Number field search results

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

Results (1-50 of 117337 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
6.0.65499561791.1	$x^{6} - 2 x^{5} - 2 x^{4} - 60 x^{3} + 1073 x^{2} + 2110 x + 2000$	$6$	[0,3]	$-\,29^{3}\cdot 139^{3}$	$2$	$63.4901567174$	$63.490156717399906$		✓		$S_3$ (as 6T2)	$[7, 7, 28]$	$2$	$2$	$54.5569404025$
6.0.125535755376.1	$x^{6} - x^{5} + 10 x^{4} + 60 x^{3} + 75 x^{2} + 909 x + 3042$	$6$	[0,3]	$-\,2^{4}\cdot 3^{2}\cdot 31\cdot 5303^{2}$	$4$	$70.7610996494$	$1404.5340864500229$	✓			$S_4\times C_2$ (as 6T11)	$[1120]$	$2$	$2$	$38.523174632800114$
6.0.140655018863.1	$x^{6} - x^{5} + 127 x^{4} - 259 x^{3} + 4880 x^{2} - 4748 x + 42688$	$6$	[0,3]	$-\,17^{3}\cdot 31^{5}$	$2$	$72.1150438986$	$72.1150438985958$	✓	✓		$C_6$ (as 6T1)	$[1026]$	$2$	$2$	$48.7831276503$
6.0.191666276487.2	$x^{6} - 3 x^{5} - 21 x^{4} - 9 x^{3} + 588 x^{2} + 1572 x + 3968$	$6$	[0,3]	$-\,3^{8}\cdot 7^{4}\cdot 23^{3}$	$3$	$75.9319030069$	$75.93190300685129$	✓	✓		$C_6$ (as 6T1)	$[3, 657]$	$2$	$2$	$50.3767558277$
6.0.197356395591.1	$x^{6} + 15 x^{4} - 116 x^{3} + 756 x^{2} - 2736 x + 4608$	$6$	[0,3]	$-\,3^{8}\cdot 311^{3}$	$2$	$76.303044636$	$76.3030446359926$		✓		$S_3$ (as 6T2)	$[6, 342]$	$2$	$2$	$85.3024664406$
6.0.231440493375.7	$x^{6} - x^{5} - 49 x^{4} - 75 x^{3} + 1008 x^{2} + 4156 x + 6544$	$6$	[0,3]	$-\,3^{3}\cdot 5^{3}\cdot 7^{4}\cdot 13^{4}$	$4$	$78.3561744395$	$78.35617443954843$	✓	✓		$C_6$ (as 6T1)	$[5, 210]$	$2$	$2$	$62.4891977899$
6.0.231946969919.1	$x^{6} - x^{5} + 71 x^{4} - 57 x^{3} + 2759 x^{2} + 55 x + 45382$	$6$	[0,3]	$-\,7^{5}\cdot 17^{3}\cdot 53^{2}$	$3$	$78.3847270825$	$151.9185344621086$	✓			$D_{6}$ (as 6T3)	$[2, 660]$	$2$	$2$	$19.1839622215$
6.0.269997268464.3	$x^{6} - x^{5} + 167 x^{4} - 111 x^{3} + 10044 x^{2} - 3368 x + 215758$	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 7^{3}\cdot 11^{3}\cdot 37^{2}$	$5$	$80.3945413199$	$146.7552057914913$	✓		?	$D_{6}$ (as 6T3)	$[2, 522]$	$2$	$2$	$6.64934608307$
6.0.296019302976.3	$x^{6} + 261 x^{4} - 2 x^{3} + 23772 x^{2} + 540 x + 753297$	$6$	[0,3]	$-\,2^{6}\cdot 3^{8}\cdot 89^{3}$	$3$	$81.636931404$	$81.63693140398101$	✓	✓	?	$C_6$ (as 6T1)	$[2, 2, 252]$	$2$	$2$	$3.39714980258$
6.0.305559728327.2	$x^{6} - x^{5} + 373 x^{4} - 249 x^{3} + 47507 x^{2} - 15625 x + 2064257$	$6$	[0,3]	$-\,7^{4}\cdot 503^{3}$	$2$	$82.0696697602$	$82.06966976015916$	✓	✓	?	$C_6$ (as 6T1)	$[4, 252]$	$2$	$2$	$2.10181872849$
6.0.310236069591.1	$x^{6} - 2 x^{5} + 35 x^{4} + 30 x^{3} + 700 x^{2} + 1448 x + 7328$	$6$	[0,3]	$-\,3^{2}\cdot 7^{4}\cdot 19\cdot 53^{2}\cdot 269$	$5$	$82.2776820778$	$3298.7560214786413$	✓			$S_4\times C_2$ (as 6T11)	$[6, 210]$	$2$	$2$	$19.183962221454046$
6.0.312771967375.2	$x^{6} - x^{5} + 463 x^{4} - 463 x^{3} + 61447 x^{2} - 61447 x + 2073919$	$6$	[0,3]	$-\,5^{3}\cdot 7^{5}\cdot 53^{3}$	$3$	$82.38939308$	$82.38939308001129$	✓	✓	?	$C_6$ (as 6T1)	$[2, 518]$	$2$	$2$	$2.10181872849$
6.0.321575167088.1	$x^{6} - 2 x^{5} - 3 x^{4} + 152 x^{3} + 599 x^{2} - 1782 x + 6219$	$6$	[0,3]	$-\,2^{4}\cdot 7^{2}\cdot 743^{3}$	$3$	$82.7714221818$	$144.23591785682234$				$D_{6}$ (as 6T3)	$[3, 336]$	$2$	$2$	$158.393161355$
6.0.329868818496.3	$x^{6} - 2 x^{5} + 384 x^{4} - 510 x^{3} + 50183 x^{2} - 33544 x + 2230669$	$6$	[0,3]	$-\,2^{6}\cdot 3^{3}\cdot 7^{4}\cdot 43^{3}$	$4$	$83.1234469459$	$83.1234469459362$	✓	✓	?	$C_6$ (as 6T1)	$[2, 2, 2, 126]$	$2$	$2$	$2.10181872849$
6.0.330538324631.1	$x^{6} - x^{5} + 33 x^{4} - 31 x^{3} + 1062 x^{2} + 232 x + 13952$	$6$	[0,3]	$-\,31^{4}\cdot 71^{3}$	$2$	$83.151541272$	$83.15154127202608$	✓	✓		$C_6$ (as 6T1)	$[1141]$	$2$	$2$	$48.7831276503$
6.0.354110810319.1	$x^{6} + 24 x^{4} - 14 x^{3} + 423 x^{2} - 546 x + 3088$	$6$	[0,3]	$-\,3^{9}\cdot 7^{4}\cdot 59\cdot 127$	$4$	$84.1117232739$	$1645.9189359215277$	✓			$A_4\times C_2$ (as 6T6)	$[2, 876]$	$2$	$2$	$50.37675582767471$
6.0.372914405087.2	$x^{6} - x^{5} + 491 x^{4} - 491 x^{3} + 69091 x^{2} - 69091 x + 2470091$	$6$	[0,3]	$-\,7^{5}\cdot 281^{3}$	$2$	$84.8401693281$	$84.84016932806762$	✓	✓	?	$C_6$ (as 6T1)	$[2, 6, 108]$	$2$	$2$	$2.10181872849$
6.0.384407319807.2	$x^{6} - x^{5} + 403 x^{4} - 269 x^{3} + 55357 x^{2} - 18225 x + 2589847$	$6$	[0,3]	$-\,3^{3}\cdot 7^{4}\cdot 181^{3}$	$3$	$85.2704604521$	$85.27046045212757$	✓	✓	?	$C_6$ (as 6T1)	$[2, 2, 252]$	$2$	$2$	$2.10181872849$
6.0.384986251328.3	$x^{6} + 497 x^{4} + 70574 x^{2} + 2505377$	$6$	[0,3]	$-\,2^{6}\cdot 7^{5}\cdot 71^{3}$	$3$	$85.2918504403$	$85.29185044027165$	✓	✓	?	$C_6$ (as 6T1)	$[2, 4, 4, 36]$	$2$	$2$	$2.10181872849$
6.0.402411370167.3	$x^{6} + 378 x^{4} - 362 x^{3} + 35445 x^{2} - 21222 x + 970701$	$6$	[0,3]	$-\,3^{8}\cdot 23^{3}\cdot 71^{2}$	$3$	$85.92345013892007$	$174.84562318626632$	✓		?	$A_4\times C_2$ (as 6T6)	$[2, 568]$	$2$	$2$	$3.39714980258477$
6.0.404353609875.6	$x^{6} - 3 x^{5} + 294 x^{4} - 581 x^{3} + 29697 x^{2} - 30006 x + 1029999$	$6$	[0,3]	$-\,3^{8}\cdot 5^{3}\cdot 79^{3}$	$3$	$85.9924298468$	$85.99242984675755$	✓	✓	?	$C_6$ (as 6T1)	$[1176]$	$2$	$2$	$3.39714980258$
6.0.435944600944.2	$x^{6} - x^{5} + 197 x^{4} - 131 x^{3} + 13814 x^{2} - 4628 x + 342718$	$6$	[0,3]	$-\,2^{4}\cdot 37^{2}\cdot 271^{3}$	$3$	$87.0773526917$	$158.95425988186597$	✓		?	$D_{6}$ (as 6T3)	$[11, 99]$	$2$	$2$	$6.64934608307$
6.0.440311012911.5	$x^{6} + 105 x^{4} - 238 x^{3} + 3276 x^{2} - 4872 x + 42112$	$6$	[0,3]	$-\,3^{9}\cdot 7^{5}\cdot 11^{3}$	$3$	$87.2221105634$	$87.2221105634217$	✓	✓		$C_6$ (as 6T1)	$[6, 342]$	$2$	$2$	$50.3767558277$
6.0.441230583744.1	$x^{6} - x^{5} + 71 x^{4} - 39 x^{3} + 2358 x^{2} - 1514 x + 32440$	$6$	[0,3]	$-\,2^{6}\cdot 3^{3}\cdot 37^{3}\cdot 71^{2}$	$4$	$87.2524441232$	$251.09360804289702$	✓			$D_{6}$ (as 6T3)	$[8, 128]$	$2$	$2$	$24.349563628547063$
6.0.442336997223.6	$x^{6} - 3 x^{5} + 303 x^{4} - 599 x^{3} + 31515 x^{2} - 31833 x + 1124553$	$6$	[0,3]	$-\,3^{8}\cdot 11^{3}\cdot 37^{3}$	$3$	$87.2888712485$	$87.28887124851097$	✓	✓	?	$C_6$ (as 6T1)	$[2, 2, 336]$	$2$	$2$	$3.39714980258$
6.0.454849890599.1	$x^{6} - x^{5} + 346 x^{4} - 347 x^{3} + 18258 x^{2} + 348 x + 265355$	$6$	[0,3]	$-\,13^{5}\cdot 107^{3}$	$2$	$87.6956427984$	$87.69564279841565$	✓	✓		$C_6$ (as 6T1)	$[5, 220]$	$2$	$2$	$5.46019947038$
6.0.455331870319.2	$x^{6} - x^{5} + 39 x^{4} - 35 x^{3} + 1288 x^{2} + 212 x + 17824$	$6$	[0,3]	$-\,31^{4}\cdot 79^{3}$	$2$	$87.7111236828$	$87.71112368284038$	✓	✓		$C_6$ (as 6T1)	$[3, 465]$	$2$	$2$	$48.7831276503$
6.0.459288853051.1	$x^{6} - x^{5} + 479 x^{4} - 308 x^{3} + 67709 x^{2} - 22584 x + 3023861$	$6$	[0,3]	$-\,7^{4}\cdot 19^{3}\cdot 167^{2}$	$3$	$87.83770582464597$	$206.1264526948386$	✓		?	$A_4\times C_2$ (as 6T6)	$[2, 504]$	$2$	$2$	$2.1018187284902896$
6.0.463403630576.4	$x^{6} - 3 x^{5} + 313 x^{4} - 579 x^{3} + 20328 x^{2} - 29678 x + 356938$	$6$	[0,3]	$-\,2^{4}\cdot 37^{3}\cdot 83^{3}$	$3$	$87.968375502$	$87.9683755019627$	✓		?	$D_{6}$ (as 6T3)	$[1140]$	$2$	$2$	$6.64934608307$
6.0.469296461151.6	$x^{6} - 3 x^{5} - 15 x^{4} - 21 x^{3} + 678 x^{2} + 1824 x + 6112$	$6$	[0,3]	$-\,3^{8}\cdot 7^{4}\cdot 31^{3}$	$3$	$88.1538355775$	$88.15383557748156$	✓	✓		$C_6$ (as 6T1)	$[6, 342]$	$2$	$2$	$50.3767558277$
6.0.476858708375.2	$x^{6} - x^{5} + 533 x^{4} - 533 x^{3} + 81397 x^{2} - 81397 x + 3154229$	$6$	[0,3]	$-\,5^{3}\cdot 7^{5}\cdot 61^{3}$	$3$	$88.3890134061$	$88.38901340607352$	✓	✓	?	$C_6$ (as 6T1)	$[10, 110]$	$2$	$2$	$2.10181872849$
6.0.478223266304.2	$x^{6} - 2 x^{5} + 435 x^{4} - 578 x^{3} + 64242 x^{2} - 42928 x + 3219593$	$6$	[0,3]	$-\,2^{9}\cdot 7^{4}\cdot 73^{3}$	$3$	$88.4311182513$	$88.43111825128939$	✓	✓	?	$C_6$ (as 6T1)	$[5, 240]$	$2$	$2$	$2.10181872849$
6.0.480232637191.1	$x^{6} - 2 x^{5} - 30 x^{4} + 24 x^{3} + 2205 x^{2} - 11638 x + 17632$	$6$	[0,3]	$-\,41^{3}\cdot 191^{3}$	$2$	$88.4929375713$	$88.4929375713113$		✓		$S_3$ (as 6T2)	$[7, 154]$	$2$	$2$	$109.720442807$
6.0.510465535488.3	$x^{6} + 444 x^{4} + 49284 x^{2} + 1215672$	$6$	[0,3]	$-\,2^{9}\cdot 3^{9}\cdot 37^{3}$	$3$	$89.3979865545$	$89.39798655450804$	✓	✓	?	$C_6$ (as 6T1)	$[2, 2, 2, 126]$	$2$	$2$	$3.39714980258$
6.0.516027239399.2	$x^{6} - x^{5} + 445 x^{4} - 297 x^{3} + 67355 x^{2} - 22201 x + 3465449$	$6$	[0,3]	$-\,7^{4}\cdot 599^{3}$	$2$	$89.5595916101$	$89.55959161008177$	✓	✓	?	$C_6$ (as 6T1)	$[1075]$	$2$	$2$	$2.10181872849$
6.0.525293283951.2	$x^{6} - 3 x^{5} + 321 x^{4} - 635 x^{3} + 35313 x^{2} - 35649 x + 1330671$	$6$	[0,3]	$-\,3^{8}\cdot 431^{3}$	$2$	$89.8256374852$	$89.82563748517644$	✓	✓	?	$C_6$ (as 6T1)	$[4, 252]$	$2$	$2$	$3.39714980258$
6.0.525515088384.3	$x^{6} - 2 x^{5} + 191 x^{4} - 258 x^{3} + 13218 x^{2} - 7780 x + 327625$	$6$	[0,3]	$-\,2^{9}\cdot 3^{3}\cdot 11^{3}\cdot 13^{4}$	$4$	$89.8319578338$	$89.83195783382237$	✓	✓		$C_6$ (as 6T1)	$[2, 516]$	$2$	$2$	$5.46019947038$
6.0.535691912000.1	$x^{6} + 505 x^{4} + 75150 x^{2} + 3486125$	$6$	[0,3]	$-\,2^{6}\cdot 5^{3}\cdot 7^{4}\cdot 167^{2}$	$4$	$90.1195846729108$	$211.48127825700897$	✓		?	$A_4\times C_2$ (as 6T6)	$[2, 2, 288]$	$2$	$2$	$2.1018187284902896$
6.0.536980151743.3	$x^{6} - x^{5} + 451 x^{4} - 301 x^{3} + 69165 x^{2} - 22801 x + 3604679$	$6$	[0,3]	$-\,7^{4}\cdot 607^{3}$	$2$	$90.1556686826$	$90.15566868256195$	✓	✓	?	$C_6$ (as 6T1)	$[1443]$	$2$	$2$	$2.10181872849$
6.0.541760081751.3	$x^{6} - 3 x^{5} + 51 x^{4} - 41 x^{3} + 3084 x^{2} - 9252 x + 81264$	$6$	[0,3]	$-\,3^{8}\cdot 7^{5}\cdot 17^{3}$	$3$	$90.2889287588$	$90.28892875875027$	✓	✓		$C_6$ (as 6T1)	$[3, 3, 390]$	$2$	$2$	$50.3767558277$
6.0.543691854704.1	$x^{6} + 263 x^{4} - 348 x^{3} + 18102 x^{2} - 13372 x + 354176$	$6$	[0,3]	$-\,2^{4}\cdot 41^{3}\cdot 79^{3}$	$3$	$90.3425069456$	$113.82442620105756$	✓			$D_{6}$ (as 6T3)	$[10, 140]$	$2$	$2$	$15.6538339685$
6.0.553914311104.3	$x^{6} - x^{5} - 9 x^{4} + x^{3} + 448 x^{2} + 56 x + 4480$	$6$	[0,3]	$-\,2^{6}\cdot 7^{4}\cdot 11^{2}\cdot 31^{3}$	$4$	$90.6234164867$	$191.1264865637977$	✓			$D_{6}$ (as 6T3)	$[3, 3, 144]$	$2$	$2$	$28.9154471068$
6.0.558492708375.3	$x^{6} - x^{5} + 457 x^{4} - 305 x^{3} + 70999 x^{2} - 23409 x + 3747589$	$6$	[0,3]	$-\,3^{3}\cdot 5^{3}\cdot 7^{4}\cdot 41^{3}$	$4$	$90.7478305076$	$90.7478305075947$	✓	✓	?	$C_6$ (as 6T1)	$[2, 2, 2, 210]$	$2$	$2$	$2.10181872849$
6.0.558892224000.14	$x^{6} + 324 x^{4} - 2 x^{3} + 36309 x^{2} + 666 x + 1404591$	$6$	[0,3]	$-\,2^{9}\cdot 3^{8}\cdot 5^{3}\cdot 11^{3}$	$4$	$90.7586466365$	$90.75864663648053$	✓	✓	?	$C_6$ (as 6T1)	$[14, 126]$	$2$	$2$	$3.39714980258$
6.0.562327702000.2	$x^{6} - x^{5} + 215 x^{4} - 143 x^{3} + 16364 x^{2} - 5480 x + 438670$	$6$	[0,3]	$-\,2^{4}\cdot 5^{3}\cdot 37^{2}\cdot 59^{3}$	$4$	$90.8513907348$	$165.8435302301693$	✓		?	$D_{6}$ (as 6T3)	$[2, 8, 72]$	$2$	$2$	$6.64934608307$
6.0.568435616671.2	$x^{6} - x^{5} + 195 x^{4} - 125 x^{3} + 13819 x^{2} - 5599 x + 352585$	$6$	[0,3]	$-\,13^{4}\cdot 271^{3}$	$2$	$91.015120199$	$91.01512019900994$	✓	✓		$C_6$ (as 6T1)	$[1067]$	$2$	$2$	$5.46019947038$
6.0.568803016375.3	$x^{6} - x^{5} + 13 x^{4} + 17 x^{3} + 762 x^{2} - 1672 x + 11264$	$6$	[0,3]	$-\,5^{3}\cdot 11^{3}\cdot 43^{4}$	$3$	$91.0249219325$	$91.02492193248288$	✓	✓		$C_6$ (as 6T1)	$[2, 6, 84]$	$2$	$2$	$75.6874575318$
6.0.570402232227.3	$x^{6} - 3 x^{5} + 330 x^{4} - 653 x^{3} + 37293 x^{2} - 37638 x + 1442559$	$6$	[0,3]	$-\,3^{8}\cdot 443^{3}$	$2$	$91.06752551$	$91.06752550996399$	✓	✓	?	$C_6$ (as 6T1)	$[1005]$	$2$	$2$	$3.39714980258$
6.0.575100098496.10	$x^{6} + 111 x^{4} - 342 x^{3} + 3600 x^{2} - 7200 x + 96000$	$6$	[0,3]	$-\,2^{6}\cdot 3^{9}\cdot 7^{3}\cdot 11^{3}$	$4$	$91.1921049214$	$128.96511156122807$				$D_{6}$ (as 6T3)	$[2, 6, 90]$	$2$	$2$	$49.0990128292$
6.0.583202214000.1	$x^{6} - x^{5} + 339 x^{4} - 471 x^{3} + 29408 x^{2} - 58400 x + 463744$	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 5^{3}\cdot 7^{3}\cdot 23\cdot 37^{2}$	$6$	$91.40498056997508$	$474.510791054021$	✓		?	$S_4\times C_2$ (as 6T11)	$[2, 2, 2, 128]$	$2$	$2$	$6.649346083071585$