Number field search results

Results (1-50 of 5261 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
6.2.153664.1	$x^{6} + x^{4} - 2 x^{2} - 1$	$6$	[2,2]	$2^{6}\cdot 7^{4}$	$2$	$7.31861142005$	$10.350079527967589$			✓	$A_4$ (as 6T4)	trivial	$2$	$3$	$1.52284619555$
6.2.405769.1	$x^{6} - x^{5} - 2 x^{4} + x^{3} - 7$	$6$	[2,2]	$7^{4}\cdot 13^{2}$	$2$	$8.60425244895$	$13.193814370085985$			?	$A_4$ (as 6T4)	trivial	$2$	$3$	$2.79744795214$
6.2.419904.1	$x^{6} - 3 x^{2} - 1$	$6$	[2,2]	$2^{6}\cdot 3^{8}$	$2$	$8.65349742184$	$12.237893415933033$			✓	$A_4$ (as 6T4)	trivial	$2$	$3$	$4.03075255961$
6.2.714025.1	$x^{6} - x^{5} - x^{4} - 3 x^{3} - x^{2} - x + 1$	$6$	[2,2]	$5^{2}\cdot 13^{4}$	$2$	$9.45407194598$	$12.362716315674692$			✓	$A_4$ (as 6T4)	trivial	$2$	$3$	$4.29431935449$
6.2.1827904.1	$x^{6} - x^{4} - 4 x^{2} - 1$	$6$	[2,2]	$2^{6}\cdot 13^{4}$	$2$	$11.0575496274$	$15.637736649622886$			✓	$A_4$ (as 6T4)	trivial	$2$	$3$	$6.77790970632$
6.2.1896129.1	$x^{6} - 7 x^{3} - 6 x^{2} - 9 x - 3$	$6$	[2,2]	$3^{8}\cdot 17^{2}$	$2$	$11.1252893078$	$17.839641950637386$			?	$A_4$ (as 6T4)	trivial	$2$	$3$	$10.0751544903$
6.2.2019241.1	$x^{6} - x^{5} + 3 x^{4} + 7 x^{3} - 9 x^{2} + 19 x - 13$	$6$	[2,2]	$7^{4}\cdot 29^{2}$	$2$	$11.2425465032$	$19.705964328162043$			?	$A_4$ (as 6T4)	trivial	$2$	$3$	$6.76604282747$
6.2.2368521.1	$x^{6} - 3 x^{4} - 10 x^{3} - 18 x^{2} - 18 x - 9$	$6$	[2,2]	$3^{8}\cdot 19^{2}$	$2$	$11.5455033938$	$18.859860385004858$			?	$A_4$ (as 6T4)	$[2]$	$2$	$3$	$5.7913405411$
6.2.4036081.1	$x^{6} - 2 x^{5} + 8 x^{4} + 3 x^{3} - 4 x^{2} + 31 x - 29$	$6$	[2,2]	$7^{4}\cdot 41^{2}$	$2$	$12.6180810371$	$23.430989084024507$			?	$A_4$ (as 6T4)	trivial	$2$	$3$	$9.97288495016$
6.2.4439449.1	$x^{6} - 2 x^{5} - x^{4} + x^{3} - 14 x^{2} + 28 x - 56$	$6$	[2,2]	$7^{4}\cdot 43^{2}$	$2$	$12.8200045269$	$23.99567223510292$			?	$A_4$ (as 6T4)	$[2]$	$2$	$3$	$5.08829060986$
6.2.6385729.1	$x^{6} - 2 x^{5} + 5 x^{3} + 5 x - 1$	$6$	[2,2]	$7^{2}\cdot 19^{4}$	$2$	$13.6207727536$	$18.838721275076466$			?	$A_4$ (as 6T4)	$[2]$	$2$	$3$	$7.95006507529$
6.2.8340544.2	$x^{6} - 2 x^{4} - 5 x^{2} - 1$	$6$	[2,2]	$2^{6}\cdot 19^{4}$	$2$	$14.2407347178$	$20.13944017607579$			✓	$A_4$ (as 6T4)	trivial	$2$	$3$	$14.2634951701$
6.2.8982009.1	$x^{6} + 3 x^{4} - 5 x^{3} - 12 x^{2} - 36 x - 24$	$6$	[2,2]	$3^{8}\cdot 37^{2}$	$2$	$14.4176866011$	$26.318584936813835$			?	$A_4$ (as 6T4)	trivial	$2$	$3$	$24.7772957643$
6.2.12103441.1	$x^{6} - 3 x^{5} + 3 x^{4} - x^{3} - 49 x^{2} + 49 x - 91$	$6$	[2,2]	$7^{4}\cdot 71^{2}$	$2$	$15.1525180346$	$30.833857978493015$			?	$A_4$ (as 6T4)	$[2]$	$2$	$3$	$10.2217300636$
6.2.14776336.1	$x^{6} + 4 x^{4} - 5 x^{2} - 16$	$6$	[2,2]	$2^{4}\cdot 31^{4}$	$2$	$15.664905994$	$19.736544806437948$				$A_4$ (as 6T4)	$[2]$	$2$	$3$	$71.4422669254$
6.2.15768841.1	$x^{6} - x^{5} - x^{4} - 9 x^{3} + 11 x^{2} - 7 x - 1$	$6$	[2,2]	$11^{2}\cdot 19^{4}$	$2$	$15.8355552437$	$23.615586898971756$			?	$A_4$ (as 6T4)	$[2]$	$2$	$3$	$11.7474519883$
6.2.16540489.1	$x^{6} - x^{5} + 10 x^{4} + 7 x^{3} - 2 x^{2} + 96 x - 104$	$6$	[2,2]	$7^{4}\cdot 83^{2}$	$2$	$15.9621501156$	$33.33786161694775$			?	$A_4$ (as 6T4)	$[2]$	$2$	$3$	$12.028252518$
6.2.18429849.1	$x^{6} - 3 x^{5} + 9 x^{4} - 13 x^{3} - 21 x^{2} + 27 x - 51$	$6$	[2,2]	$3^{8}\cdot 53^{2}$	$2$	$16.2525045449$	$31.499206078816627$			?	$A_4$ (as 6T4)	trivial	$2$	$3$	$37.1935128481$
6.2.22591009.1	$x^{6} - 3 x^{5} - x^{4} + 7 x^{3} - 85 x^{2} + 81 x - 167$	$6$	[2,2]	$7^{4}\cdot 97^{2}$	$2$	$16.8134152107$	$36.039981591316774$			?	$A_4$ (as 6T4)	trivial	$2$	$3$	$23.8876505618$
6.2.25969216.1	$x^{6} + x^{4} - 65 x^{2} - 169$	$6$	[2,2]	$2^{6}\cdot 7^{4}\cdot 13^{2}$	$3$	$17.2085048979$	$37.31774244321726$			?	$A_4$ (as 6T4)	$[2]$	$2$	$3$	$13.2315118109$
6.6.25969216.1	$x^{6} - 19 x^{4} + 104 x^{2} - 169$	$6$	[6,0]	$2^{6}\cdot 7^{4}\cdot 13^{2}$	$3$	$17.2085048979$	$37.31774244321726$			?	$A_4$ (as 6T4)	trivial	$2$	$5$	$50.4782232641$
6.2.25969216.2	$x^{6} + 4 x^{4} - 39 x^{2} - 169$	$6$	[2,2]	$2^{6}\cdot 7^{4}\cdot 13^{2}$	$3$	$17.2085048979$	$37.31774244321726$			?	$A_4$ (as 6T4)	$[2]$	$2$	$3$	$13.3218351871$
6.2.27447121.1	$x^{6} - 2 x^{5} + 5 x^{4} - 23 x^{3} + 22 x^{2} - 20 x - 8$	$6$	[2,2]	$13^{4}\cdot 31^{2}$	$2$	$17.3679862311$	$30.78291537771342$			?	$A_4$ (as 6T4)	$[2]$	$2$	$3$	$15.6112172243$
6.2.30658369.1	$x^{6} - 2 x^{5} - 2 x^{4} + 28 x^{3} - 109 x^{2} + 146 x - 251$	$6$	[2,2]	$7^{4}\cdot 113^{2}$	$2$	$17.6912359391$	$38.898953270916685$			?	$A_4$ (as 6T4)	trivial	$2$	$3$	$30.1850208829$
6.6.33074001.1	$x^{6} - 18 x^{4} - 16 x^{3} + 57 x^{2} + 36 x - 57$	$6$	[6,0]	$3^{8}\cdot 71^{2}$	$2$	$17.9162778595$	$36.45783266912841$			?	$A_4$ (as 6T4)	trivial	$2$	$5$	$94.9877636452$
6.2.34963569.1	$x^{6} - 3 x^{5} + 6 x^{4} + 9 x^{3} - 60 x^{2} + 132 x - 136$	$6$	[2,2]	$3^{8}\cdot 73^{2}$	$2$	$18.0829504804$	$36.967757191167294$			?	$A_4$ (as 6T4)	trivial	$2$	$3$	$51.9383649006$
6.2.38725729.1	$x^{6} - x^{5} + 10 x^{4} - 21 x^{3} - 16 x^{2} - 142 x - 223$	$6$	[2,2]	$7^{4}\cdot 127^{2}$	$2$	$18.3935941784$	$41.23828102000196$			?	$A_4$ (as 6T4)	$[4]$	$2$	$3$	$7.70325286823$
6.2.45697600.1	$x^{6} + x^{4} - 30 x^{2} - 25$	$6$	[2,2]	$2^{6}\cdot 5^{2}\cdot 13^{4}$	$3$	$18.908143892$	$34.96704216279658$			?	$A_4$ (as 6T4)	$[2]$	$2$	$3$	$24.5715800966$
6.6.45697600.1	$x^{6} - 12 x^{4} + 35 x^{2} - 25$	$6$	[6,0]	$2^{6}\cdot 5^{2}\cdot 13^{4}$	$3$	$18.908143892$	$34.96704216279658$			?	$A_4$ (as 6T4)	trivial	$2$	$5$	$77.3799397685$
6.2.45697600.2	$x^{6} - 4 x^{4} - 25 x^{2} - 25$	$6$	[2,2]	$2^{6}\cdot 5^{2}\cdot 13^{4}$	$3$	$18.908143892$	$34.96704216279658$			?	$A_4$ (as 6T4)	$[2]$	$2$	$3$	$26.2306646252$
6.2.46389721.1	$x^{6} - 2 x^{5} + x^{4} - 32 x^{3} - 88 x^{2} - 32 x - 281$	$6$	[2,2]	$7^{4}\cdot 139^{2}$	$2$	$18.9555748781$	$43.14257805043105$			?	$A_4$ (as 6T4)	$[2]$	$2$	$3$	$16.2232789595$
6.2.51969681.1	$x^{6} - 3 x^{5} + 9 x^{4} + x^{3} - 27 x^{2} - 9 x - 153$	$6$	[2,2]	$3^{8}\cdot 89^{2}$	$2$	$19.3178300869$	$40.818465701990505$			?	$A_4$ (as 6T4)	trivial	$2$	$3$	$55.5653443236$
6.2.54700816.2	$x^{6} + 4 x^{4} - 9 x^{2} - 4$	$6$	[2,2]	$2^{4}\cdot 43^{4}$	$2$	$19.4834398085$	$24.54759593904292$			?	$A_4$ (as 6T4)	$[2]$	$2$	$3$	$69.9269134573$
6.6.59105344.1	$x^{6} - 11 x^{4} + 30 x^{2} - 16$	$6$	[6,0]	$2^{6}\cdot 31^{4}$	$2$	$19.7365448064$	$27.911689339648817$			?	$A_4$ (as 6T4)	trivial	$2$	$5$	$234.512628478$
6.2.59105344.3	$x^{6} - x^{5} - 9 x^{3} + 31 x^{2} - 18 x - 2$	$6$	[2,2]	$2^{6}\cdot 31^{4}$	$2$	$19.7365448064$	$27.911689339648817$			?	$A_4$ (as 6T4)	trivial	$2$	$3$	$108.645790625$
6.6.63091249.1	$x^{6} - 2 x^{5} - 16 x^{4} + 5 x^{3} + 52 x^{2} + 13 x - 13$	$6$	[6,0]	$13^{4}\cdot 47^{2}$	$2$	$19.9523867388$	$37.90337048597898$			?	$A_4$ (as 6T4)	trivial	$2$	$5$	$100.954842494$
6.6.66961489.1	$x^{6} - x^{5} - 26 x^{4} + 17 x^{3} + 194 x^{2} - 64 x - 344$	$6$	[6,0]	$7^{4}\cdot 167^{2}$	$2$	$20.1513517433$	$47.28865141512203$			?	$A_4$ (as 6T4)	trivial	$2$	$5$	$92.192814546$
6.2.75116889.1	$x^{6} + 12 x^{4} - 14 x^{3} + 15 x^{2} - 144 x - 159$	$6$	[2,2]	$3^{8}\cdot 107^{2}$	$2$	$20.5410638327$	$44.75623667824389$			?	$A_4$ (as 6T4)	$[2]$	$2$	$3$	$39.3099737675$
6.2.77951241.1	$x^{6} - 3 x^{5} + 15 x^{4} - 9 x^{3} - 33 x^{2} - 93 x - 199$	$6$	[2,2]	$3^{8}\cdot 109^{2}$	$2$	$20.6682563236$	$45.17258272906164$			?	$A_4$ (as 6T4)	trivial	$2$	$3$	$70.0671890391$
6.6.78659161.1	$x^{6} - x^{5} - 26 x^{4} + 17 x^{3} + 194 x^{2} - 64 x - 449$	$6$	[6,0]	$7^{4}\cdot 181^{2}$	$2$	$20.6994219852$	$49.23092329595919$			?	$A_4$ (as 6T4)	$[2]$	$2$	$5$	$50.3362726526$
6.2.80227849.1	$x^{6} - 2 x^{5} + 7 x^{4} + 9 x^{3} - 20 x^{2} + 76 x - 40$	$6$	[2,2]	$13^{4}\cdot 53^{2}$	$2$	$20.7676580709$	$40.250088196668614$			?	$A_4$ (as 6T4)	trivial	$2$	$3$	$52.0374642139$
6.2.93180409.1	$x^{6} - 2 x^{5} + 5 x^{4} - 14 x^{3} - 102 x^{2} + 216 x - 783$	$6$	[2,2]	$7^{4}\cdot 197^{2}$	$2$	$21.2922113661$	$51.36080315808082$			?	$A_4$ (as 6T4)	trivial	$2$	$3$	$49.9516527503$
6.2.105822369.1	$x^{6} - 3 x^{5} + 15 x^{4} + 9 x^{3} - 87 x^{2} + 213 x - 307$	$6$	[2,2]	$3^{8}\cdot 127^{2}$	$2$	$21.7485135726$	$48.75998164220662$			?	$A_4$ (as 6T4)	$[2]$	$2$	$3$	$41.8270548875$
6.2.106894921.1	$x^{6} - 2 x^{5} + 6 x^{4} - 34 x^{3} - 105 x^{2} - 196 x - 637$	$6$	[2,2]	$7^{4}\cdot 211^{2}$	$2$	$21.7850976905$	$53.154485765124456$			?	$A_4$ (as 6T4)	$[2]$	$2$	$3$	$33.2869353447$
6.2.119399329.1	$x^{6} - x^{5} + 2 x^{4} + 31 x^{3} - 170 x^{2} + 314 x - 841$	$6$	[2,2]	$7^{4}\cdot 223^{2}$	$2$	$22.1904945373$	$54.645087394089686$			?	$A_4$ (as 6T4)	$[2]$	$2$	$3$	$34.0742908414$
6.2.119946304.2	$x^{6} - 4 x^{4} - 7 x^{2} - 1$	$6$	[2,2]	$2^{6}\cdot 37^{4}$	$2$	$22.2074049372$	$31.406013247262095$			✓	$A_4$ (as 6T4)	trivial	$2$	$3$	$61.3299314887$
6.2.121352256.1	$x^{6} + 9 x^{4} - 102 x^{2} - 289$	$6$	[2,2]	$2^{6}\cdot 3^{8}\cdot 17^{2}$	$3$	$22.2505786156$	$50.45812718894282$			?	$A_4$ (as 6T4)	$[2]$	$2$	$3$	$46.7649395673$
6.6.121352256.1	$x^{6} - 24 x^{4} + 153 x^{2} - 289$	$6$	[6,0]	$2^{6}\cdot 3^{8}\cdot 17^{2}$	$3$	$22.2505786156$	$50.45812718894282$			?	$A_4$ (as 6T4)	trivial	$2$	$5$	$178.027748923$
6.2.121352256.2	$x^{6} + 18 x^{4} + 51 x^{2} - 289$	$6$	[2,2]	$2^{6}\cdot 3^{8}\cdot 17^{2}$	$3$	$22.2505786156$	$50.45812718894282$			?	$A_4$ (as 6T4)	$[4]$	$2$	$3$	$20.1210871096$
6.6.124612569.1	$x^{6} - 2 x^{5} - 12 x^{4} + 22 x^{3} + 33 x^{2} - 38 x - 37$	$6$	[6,0]	$3^{2}\cdot 61^{4}$	$2$	$22.3491138686$	$26.839876760292654$			?	$A_4$ (as 6T4)	trivial	$2$	$5$	$218.256422501$