Number field search results

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

Results (26 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
22.4.931...016.1	$x^{22} - 4 x^{21} + 5 x^{20} + 4 x^{19} - 26 x^{18} + 31 x^{17} + 15 x^{16} - 79 x^{15} + 76 x^{14} + 60 x^{13} - 153 x^{12} + 84 x^{11} + 83 x^{10} - 192 x^{9} + 24 x^{8} + 58 x^{7} - 150 x^{6} + 30 x^{5} + 19 x^{4} - 23 x^{3} + 6 x^{2} + 29 x + 1$	$22$	[4,9]	$-\,2^{12}\cdot 11^{7}\cdot 19^{4}\cdot 547^{4}$	$4$	$16.8215855911$	$1193.6702363351474$			?	$C_2^{11}.A_{11}$ (as 22T52)	trivial	$2$	$12$	$56735.8548792$
22.4.951...707.1	$x^{22} - 11 x^{21} + 66 x^{20} - 275 x^{19} + 879 x^{18} - 2268 x^{17} + 4871 x^{16} - 8878 x^{15} + 13903 x^{14} - 18847 x^{13} + 22192 x^{12} - 22691 x^{11} + 20056 x^{10} - 15173 x^{9} + 9644 x^{8} - 4974 x^{7} + 1932 x^{6} - 448 x^{5} - 27 x^{4} + 71 x^{3} - 24 x^{2} + x + 1$	$22$	[4,9]	$-\,139\cdot 1583^{2}\cdot 2731^{2}\cdot 6217^{2}\cdot 9473$	$5$	$16.8377853307$	$188123439.29282743$			✓	$C_2^{10}.(C_2\times S_{11})$ (as 22T53)	trivial	$2$	$12$	$43108.9874663$
22.4.969...159.1	$x^{22} - x^{21} + 3 x^{20} + 3 x^{18} + 5 x^{17} + 7 x^{16} + 4 x^{15} + 12 x^{14} - 17 x^{13} - 35 x^{11} - 28 x^{10} - 29 x^{9} - 20 x^{8} - 6 x^{7} - 11 x^{6} - 26 x^{5} - 22 x^{4} - 11 x^{3} - 4 x^{2} + 9 x - 1$	$22$	[4,9]	$-\,173\cdot 7043\cdot 28208540809^{2}$	$3$	$16.8524111845$	$185392519.41428798$			?	$C_2^{10}.(C_2\times S_{11})$ (as 22T53)	trivial	$2$	$12$	$42357.726741$
22.4.153...375.1	$x^{22} - 2 x^{21} + 7 x^{20} - 20 x^{19} + 38 x^{18} - 74 x^{17} + 107 x^{16} - 167 x^{15} + 185 x^{14} - 284 x^{13} + 308 x^{12} - 417 x^{11} + 466 x^{10} - 462 x^{9} + 446 x^{8} - 292 x^{7} + 170 x^{6} - 55 x^{5} - 7 x^{4} + 11 x^{3} - 8 x^{2} + x + 1$	$22$	[4,9]	$-\,5^{4}\cdot 7^{4}\cdot 83^{5}\cdot 127^{4}\cdot 997$	$5$	$17.2071065975$	$187563.85877253$			?	$C_2^{11}.A_{11}$ (as 22T52)	trivial	$2$	$12$	$56909.7191275$
22.4.189...683.1	$x^{22} - x^{21} + x^{20} + x^{19} + x^{18} + 5 x^{17} - 11 x^{16} + 6 x^{15} + 19 x^{14} - 22 x^{13} - 4 x^{12} + 6 x^{11} + 13 x^{10} + 26 x^{9} - 75 x^{8} - 11 x^{7} + 101 x^{6} - 32 x^{5} - 59 x^{4} + 28 x^{3} + 15 x^{2} - 6 x - 1$	$22$	[4,9]	$-\,47147\cdot 200601609583^{2}$	$2$	$17.3745944722$	$97251036.43154505$			?	$C_2^{10}.(C_2\times S_{11})$ (as 22T53)	trivial	$2$	$12$	$64048.1745685$
22.4.255...823.1	$x^{22} - x^{21} - 4 x^{20} + 5 x^{19} + 9 x^{18} - 14 x^{17} - 15 x^{16} + 28 x^{15} + 20 x^{14} - 44 x^{13} - 20 x^{12} + 55 x^{11} + 15 x^{10} - 55 x^{9} - 9 x^{8} + 45 x^{7} + x^{6} - 28 x^{5} + 2 x^{4} + 12 x^{3} - 2 x^{2} - 3 x + 1$	$22$	[4,9]	$-\,13\cdot 769\cdot 941\cdot 27630898417\cdot 98112787247$	$5$	$19.5527649214$	$159694503199018.72$			?	$S_{22}$ (as 22T59)	trivial	$2$	$12$	$336664.263278$
22.4.120...063.1	$x^{22} - 3 x^{21} + 2 x^{20} + 6 x^{19} - 15 x^{18} + 11 x^{17} + 10 x^{16} - 31 x^{15} + 28 x^{14} + 2 x^{13} - 32 x^{12} + 35 x^{11} - 11 x^{10} - 16 x^{9} + 25 x^{8} - 14 x^{7} - 4 x^{6} + 10 x^{5} - 8 x^{4} + 2 x^{3} + 2 x^{2} - 2 x + 1$	$22$	[4,9]	$-\,13\cdot 9292748844744727822944291851$	$2$	$20.9851979667$	$347571194119537.9$			?	$S_{22}$ (as 22T59)	trivial	$2$	$12$	$1008504.24777$
22.4.156...136.1	$x^{22} + 10 x^{20} + 41 x^{18} + 85 x^{16} + 79 x^{14} - 14 x^{12} - 98 x^{10} - 74 x^{8} - 3 x^{6} + 22 x^{4} + 9 x^{2} + 1$	$22$	[4,9]	$-\,2^{22}\cdot 610429790897^{2}$	$2$	$23.5749849842$				?	$C_2^{10}.(C_2\times S_{11})$ (as 22T53)	trivial	$2$	$12$	$1423923.02805$
22.4.156...136.2	$x^{22} - 7 x^{20} + 15 x^{18} - 4 x^{16} - 28 x^{14} + 36 x^{12} + 7 x^{10} - 49 x^{8} - 5 x^{6} + 24 x^{4} + 10 x^{2} + 1$	$22$	[4,9]	$-\,2^{22}\cdot 610429790897^{2}$	$2$	$23.5749849842$				?	$C_2^{10}.(C_2\times S_{11})$ (as 22T53)	trivial	$2$	$12$	$1658767.52591$
22.4.121...376.1	$x^{22} - 2 x^{21} - x^{20} + 10 x^{19} - 11 x^{18} - 10 x^{17} + 34 x^{16} - 18 x^{15} - 34 x^{14} + 50 x^{13} + x^{12} - 52 x^{11} + 28 x^{10} + 28 x^{9} - 36 x^{8} - 2 x^{7} + 23 x^{6} - 8 x^{5} - 6 x^{4} + 6 x^{3} - x^{2} - 2 x + 1$	$22$	[4,9]	$-\,2^{33}\cdot 1416632312516459164303$	$2$	$25.8800894313$				✓	$S_{11}\wr C_2$ (as 22T57)	trivial	$2$	$12$	$7756722.0684$
22.4.319...072.1	$x^{22} - 2 x^{21} + 3 x^{20} - 2 x^{19} - 3 x^{18} + 6 x^{17} - 10 x^{16} + 6 x^{15} + 2 x^{14} - 6 x^{13} + 13 x^{12} - 4 x^{11} + 4 x^{9} - 8 x^{8} - 2 x^{7} - x^{6} - 4 x^{5} + 2 x^{4} + 2 x^{3} + x^{2} + 2 x - 1$	$22$	[4,9]	$-\,2^{33}\cdot 235475711\cdot 15802753811681$	$3$	$27.0414762933$				?	$S_{11}\wr C_2$ (as 22T57)	trivial	$2$	$12$	$12970191.905$
22.4.178...423.1	$x^{22} - 3 x^{21} - 4 x^{20} + 21 x^{19} - 34 x^{18} - 64 x^{17} + 209 x^{16} - 79 x^{15} - 626 x^{14} + 986 x^{13} + 469 x^{12} - 2461 x^{11} + 890 x^{10} + 2535 x^{9} - 360 x^{8} - 4500 x^{7} - 1390 x^{6} + 7497 x^{5} - 2384 x^{4} - 6847 x^{3} + 1939 x^{2} + 3881 x - 2897$	$22$	[4,9]	$-\,23^{20}\cdot 47^{3}$	$2$	$29.2380053103$	$118.57232216797493$			?	$C_{15}\times C_{420}$ (as 22T28)	trivial	$2$	$12$	$18036839.011$
22.4.315...056.1	$x^{22} + 12 x^{20} + 58 x^{18} + 144 x^{16} + 193 x^{14} + 130 x^{12} + 21 x^{10} - 40 x^{8} - 45 x^{6} - 18 x^{4} + 1$	$22$	[4,9]	$-\,2^{22}\cdot 8674315276967^{2}$	$2$	$30.0077336219$				✓	$C_2^{10}.(C_2\times S_{11})$ (as 22T53)	trivial	$2$	$12$	$22686333.3679$
22.4.316...496.1	$x^{22} + 14 x^{20} + 84 x^{18} + 285 x^{16} + 607 x^{14} + 843 x^{12} + 745 x^{10} + 363 x^{8} + 45 x^{6} - 29 x^{4} - 6 x^{2} + 1$	$22$	[4,9]	$-\,2^{22}\cdot 151^{2}\cdot 2311^{2}\cdot 24910163^{2}$	$4$	$30.0135021259$				✓	$C_2^{10}.(C_2\times S_{11})$ (as 22T53)	trivial	$2$	$12$	$31745730.4838$
22.4.529...664.1	$x^{22} + 3 x^{20} + 23 x^{18} - 39 x^{16} + 58 x^{14} + 58 x^{12} - 275 x^{10} + 455 x^{8} - 258 x^{6} + 12 x^{4} + 12 x^{2} + 1$	$22$	[4,9]	$-\,2^{22}\cdot 1831^{8}$	$2$	$30.7228938871$				?	$C_2^{11}.\PSL(2,11)$ (as 22T42)	trivial	$2$	$12$	$80983919.0392$
22.4.529...664.2	$x^{22} - 3 x^{20} - x^{18} + 4 x^{16} + 12 x^{14} - 14 x^{12} - 6 x^{10} + 6 x^{8} - 8 x^{6} + 11 x^{4} - 6 x^{2} + 1$	$22$	[4,9]	$-\,2^{22}\cdot 1831^{8}$	$2$	$30.7228938871$				?	$C_2^{11}.\PSL(2,11)$ (as 22T42)	trivial	$2$	$12$	$80016323.2055$
22.4.529...664.3	$x^{22} + 7 x^{20} + 3 x^{18} - 38 x^{16} - 33 x^{14} + 67 x^{12} + 54 x^{10} - 34 x^{8} - x^{6} - 8 x^{4} - 32 x^{2} + 1$	$22$	[4,9]	$-\,2^{22}\cdot 1831^{8}$	$2$	$30.722893887080275$				?	$C_2^{11}.\PSL(2,11)$ (as 22T42)	trivial	$2$	$12$	$73988407.3308737$
22.4.529...664.4	$x^{22} - 6 x^{20} + 27 x^{18} - 45 x^{16} + 75 x^{14} + 14 x^{12} + 186 x^{10} - 50 x^{8} - 26 x^{6} + 19 x^{4} - 7 x^{2} + 1$	$22$	[4,9]	$-\,2^{22}\cdot 1831^{8}$	$2$	$30.722893887080275$				?	$C_2^{11}.\PSL(2,11)$ (as 22T42)	trivial	$2$	$12$	$146862423.21781206$
22.4.719...104.1	$x^{22} + 17 x^{20} + 100 x^{18} + 265 x^{16} + 265 x^{14} - 217 x^{12} - 833 x^{10} - 861 x^{8} - 405 x^{6} - 79 x^{4} - x^{2} + 1$	$22$	[4,9]	$-\,2^{22}\cdot 23^{20}$	$2$	$34.5911015298$				✓	$C_{15}\times C_{420}$ (as 22T28)	trivial	$2$	$12$	$116519071.103$
22.4.338...896.1	$x^{22} + 16 x^{20} + 105 x^{18} + 363 x^{16} + 700 x^{14} + 709 x^{12} + 248 x^{10} - 146 x^{8} - 135 x^{6} - 20 x^{4} + 5 x^{2} + 1$	$22$	[4,9]	$-\,2^{22}\cdot 2053^{2}\cdot 43747835269^{2}$	$3$	$37.112136067$				✓	$C_2^{10}.(C_2\times S_{11})$ (as 22T53)	trivial	$2$	$12$	$226542958.357$
22.4.390...976.1	$x^{22} + 15 x^{20} + 91 x^{18} + 279 x^{16} + 417 x^{14} + 130 x^{12} - 453 x^{10} - 544 x^{8} - 66 x^{6} + 185 x^{4} + 75 x^{2} + 1$	$22$	[4,9]	$-\,2^{22}\cdot 137^{2}\cdot 293^{2}\cdot 11093^{2}\cdot 216649^{2}$	$5$	$37.3541218434$				✓	$C_2^{10}.(C_2\times S_{11})$ (as 22T53)	trivial	$2$	$12$	$311350306.426$
22.4.153...043.1	$x^{22} - 11 x^{21} + 72 x^{20} - 335 x^{19} + 1211 x^{18} - 3546 x^{17} + 8610 x^{16} - 17574 x^{15} + 30322 x^{14} - 44228 x^{13} + 54150 x^{12} - 54734 x^{11} + 44075 x^{10} - 25887 x^{9} + 7693 x^{8} + 4031 x^{7} - 7645 x^{6} + 6006 x^{5} - 3064 x^{4} + 1060 x^{3} - 235 x^{2} + 28 x - 1$	$22$	[4,9]	$-\,151\cdot 757\cdot 1297^{10}$	$3$	$44.1453655736$	$12176.049400359709$			?	$C_2^{10}.D_{22}$ (as 22T32)	trivial	$2$	$12$	$1728453729.71$
22.4.565...896.1	$x^{22} + 14 x^{20} + 48 x^{18} - 43 x^{16} - 492 x^{14} - 675 x^{12} + 603 x^{10} + 2355 x^{8} + 2294 x^{6} + 937 x^{4} + 136 x^{2} + 1$	$22$	[4,9]	$-\,2^{22}\cdot 1297^{10}$	$2$	$51.9999243795$				?	$C_2^{10}.D_{22}$ (as 22T32)	trivial	$2$	$12$	$14806795493.8$
22.4.162...712.1	$x^{22} + 22 x^{20} - 44 x^{19} + 308 x^{18} - 682 x^{17} + 5148 x^{16} - 4884 x^{15} + 20746 x^{14} - 37576 x^{13} + 458128 x^{12} + 582788 x^{11} + 2492600 x^{10} - 5616732 x^{9} + 12766776 x^{8} + 72829196 x^{7} + 27797264 x^{6} - 125806824 x^{5} - 187011000 x^{4} - 118806292 x^{3} - 39878476 x^{2} - 6794304 x - 306180$	$22$	[4,9]	$-\,2^{22}\cdot 7^{15}\cdot 11^{22}$	$3$	$82.9136225033$				?	$C_2\times C_2^{10}.F_{11}$ (as 22T37)	trivial	$2$	$12$	$17902679661000$
22.4.469...000.1	$x^{22} + 48 x^{20} + 915 x^{18} + 8805 x^{16} + 44865 x^{14} + 113886 x^{12} + 96498 x^{10} - 129690 x^{8} - 305910 x^{6} - 179685 x^{4} - 26136 x^{2} + 3267$	$22$	[4,9]	$-\,2^{10}\cdot 3^{21}\cdot 5^{20}\cdot 11^{16}$	$4$	$96.6205524058$	$307.89780414328396$			?	$C_2^{10}.C_{11}:C_{10}$ (as 22T36)	trivial	$2$	$12$	$99913368095300$
22.4.625...000.1	$x^{22} + 35 x^{20} + 145 x^{18} - 6780 x^{16} - 104715 x^{14} - 644565 x^{12} - 2013750 x^{10} - 3324525 x^{8} - 2834100 x^{6} - 1163300 x^{4} - 180475 x^{2} + 400$	$22$	[4,9]	$-\,2^{12}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16}$	$4$	$97.8923038661$				?	$C_2^{10}.C_{11}:C_{10}$ (as 22T36)	trivial	$2$	$12$	$60670586564600$
22.4.645...000.1	$x^{22} - 11 x^{21} + 5 x^{20} + 335 x^{19} - 810 x^{18} - 4452 x^{17} + 16362 x^{16} + 27510 x^{15} - 149325 x^{14} - 80365 x^{13} + 783995 x^{12} + 42265 x^{11} - 2559710 x^{10} + 447060 x^{9} + 5251710 x^{8} - 1715814 x^{7} - 6547836 x^{6} + 4250280 x^{5} + 4685800 x^{4} - 7571000 x^{3} - 3152200 x^{2} + 6276200 x + 3414000$	$22$	[4,9]	$-\,2^{36}\cdot 3^{17}\cdot 5^{37}$	$3$	$108.84778759$	$290.08437852363267$				$C_2^{11}.M_{11}$ (as 22T44)	trivial	$2$	$12$	$46335294924500000$
22.4.412...904.3	$x^{22} + 13 x^{20} - 95 x^{18} - 1487 x^{16} + 412 x^{14} + 38151 x^{12} + 113115 x^{10} + 117350 x^{8} + 43605 x^{6} + 6888 x^{4} + 449 x^{2} + 9$	$22$	[4,9]	$-\,2^{22}\cdot 74843^{8}$	$2$	$118.42642228905491$					$C_2^{11}.\PSL(2,11)$ (as 22T42)	trivial	$2$	$12$	$689407739728191.4$
22.4.666...496.1	$x^{22} + 14 x^{20} + 49 x^{18} - 84 x^{16} - 873 x^{14} - 2112 x^{12} - 2265 x^{10} - 576 x^{8} + 1248 x^{6} + 1432 x^{4} + 632 x^{2} + 64$	$22$	[4,9]	$-\,2^{48}\cdot 3^{28}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16}$	$5$	$1656.75242047$					$C_2^{11}.A_{11}$ (as 22T52)	trivial	$2$	$12$	$13265885053200000000000000000$