0,4]	$2^{12}\cdot 41^{2}\cdot 89^{2}$	$3$	$21.98307589800041$	$170.85666507338834$	✓			$C_2^2 \wr C_2$ (as 8T18)	$[13]$	$2$	$3$	$17.487649653532788$