Number field search results

Results (30 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	Unit group torsion	Unit group rank	Regulator
9.1.80190448927744.1	$x^{9} - 2 x^{8} + 12 x^{7} + 4 x^{6} + 14 x^{5} + 140 x^{4} - 48 x^{3} + 412 x^{2} - 51 x + 342$	$9$	[1,4]	$2^{10}\cdot 23^{8}$	$2$	$35.0673151267$	$40.90704143524191$				$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30)	$[2]$	$2$	$4$	$7789.27566117$
9.3.200476122319360.1	$x^{9} - 3 x^{8} + 4 x^{7} + 2 x^{6} + 68 x^{5} - 176 x^{4} - 104 x^{3} + 488 x^{2} - 240 x - 32$	$9$	[3,3]	$-\,2^{9}\cdot 5\cdot 23^{8}$	$3$	$38.8255907639$	$102.67264229377021$			?	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$5$	$16948.2217361$
9.1.320761795710976.1	$x^{9} - 4 x^{8} + 2 x^{7} - 14 x^{6} - 6 x^{5} + 18 x^{4} + 10 x^{3} - 118 x^{2} - 15 x - 18$	$9$	[1,4]	$2^{12}\cdot 23^{8}$	$2$	$40.9070414352$	$64.93588060720973$				$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30)	$[2]$	$2$	$4$	$33495.2045165$
9.1.541285530262272.1	$x^{9} - x^{8} + 3 x^{7} - 11 x^{6} + 21 x^{5} - 79 x^{4} + 166 x^{3} - 216 x^{2} + 213 x - 81$	$9$	[1,4]	$2^{8}\cdot 3^{3}\cdot 23^{8}$	$3$	$43.3558175214$	$70.85307415316427$			?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$14869.2766274$
9.1.1283047182843904.1	$x^{9} - 23 x^{6} + 23 x^{5} + 46 x^{4} + 138 x^{3} - 161 x^{2} - 276 x - 460$	$9$	[1,4]	$2^{14}\cdot 23^{8}$	$2$	$47.7192517574$	$109.20869844789173$				$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30)	trivial	$2$	$4$	$132501.665863$
9.1.1623856590786816.1	$x^{9} - 3 x^{8} + 4 x^{7} + 2 x^{6} - 24 x^{5} + 8 x^{4} + 126 x^{3} - 294 x^{2} + 243 x - 9$	$9$	[1,4]	$2^{8}\cdot 3^{4}\cdot 23^{8}$	$3$	$48.9847451013$	$68.5248198611294$			?	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30)	$[2]$	$2$	$4$	$28455.2312338$
9.5.3132439411240000.1	$x^{9} - 3 x^{8} - 19 x^{7} + 71 x^{6} + 22 x^{5} - 360 x^{4} + 448 x^{3} + 120 x^{2} - 608 x + 336$	$9$	[5,2]	$2^{6}\cdot 5^{4}\cdot 23^{8}$	$3$	$52.6944337722$	$86.16659076535258$			?	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30)	trivial	$2$	$6$	$161543.54302$
9.1.3247713181573632.1	$x^{9} - x^{8} + 3 x^{7} + 35 x^{6} - 94 x^{5} + 358 x^{4} - 593 x^{3} + 911 x^{2} - 661 x + 425$	$9$	[1,4]	$2^{9}\cdot 3^{4}\cdot 23^{8}$	$3$	$52.9064510038$	$104.66721719548653$				$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$160929.86488$
9.1.3653677329270336.1	$x^{9} - 4 x^{8} + 25 x^{7} - 60 x^{6} + 155 x^{5} - 212 x^{4} + 171 x^{3} + 20 x^{2} - 176 x - 64$	$9$	[1,4]	$2^{6}\cdot 3^{6}\cdot 23^{8}$	$3$	$53.603388402$	$95.7207822122898$			?	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30)	trivial	$2$	$4$	$41313.3107106$
9.1.8019044892774400.1	$x^{9} - 4 x^{8} + 2 x^{7} + 78 x^{6} - 328 x^{5} + 340 x^{4} + 401 x^{3} - 348 x^{2} - 958 x + 856$	$9$	[1,4]	$2^{12}\cdot 5^{2}\cdot 23^{8}$	$3$	$58.495807201$	$102.67264229377021$				$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30)	trivial	$2$	$4$	$199972.818026$
9.5.12529757644960000.1	$x^{9} - x^{8} - 20 x^{7} + 58 x^{6} - 94 x^{5} + 82 x^{4} - 18 x^{3} - 32 x^{2} + 75 x - 35$	$9$	[5,2]	$2^{8}\cdot 5^{4}\cdot 23^{8}$	$3$	$61.4695872193$	$81.49133019274275$			?	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30)	trivial	$2$	$6$	$375935.126178$
9.1.14614709317081344.1	$x^{9} - 3 x^{8} + 4 x^{7} + 2 x^{6} - 24 x^{5} + 238 x^{4} - 610 x^{3} - 18 x^{2} + 2773 x - 4793$	$9$	[1,4]	$2^{8}\cdot 3^{6}\cdot 23^{8}$	$3$	$62.5299091906$	$111.66107214157705$			?	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30)	$[3]$	$2$	$4$	$41776.3216215$
9.5.28191954701160000.1	$x^{9} - 2 x^{8} - 11 x^{7} - 42 x^{6} + 129 x^{5} + 600 x^{4} - 485 x^{3} - 1658 x^{2} - 626 x - 210$	$9$	[5,2]	$2^{6}\cdot 3^{2}\cdot 5^{4}\cdot 23^{8}$	$4$	$67.2653935793$	$99.80608871644023$			?	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30)	trivial	$2$	$6$	$981604.808622$
9.1.117515422287300625.1	$x^{9} - 3 x^{8} + 27 x^{7} - 67 x^{6} + 390 x^{5} - 475 x^{4} + 2633 x^{3} - 1191 x^{2} + 1669 x + 13400$	$9$	[1,4]	$5^{4}\cdot 7^{4}\cdot 23^{8}$	$3$	$78.8274009104$	$96.04146261452098$				$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30)	$[4]$	$2$	$4$	$419640.600702$
9.1.131532383853732096.1	$x^{9} - 2 x^{8} - 34 x^{7} + 50 x^{6} + 336 x^{5} - 504 x^{4} - 1060 x^{3} + 1424 x^{2} + 11656 x + 41512$	$9$	[1,4]	$2^{8}\cdot 3^{8}\cdot 23^{8}$	$3$	$79.82055505843509$	$171.1783942507293$			?	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30)	trivial	$2$	$4$	$509490.5851265325$
9.1.166470673314879684.1	$x^{9} - 69 x^{6} + 1587 x^{3} + 2116$	$9$	[1,4]	$2^{2}\cdot 3^{12}\cdot 23^{8}$	$3$	$81.9373606959$	$118.51677254412442$			?	$(C_3^3:C_3):C_2$ (as 9T21)	trivial	$2$	$4$	$229115.26089$
9.1.199...449.1	$x^{9} - 16767 x^{4} - 217971 x^{3} - 1810836 x^{2} - 7243344 x - 10814715$	$9$	[1,4]	$3^{26}\cdot 23^{8}$	$2$	$387.9493553459356$	$465.902717571641$			?	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30)	$[8]$	$2$	$4$	$30800203.2192838$
10.2.332...000.1	$x^{10} - 690 x^{7} + 158700 x^{4} - 12167000 x + 22667121$	$10$	[2,4]	$2^{11}\cdot 3^{12}\cdot 5^{8}\cdot 23^{8}$	$4$	$356.645520142$	$2601.081123171644$			?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$4199739778.22$
10.2.849...000.1	$x^{10} - 33534 x^{5} - 4471200 x^{3} - 74520000 x + 281132289$	$10$	[2,4]	$2^{15}\cdot 3^{25}\cdot 5^{8}\cdot 23^{8}$	$4$	$1962.93718682$	$17653.93490151343$			?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$26062528660400$
10.0.133...000.1	$x^{10} - 26082 x^{5} + 579600 x^{3} - 1610000 x + 170067681$	$10$	[0,5]	$-\,2^{10}\cdot 3^{10}\cdot 5^{11}\cdot 7^{8}\cdot 23^{8}$	$5$	$2053.42552398$	$30335.783313274234$			?	$S_{10}$ (as 10T45)	$[3]$	$2$	$4$	$9836152021940$
10.2.924...000.1	$x^{10} - 160 x^{8} - 1600 x^{7} + 29040 x^{6} + 111040 x^{5} - 1933280 x^{4} - 4310400 x^{3} + 66307880 x^{2} + 65270400 x - 917798472$	$10$	[2,4]	$2^{19}\cdot 3^{10}\cdot 5^{18}\cdot 23^{8}$	$4$	$2492.33561264$	$26367.317845528076$				$S_{10}$ (as 10T45)	trivial	$2$	$5$	$136616577799000$
10.2.711...000.1	$x^{10} - 3450 x^{7} + 3967500 x^{4} - 1520875000 x + 5100102225$	$10$	[2,4]	$2^{11}\cdot 3^{19}\cdot 5^{18}\cdot 23^{8}$	$4$	$3847.61541325$	$29073.309426575124$			?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$533778400213000$
10.0.431...000.1	$x^{10} + 900 x^{8} - 19800 x^{7} + 317250 x^{6} - 2485080 x^{5} + 13271400 x^{4} - 32329800 x^{3} + 49679325 x^{2} + 33742200 x + 165200580$	$10$	[0,5]	$-\,2^{10}\cdot 3^{24}\cdot 5^{19}\cdot 23^{8}$	$4$	$7303.75647012$	$40833.874212151415$			?	$S_{10}$ (as 10T45)	$[2, 2]$	$2$	$4$	$1406320448360000$
10.0.758...000.1	$x^{10} + 1152 x^{8} - 360 x^{7} + 517050 x^{6} - 37800 x^{5} + 115470000 x^{4} - 675000 x^{3} + 12969703125 x^{2} - 1875000 x + 583571250000$	$10$	[0,5]	$-\,2^{11}\cdot 3^{24}\cdot 5^{7}\cdot 11^{8}\cdot 23^{8}$	$5$	$7726.79564806$	$119435.79829978883$			?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$10007039169600000$
10.0.414...000.1	$x^{10} - 838350 x^{5} + 558900000 x^{3} - 46575000000 x + 175707680625$	$10$	[0,5]	$-\,2^{15}\cdot 3^{25}\cdot 5^{19}\cdot 23^{8}$	$4$	$11528.5160187$	$78442.91514510846$			?	$S_{10}$ (as 10T45)	$[2, 2]$	$2$	$4$	$23449906840200000$
10.0.221...000.1	$x^{10} + 450 x^{8} - 14400 x^{7} + 599400 x^{6} - 8536320 x^{5} + 96325200 x^{4} - 568684800 x^{3} + 3016731600 x^{2} - 6999859200 x + 23436876960$	$10$	[0,5]	$-\,2^{19}\cdot 3^{24}\cdot 5^{19}\cdot 23^{8}$	$4$	$13629.2914976$	$76198.70362440265$			?	$S_{10}$ (as 10T45)	$[2]$	$2$	$4$	$68649670193200000$
10.0.802...000.1	$x^{10} - 1639440 x^{5} + 1457280000 x^{3} - 161920000000 x + 671940878400$	$10$	[0,5]	$-\,2^{19}\cdot 3^{14}\cdot 5^{19}\cdot 11^{8}\cdot 23^{8}$	$5$	$30936.1434976$	$146446.58955424774$			?	$S_{10}$ (as 10T45)	$[2]$	$2$	$4$	$7146134103780000000$
10.0.442...000.1	$x^{10} - 70421400 x^{5} + 281685600000 x^{3} - 140842800000000 x + 1239793394490000$	$10$	[0,5]	$-\,2^{14}\cdot 3^{22}\cdot 5^{19}\cdot 7^{8}\cdot 23^{8}$	$5$	$36695.4707443$	$144594.38809596232$			?	$S_{10}$ (as 10T45)	$[2, 2]$	$2$	$4$	$6809849089430000000$
12.2.233...112.1	$x^{12} - 64 x^{9} + 368 x^{3} + 2944$	$12$	[2,5]	$-\,2^{8}\cdot 3^{19}\cdot 23^{8}$	$3$	$73.1050212624$	$171.1783942507293$			?	$C_3^3:S_4$ (as 12T177)	trivial	$2$	$6$	$15403399.8971$
12.2.597...347.1	$x^{12} - x^{11} + 13 x^{10} + 54 x^{9} + 348 x^{8} + 1416 x^{7} + 2856 x^{6} + 6720 x^{5} + 6816 x^{4} + 4528 x^{3} + 215 x^{2} - 338 x - 57$	$12$	[2,5]	$-\,3^{27}\cdot 23^{8}$	$2$	$95.7946776735$	$465.902717571641$			?	$C_3^3:S_4$ (as 12T177)	trivial	$2$	$6$	$63508116.7925$

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