Number field search results

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

Results (19 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
11.5.132326332471.1	$x^{11} - 2 x^{10} + 2 x^{7} + x^{6} - 3 x^{5} + 2 x^{2} + x - 1$	$11$	[5,3]	$-\,211441\cdot 625831$	$2$	$10.2579068817$	$363766.8655485268$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$15.3396861125$
11.5.145065457639.1	$x^{11} - x^{10} - 4 x^{9} + 7 x^{8} + 4 x^{7} - 9 x^{6} - 5 x^{5} + 2 x^{4} + 8 x^{3} + 2 x^{2} - 3 x - 1$	$11$	[5,3]	$-\,2389\cdot 2617\cdot 23203$	$3$	$10.3439791741$	$380874.5956860342$			?	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$16.2407020956$
11.5.157519649831.1	$x^{11} - x^{10} - x^{9} - x^{7} + x^{6} + 2 x^{4} + 3 x^{3} - 2 x - 1$	$11$	[5,3]	$-\,19457\cdot 8095783$	$2$	$10.4217228987$	$396887.4523476397$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$17.2118083495$
11.5.167050542839.1	$x^{11} - 2 x^{10} + 2 x^{9} - 3 x^{7} + x^{6} - x^{5} + 2 x + 1$	$11$	[5,3]	$-\,2089\cdot 79966751$	$2$	$10.4775296669$	$408718.1704292091$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$17.654115853304827$
11.5.167720394923.1	$x^{11} - 2 x^{10} - 3 x^{9} + 9 x^{8} - x^{7} - 13 x^{6} + 9 x^{5} + 7 x^{4} - 5 x^{3} - 1$	$11$	[5,3]	$-\,167720394923$	$1$	$10.4813421415$	$409536.80533378193$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$17.7118832979$
11.5.200601609583.1	$x^{11} + x^{9} - 2 x^{7} - x^{6} - 3 x^{5} + x^{4} + x^{3} + x^{2} + x - 1$	$11$	[5,3]	$-\,200601609583$	$1$	$10.6533193695$	$447885.7104027767$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$19.635566037183242$
11.5.234360387559.1	$x^{11} + x^{9} - 2 x^{8} - x^{7} - x^{5} - x^{3} + 2 x^{2} + x - 1$	$11$	[5,3]	$-\,71\cdot 3300850529$	$2$	$10.8050265172$	$484107.8263765212$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$21.919668485422946$
11.5.236131740703.1	$x^{11} - x^{10} - 2 x^{9} + 2 x^{8} - x^{7} + 2 x^{5} - x^{4} + x^{3} + x^{2} - 1$	$11$	[5,3]	$-\,372881\cdot 633263$	$2$	$10.8124254085$	$485933.8851150432$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$22.027596379016778$
11.5.248686333151.1	$x^{11} - 2 x^{9} - x^{7} - x^{6} + 2 x^{3} + x + 1$	$11$	[5,3]	$-\,2381\cdot 104446171$	$2$	$10.863464669$	$498684.6028814204$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$22.52935578711483$
11.5.987614208000000000.1	$x^{11} - x^{10} + 9 x^{9} - 45 x^{8} - 180 x^{6} + 120 x^{5} + 720 x^{4} + 285 x^{3} + 455 x^{2} - 35 x - 105$	$11$	[5,3]	$-\,2^{19}\cdot 3^{9}\cdot 5^{9}\cdot 7^{2}$	$4$	$43.2385951874$	$267.5908462678598$				$S_{11}$ (as 11T8)	trivial	$2$	$7$	$1376067.70771$
11.5.195...000.1	$x^{11} - 5 x^{10} + 10 x^{9} + 8 x^{8} - 115 x^{7} + 47 x^{6} + 425 x^{5} + 65 x^{4} - 184 x^{3} - 1020 x^{2} - 960 x - 240$	$11$	[5,3]	$-\,2^{15}\cdot 3^{13}\cdot 5^{6}\cdot 7^{4}$	$4$	$46.0183207242$	$288.40767800645347$			?	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$1139358.89632$
11.5.520...000.1	$x^{11} - x^{10} - 18 x^{9} + 90 x^{7} - 114 x^{6} - 390 x^{5} + 678 x^{4} - 405 x^{3} - 1035 x^{2} + 1080 x + 270$	$11$	[5,3]	$-\,2^{23}\cdot 3^{10}\cdot 5^{4}\cdot 7^{5}$	$4$	$50.2897333839$	$747.7885817500154$				$S_{11}$ (as 11T8)	trivial	$2$	$7$	$5645514.82931$
11.5.637...000.1	$x^{11} - x^{10} - 20 x^{9} + 30 x^{8} + 90 x^{7} - 90 x^{6} - 30 x^{5} - 1110 x^{4} + 2280 x^{3} - 1000 x^{2} + 328 x - 568$	$11$	[5,3]	$-\,2^{14}\cdot 3^{13}\cdot 5^{12}$	$3$	$51.2285886435$	$293.8430827385019$			?	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$2859461.06402$
11.5.967...000.1	$x^{11} - 4 x^{10} + 6 x^{9} - 8 x^{8} - 31 x^{7} + 168 x^{6} + 106 x^{5} - 748 x^{4} - 396 x^{3} + 1008 x^{2} + 882 x + 168$	$11$	[5,3]	$-\,2^{19}\cdot 3^{9}\cdot 5^{8}\cdot 7^{4}$	$4$	$53.2087475948$	$332.46081383675426$				$S_{11}$ (as 11T8)	trivial	$2$	$7$	$8123279.63873$
11.5.847...000.1	$x^{11} - x^{10} + 10 x^{9} - 405 x^{3} + 405 x^{2} + 324 x - 324$	$11$	[5,3]	$-\,2^{8}\cdot 3^{25}\cdot 5^{8}$	$3$	$64.8095812334$	$202.89500913181897$			?	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$5378394.89404$
11.5.245...000.1	$x^{11} - 4 x^{10} - 2 x^{9} + 36 x^{8} - 30 x^{7} - 264 x^{6} - 16 x^{5} + 1078 x^{4} + 2261 x^{3} - 1220 x^{2} - 5185 x - 1382$	$11$	[5,3]	$-\,2^{10}\cdot 3^{12}\cdot 5^{7}\cdot 7^{8}$	$4$	$71.3798114949$	$740.633570458652$			?	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$10477083.7506$
11.5.287...000.1	$x^{11} - 2 x^{10} - 20 x^{9} + 105 x^{8} - 255 x^{7} - 444 x^{6} + 4878 x^{5} - 12735 x^{4} + 14040 x^{3} - 3040 x^{2} - 6016 x - 1048$	$11$	[5,3]	$-\,2^{20}\cdot 3^{15}\cdot 5^{8}\cdot 7^{2}$	$4$	$72.4341166334$	$1261.9981524803231$				$S_{11}$ (as 11T8)	trivial	$2$	$7$	$60162090.9342$
11.5.941...000.1	$x^{11} - 2 x^{10} - 14 x^{9} + 63 x^{8} + 108 x^{7} - 351 x^{6} - 1119 x^{5} - 957 x^{4} + 375 x^{3} + 812 x^{2} + 203 x - 91$	$11$	[5,3]	$-\,2^{9}\cdot 3^{14}\cdot 5^{6}\cdot 7^{5}\cdot 11^{4}$	$5$	$99.4540768028$	$6154.131433480169$			?	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$85295653.9896$
11.5.467...000.1	$x^{11} - 3 x^{10} - 50 x^{9} + 142 x^{8} + 299 x^{7} - 1207 x^{6} + 1430 x^{5} - 3722 x^{4} + 10566 x^{3} - 12480 x^{2} + 4650 x + 630$	$11$	[5,3]	$-\,2^{13}\cdot 3^{7}\cdot 5^{8}\cdot 7^{3}\cdot 11^{7}$	$5$	$115.056955954$	$4670.1112810272725$				$S_{11}$ (as 11T8)	trivial	$2$	$7$	$1057226413.01$