Number field search results

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

Results (9 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
22.0.719...000.1	$x^{22} - 2 x^{21} + 91 x^{20} - 162 x^{19} + 4154 x^{18} - 6608 x^{17} + 123265 x^{16} - 174450 x^{15} + 2616392 x^{14} - 3263164 x^{13} + 41456020 x^{12} - 44873920 x^{11} + 498358184 x^{10} - 457441488 x^{9} + 4533809731 x^{8} - 3404345062 x^{7} + 30545809231 x^{6} - 17679217442 x^{5} + 145074301925 x^{4} - 57845366150 x^{3} + 437292880806 x^{2} - 90650889312 x + 634556225161$	$22$	[0,11]	$-\,2^{33}\cdot 5^{11}\cdot 23^{20}$	$3$	$109.386667608$	$109.38666760841207$	✓	✓	?	$C_{22}$ (as 22T1)	$[17310766]$	$2$	$10$	$1038656.8243805699$
22.0.165...696.1	$x^{22} + 201 x^{20} + 15678 x^{18} + 613251 x^{16} + 12981384 x^{14} + 149068836 x^{12} + 883227969 x^{10} + 2478977622 x^{8} + 3362840550 x^{6} + 2090236185 x^{4} + 462885111 x^{2} + 11868849$	$22$	[0,11]	$-\,2^{22}\cdot 3^{11}\cdot 67^{21}$	$3$	$191.717618508$	$191.71761850787755$	✓	✓	?	$C_{22}$ (as 22T1)	$[2, 11548686]$	$2$	$10$	$338444542.042557$
22.0.277...811.1	$x^{22} - 9 x^{21} - 12 x^{20} + 337 x^{19} - 383 x^{18} - 5876 x^{17} + 18523 x^{16} + 16196 x^{15} - 84841 x^{14} - 300133 x^{13} + 1731641 x^{12} - 3103687 x^{11} + 4035441 x^{10} - 12380083 x^{9} + 63615149 x^{8} - 174132886 x^{7} + 358371438 x^{6} - 556676137 x^{5} + 1436734353 x^{4} - 2616581008 x^{3} + 5644816006 x^{2} - 5254555364 x + 5354971187$	$22$	[0,11]	$-\,11^{11}\cdot 89^{20}$	$2$	$196.27684838$	$196.27684838007025$	✓	✓	?	$C_{22}$ (as 22T1)	$[23, 517891]$	$2$	$10$	$866679281.3791491$
22.0.398...879.1	$x^{22} - x^{21} + 203 x^{20} + 241 x^{19} + 15645 x^{18} + 49907 x^{17} + 645544 x^{16} + 2979464 x^{15} + 17383054 x^{14} + 82563250 x^{13} + 322791094 x^{12} + 1212821214 x^{11} + 3698021698 x^{10} + 9684850830 x^{9} + 21693864639 x^{8} + 38502084388 x^{7} + 50771931117 x^{6} + 47768698105 x^{5} + 38829007897 x^{4} + 30616690773 x^{3} + 52753103834 x^{2} + 67713149325 x + 81132029807$	$22$	[0,11]	$-\,13^{11}\cdot 67^{21}$	$2$	$199.546023973$	$199.54602397323382$	✓	✓	?	$C_{22}$ (as 22T1)	$[63265334]$	$2$	$10$	$338444542.042557$
22.0.743...288.1	$x^{22} + 178 x^{20} + 12104 x^{18} + 412248 x^{16} + 7832000 x^{14} + 86100736 x^{12} + 542401600 x^{10} + 1874827008 x^{8} + 3411995136 x^{6} + 3194544640 x^{4} + 1447148544 x^{2} + 249530368$	$22$	[0,11]	$-\,2^{33}\cdot 89^{21}$	$2$	$205.270416482$	$205.2704164821792$	✓	✓	?	$C_{22}$ (as 22T1)	$[25518776]$	$2$	$10$	$866679281.3791491$
22.0.246...179.1	$x^{22} - x^{21} + 225 x^{20} - 230 x^{19} + 19126 x^{18} - 28841 x^{17} + 812810 x^{16} - 1847925 x^{15} + 20490513 x^{14} - 63602020 x^{13} + 333560957 x^{12} - 1208195986 x^{11} + 3941677367 x^{10} - 12395573094 x^{9} + 35724961604 x^{8} - 72371663593 x^{7} + 199796166276 x^{6} - 333264099002 x^{5} + 549328483842 x^{4} - 675845066158 x^{3} + 728343357757 x^{2} - 383812617252 x + 364599064657$	$22$	[0,11]	$-\,11^{11}\cdot 89^{21}$	$2$	$240.700899123$	$240.7008991233831$	✓	✓	?	$C_{22}$ (as 22T1)	$[82867144]$	$2$	$10$	$866679281.3791491$
22.0.527...819.1	$x^{22} - 11 x^{21} + 319 x^{19} + 77 x^{18} - 8184 x^{17} + 22033 x^{16} + 41206 x^{15} + 72600 x^{14} - 1384724 x^{13} + 5317631 x^{12} - 6619506 x^{11} + 53555326 x^{10} - 198441551 x^{9} + 748155507 x^{8} - 1494976967 x^{7} + 6065332130 x^{6} - 11812333698 x^{5} + 38104926805 x^{4} - 54759490940 x^{3} + 163349993499 x^{2} - 142892130293 x + 478967764799$	$22$	[0,11]	$-\,11^{40}\cdot 19^{11}$	$2$	$341.049993994$	$341.04999399363896$	✓	✓		$C_{22}$ (as 22T1)	$[11, 4007531]$	$2$	$10$	$285114946276.13544$
22.0.921...875.1	$x^{22} - x^{21} + 204 x^{20} + 300 x^{19} + 17203 x^{18} + 68673 x^{17} + 825513 x^{16} + 4874907 x^{15} + 29311275 x^{14} + 165265669 x^{13} + 760942580 x^{12} + 3191438973 x^{11} + 12791899873 x^{10} + 37757317040 x^{9} + 122682543835 x^{8} + 272442102752 x^{7} + 760956148725 x^{6} + 1683377741263 x^{5} + 5010846934880 x^{4} + 10572689320889 x^{3} + 20272483083031 x^{2} + 19526867163395 x + 6857181839381$	$22$	[0,11]	$-\,5^{11}\cdot 199^{21}$	$2$	$349.820097846$	$349.8200978455147$	✓	✓	?	$C_{22}$ (as 22T1)	$[69273608]$	$2$	$10$	$117135822355.96071$
22.0.318...747.1	$x^{22} - x^{21} + 22 x^{20} - 638 x^{19} - 4834 x^{18} - 68736 x^{17} + 29342 x^{16} + 3003492 x^{15} + 72912964 x^{14} + 585651628 x^{13} + 4884348545 x^{12} + 23061834780 x^{11} + 126935713555 x^{10} + 321183439624 x^{9} + 1442099273183 x^{8} - 352417867544 x^{7} + 11302889577644 x^{6} - 29371703518119 x^{5} + 285911612185382 x^{4} - 92001319669394 x^{3} + 2756828139456442 x^{2} - 7067594870875052 x + 10971649548548503$	$22$	[0,11]	$-\,947^{21}$	$1$	$693.523758529$	$693.5237585285587$	✓	✓	?	$C_{22}$ (as 22T1)	$[18795485]$	$2$	$10$	$1130622785561068.5$