Number field search results

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

Results (20 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
22.0.293...624.1	$x^{22} + 69 x^{20} + 2070 x^{18} + 35397 x^{16} + 380052 x^{14} + 2660364 x^{12} + 12206376 x^{10} + 35965215 x^{8} + 64737387 x^{6} + 64737387 x^{4} + 29878794 x^{2} + 4074381$	$22$	[0,11]	$-\,2^{22}\cdot 3^{11}\cdot 23^{21}$	$3$	$69.0910414679$	$69.09104146788619$	✓	✓	?	$C_{22}$ (as 22T1)	$[2, 56764]$	$2$	$10$	$1038656.82438$
22.0.707...051.1	$x^{22} - x^{21} + 70 x^{20} - 70 x^{19} + 2140 x^{18} - 2140 x^{17} + 37537 x^{16} - 37537 x^{15} + 417589 x^{14} - 417589 x^{13} + 3077953 x^{12} - 3077953 x^{11} + 15284329 x^{10} - 15284329 x^{9} + 51249544 x^{8} - 51249544 x^{7} + 115986931 x^{6} - 115986931 x^{5} + 180724318 x^{4} - 180724318 x^{3} + 210603112 x^{2} - 210603112 x + 214677493$	$22$	[0,11]	$-\,13^{11}\cdot 23^{21}$	$2$	$71.9122359457$	$71.91223594570167$	✓	✓	?	$C_{22}$ (as 22T1)	$[138344]$	$2$	$10$	$1038656.82438$
22.0.199...019.1	$x^{22} - 9 x^{21} + 70 x^{20} - 363 x^{19} + 1845 x^{18} - 7462 x^{17} + 30023 x^{16} - 100740 x^{15} + 341082 x^{14} - 977548 x^{13} + 2866861 x^{12} - 7075946 x^{11} + 18221714 x^{10} - 38558891 x^{9} + 87678393 x^{8} - 156007735 x^{7} + 313286973 x^{6} - 448933295 x^{5} + 793158991 x^{4} - 832219241 x^{3} + 1285528692 x^{2} - 758821285 x + 1019110541$	$22$	[0,11]	$-\,19^{11}\cdot 23^{20}$	$2$	$75.3895579572$	$75.38955795715201$	✓	✓	?	$C_{22}$ (as 22T1)	$[408991]$	$2$	$10$	$1038656.82438$
22.0.351...000.1	$x^{22} - 2 x^{21} + 36 x^{20} - 62 x^{19} + 779 x^{18} - 1208 x^{17} + 11785 x^{16} - 16330 x^{15} + 135402 x^{14} - 166994 x^{13} + 1216660 x^{12} - 1317110 x^{11} + 8641614 x^{10} - 8043038 x^{9} + 48218481 x^{8} - 37307012 x^{7} + 206484136 x^{6} - 125495212 x^{5} + 645715650 x^{4} - 276536200 x^{3} + 1328901156 x^{2} - 304156912 x + 1368706081$	$22$	[0,11]	$-\,2^{22}\cdot 5^{11}\cdot 23^{20}$	$3$	$77.3480544373$	$77.34805443730704$	✓	✓	?	$C_{22}$ (as 22T1)	$[374638]$	$2$	$10$	$1038656.82438$
22.0.135...359.1	$x^{22} - x^{21} + 93 x^{20} - 93 x^{19} + 3773 x^{18} - 3773 x^{17} + 87677 x^{16} - 87677 x^{15} + 1288829 x^{14} - 1288829 x^{13} + 12499581 x^{12} - 12499581 x^{11} + 81083005 x^{10} - 81083005 x^{9} + 350517885 x^{8} - 350517885 x^{7} + 997161597 x^{6} - 997161597 x^{5} + 1859353213 x^{4} - 1859353213 x^{3} + 2389932669 x^{2} - 2389932669 x + 2486401661$	$22$	[0,11]	$-\,17^{11}\cdot 23^{21}$	$2$	$82.2347879494$	$82.23478794939922$	✓	✓	?	$C_{22}$ (as 22T1)	$[23, 28658]$	$2$	$10$	$1038656.82438$
22.0.261...824.1	$x^{22} - 2 x^{21} + 47 x^{20} - 82 x^{19} + 1234 x^{18} - 1928 x^{17} + 22201 x^{16} - 30962 x^{15} + 297640 x^{14} - 368132 x^{13} + 3078660 x^{12} - 3330816 x^{11} + 24869896 x^{10} - 23035280 x^{9} + 156123875 x^{8} - 119632870 x^{7} + 744424991 x^{6} - 445564762 x^{5} + 2565595585 x^{4} - 1074775766 x^{3} + 5757368622 x^{2} - 1278298632 x + 6391493137$	$22$	[0,11]	$-\,2^{33}\cdot 3^{11}\cdot 23^{20}$	$3$	$84.7305483889$	$84.73054838890124$	✓	✓	?	$C_{22}$ (as 22T1)	$[495926]$	$2$	$10$	$1038656.82438$
22.0.152...584.1	$x^{22} + 39 x^{20} + 676 x^{18} + 6870 x^{16} + 45451 x^{14} + 205365 x^{12} + 645976 x^{10} + 1412533 x^{8} + 2100082 x^{6} + 2015893 x^{4} + 1119360 x^{2} + 270379$	$22$	[0,11]	$-\,2^{22}\cdot 1297^{10}\cdot 270379$	$3$	$91.8143520702$		✓		?	$C_2^{10}.D_{22}$ (as 22T32)	$[273030]$	$2$	$10$	$15484188.8463$
22.0.176...880.1	$x^{22} + 50 x^{20} + 1121 x^{18} + 14874 x^{16} + 129757 x^{14} + 781318 x^{12} + 3312823 x^{10} + 9888269 x^{8} + 20354408 x^{6} + 27504549 x^{4} + 21943196 x^{2} + 7822625$	$22$	[0,11]	$-\,2^{22}\cdot 5\cdot 1297^{10}\cdot 62581$	$4$	$92.4260066753$		✓		?	$C_2^{10}.D_{22}$ (as 22T32)	$[2, 144216]$	$2$	$10$	$15484188.8463$
22.0.407...104.1	$x^{22} + 81 x^{20} + 2602 x^{18} + 43459 x^{16} + 416416 x^{14} + 2360004 x^{12} + 7761381 x^{10} + 13598526 x^{8} + 9845506 x^{6} + 250429 x^{4} + 1687 x^{2} + 1$	$22$	[0,11]	$-\,2^{22}\cdot 89^{20}$	$2$	$118.359392929$	$118.35939292912164$	✓	✓	?	$C_{22}$ (as 22T1)	$[117139]$	$4$	$10$	$866679281.3791491$
22.0.412...904.1	$x^{22} + 53 x^{20} + 963 x^{18} + 8057 x^{16} + 34825 x^{14} + 83894 x^{12} + 119260 x^{10} + 102849 x^{8} + 53662 x^{6} + 16302 x^{4} + 2614 x^{2} + 169$	$22$	[0,11]	$-\,2^{22}\cdot 74843^{8}$	$2$	$118.426422289$		✓			$C_2^{11}.\PSL(2,11)$ (as 22T42)	$[193648]$	$2$	$10$	$1524996279.85$
22.0.412...904.2	$x^{22} + 53 x^{20} + 1109 x^{18} + 11954 x^{16} + 72629 x^{14} + 254808 x^{12} + 505403 x^{10} + 527803 x^{8} + 253819 x^{6} + 49582 x^{4} + 3337 x^{2} + 9$	$22$	[0,11]	$-\,2^{22}\cdot 74843^{8}$	$2$	$118.426422289$		✓		?	$C_2^{11}.\PSL(2,11)$ (as 22T42)	$[110224]$	$2$	$10$	$1524996279.85$
22.0.657...543.1	$x^{22} - 9 x^{21} - 3 x^{20} + 159 x^{19} + 231 x^{18} - 2061 x^{17} - 3685 x^{16} + 10860 x^{15} + 43511 x^{14} - 4617 x^{13} - 151828 x^{12} - 220921 x^{11} + 178157 x^{10} + 730124 x^{9} + 3092873 x^{8} + 8707748 x^{7} + 20867753 x^{6} + 33250364 x^{5} + 51453681 x^{4} + 60447125 x^{3} + 73795185 x^{2} + 59497518 x + 50167427$	$22$	[0,11]	$-\,7^{11}\cdot 67^{20}$	$2$	$120.953105223$	$120.95310522326872$	✓	✓	?	$C_{22}$ (as 22T1)	$[420607]$	$2$	$10$	$338444542.042557$
22.0.108...375.1	$x^{22} - x^{21} + 69 x^{20} + 107 x^{19} + 1709 x^{18} + 7027 x^{17} + 28072 x^{16} + 135984 x^{15} + 407666 x^{14} + 1343170 x^{13} + 3834110 x^{12} + 8660900 x^{11} + 19147508 x^{10} + 34080648 x^{9} + 46733335 x^{8} + 54976444 x^{7} + 45275429 x^{6} - 4039339 x^{5} - 25724027 x^{4} + 4152387 x^{3} + 42185124 x^{2} + 41416437 x + 48482809$	$22$	[0,11]	$-\,5^{11}\cdot 67^{21}$	$2$	$123.753190609$	$123.75319060925942$	✓	✓	?	$C_{22}$ (as 22T1)	$[306522]$	$2$	$10$	$338444542.042557$
22.0.285...792.1	$x^{22} - 2 x^{21} - 37 x^{20} + 146 x^{19} + 494 x^{18} - 3636 x^{17} + 2299 x^{16} + 29626 x^{15} - 64260 x^{14} - 124424 x^{13} + 736428 x^{12} - 1124536 x^{11} + 59133 x^{10} + 1514350 x^{9} + 3820816 x^{8} - 32528018 x^{7} + 109540538 x^{6} - 244699026 x^{5} + 410278465 x^{4} - 525754586 x^{3} + 533811683 x^{2} - 395494894 x + 210368707$	$22$	[0,11]	$-\,2^{33}\cdot 67^{20}$	$2$	$129.304308461$	$129.30430846053977$	✓	✓	?	$C_{22}$ (as 22T1)	$[232331]$	$2$	$10$	$338444542.042557$
22.0.495...744.1	$x^{22} + 33 x^{20} + 473 x^{18} + 3861 x^{16} + 19778 x^{14} + 66066 x^{12} + 144914 x^{10} + 205194 x^{8} + 179773 x^{6} + 90189 x^{4} + 22517 x^{2} + 1961$	$22$	[0,11]	$-\,2^{40}\cdot 7^{10}\cdot 11^{22}\cdot 37\cdot 53$	$5$	$132.590831812$		✓		?	$C_2\times C_2^{10}.F_{11}$ (as 22T37)	$[2, 246012]$	$2$	$10$	$2013788572.23$
22.0.362...256.1	$x^{22} + 89 x^{20} + 3026 x^{18} + 51531 x^{16} + 489500 x^{14} + 2690648 x^{12} + 8475025 x^{10} + 14647086 x^{8} + 13328106 x^{6} + 6239345 x^{4} + 1413231 x^{2} + 121841$	$22$	[0,11]	$-\,2^{22}\cdot 89^{21}$	$2$	$145.148103472$	$145.14810347153576$	✓	✓	?	$C_{22}$ (as 22T1)	$[230484]$	$2$	$10$	$866679281.3791491$
22.0.528...000.1	$x^{22} + 102 x^{20} + 4485 x^{18} + 111390 x^{16} + 1718400 x^{14} + 17034174 x^{12} + 108257478 x^{10} + 425426925 x^{8} + 949776795 x^{6} + 1000048665 x^{4} + 295274364 x^{2} + 24920313$	$22$	[0,11]	$-\,2^{20}\cdot 3^{21}\cdot 5^{20}\cdot 11^{17}$	$4$	$147.651330059$		✓		?	$C_2^{10}.C_{11}:C_{10}$ (as 22T36)	$[2, 2, 27662]$	$2$	$10$	$12475736338.1$
22.0.894...943.1	$x^{22} - 11 x^{21} - 33 x^{20} + 649 x^{19} + 77 x^{18} - 16599 x^{17} + 18073 x^{16} + 222574 x^{15} - 351846 x^{14} - 1913648 x^{13} + 3638591 x^{12} + 10421760 x^{11} - 18077708 x^{10} - 52267061 x^{9} + 88950411 x^{8} + 112398451 x^{7} - 87574498 x^{6} - 406562805 x^{5} + 515905885 x^{4} - 341803154 x^{3} + 860884596 x^{2} - 1268438105 x + 5519069021$	$22$	[0,11]	$-\,7^{11}\cdot 11^{40}$	$2$	$207.009494929$	$207.0094949286179$	✓	✓		$C_{22}$ (as 22T1)	$[173041]$	$2$	$10$	$285114946276.13544$
22.0.427...312.1	$x^{22} + 220 x^{20} + 18876 x^{18} + 825704 x^{16} + 20058896 x^{14} + 275949696 x^{12} + 2128407424 x^{10} + 9128116096 x^{8} + 20992435200 x^{6} + 23394438144 x^{4} + 9845535744 x^{2} + 1330255872$	$22$	[0,11]	$-\,2^{33}\cdot 11^{41}$	$2$	$246.786995312$	$246.7869953122683$	✓	✓		$C_{22}$ (as 22T1)	$[914894]$	$2$	$10$	$285114946276.13544$
22.0.441...347.1	$x^{22} - x^{21} + 151 x^{20} - 654 x^{19} + 16325 x^{18} - 75763 x^{17} + 995289 x^{16} - 5403558 x^{15} + 44834779 x^{14} - 205415593 x^{13} + 1133460253 x^{12} - 4321709316 x^{11} + 18785461384 x^{10} - 60845873872 x^{9} + 203712968048 x^{8} - 530942481728 x^{7} + 1408047471744 x^{6} - 3019035195648 x^{5} + 6127699221760 x^{4} - 9253854241792 x^{3} + 11744248303616 x^{2} - 9185162559488 x + 5233186963456$	$22$	[0,11]	$-\,3^{11}\cdot 331^{20}$	$2$	$338.308842287$	$338.30884228701103$	✓	✓		$C_{22}$ (as 22T1)	$[11, 23969]$	$6$	$10$	$1372307132022027.0$