Number field search results

Results (1-50 of 6206 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
8.8.410338673.1	$x^{8} - x^{7} - 7 x^{6} + 6 x^{5} + 15 x^{4} - 10 x^{3} - 10 x^{2} + 4 x + 1$	$8$	[8,0]	$17^{7}$	$1$	$11.9300648987$	$11.93006489865314$		✓	✓	$C_8$ (as 8T1)	trivial	$2$	$7$	$28.437595417$
8.8.2147483648.1	$x^{8} - 8 x^{6} + 20 x^{4} - 16 x^{2} + 2$	$8$	[8,0]	$2^{31}$	$1$	$14.6720646913$	$14.67206469127474$		✓	✓	$C_8$ (as 8T1)	trivial	$2$	$7$	$123.0777333$
8.0.2147483648.1	$x^{8} + 8 x^{6} + 20 x^{4} + 16 x^{2} + 2$	$8$	[0,4]	$2^{31}$	$1$	$14.6720646913$	$14.67206469127474$	✓	✓	✓	$C_8$ (as 8T1)	trivial	$2$	$3$	$19.534360053$
8.0.33237432513.1	$x^{8} - x^{7} + 10 x^{6} - 11 x^{5} + 15 x^{4} - 61 x^{3} + 58 x^{2} - 47 x + 103$	$8$	[0,4]	$3^{4}\cdot 17^{7}$	$2$	$20.6634785421$	$20.663478542061284$	✓	✓	?	$C_8$ (as 8T1)	$[2]$	$2$	$3$	$27.6959098582$
8.0.105046700288.1	$x^{8} + 17 x^{6} + 68 x^{4} + 85 x^{2} + 17$	$8$	[0,4]	$2^{8}\cdot 17^{7}$	$2$	$23.8601297973$	$23.86012979730628$	✓	✓		$C_8$ (as 8T1)	$[2, 2]$	$2$	$3$	$27.6959098582$
8.8.173946175488.1	$x^{8} - 24 x^{6} + 180 x^{4} - 432 x^{2} + 162$	$8$	[8,0]	$2^{31}\cdot 3^{4}$	$2$	$25.4127614972$	$25.412761497225222$		✓	?	$C_8$ (as 8T1)	trivial	$2$	$7$	$1494.12984141$
8.0.173946175488.1	$x^{8} + 24 x^{6} + 180 x^{4} + 432 x^{2} + 162$	$8$	[0,4]	$2^{31}\cdot 3^{4}$	$2$	$25.4127614972$	$25.412761497225222$	✓	✓	?	$C_8$ (as 8T1)	$[3, 6]$	$2$	$3$	$19.534360053$
8.0.194754273881.1	$x^{8} - x^{7} + 3 x^{6} - 11 x^{5} + 44 x^{4} + 53 x^{3} + 153 x^{2} + 160 x + 59$	$8$	[0,4]	$41^{7}$	$1$	$25.7742403823$	$25.774240382333762$	✓	✓	?	$C_8$ (as 8T1)	trivial	$2$	$3$	$108.197795509$
8.8.256461670625.1	$x^{8} - x^{7} - 24 x^{6} + 23 x^{5} + 151 x^{4} - 197 x^{3} - 214 x^{2} + 429 x - 169$	$8$	[8,0]	$5^{4}\cdot 17^{7}$	$2$	$26.6764360894$	$26.676436089372558$		✓	?	$C_8$ (as 8T1)	$[2]$	$2$	$7$	$636.601883042$
8.0.985223153873.1	$x^{8} - x^{7} + 27 x^{6} - 28 x^{5} + 151 x^{4} - 350 x^{3} + 500 x^{2} - 846 x + 1157$	$8$	[0,4]	$7^{4}\cdot 17^{7}$	$2$	$31.5639848467$	$31.563984846697192$	✓	✓	?	$C_8$ (as 8T1)	$[3, 6]$	$2$	$3$	$27.6959098582$
8.0.1342177280000.1	$x^{8} + 40 x^{6} + 500 x^{4} + 2000 x^{2} + 1250$	$8$	[0,4]	$2^{31}\cdot 5^{4}$	$2$	$32.80773402$	$32.807734019964784$	✓	✓	?	$C_8$ (as 8T1)	$[34]$	$2$	$3$	$19.534360053$
8.8.1342177280000.1	$x^{8} - 40 x^{6} + 500 x^{4} - 2000 x^{2} + 1250$	$8$	[8,0]	$2^{31}\cdot 5^{4}$	$2$	$32.80773402$	$32.807734019964784$		✓	?	$C_8$ (as 8T1)	$[2]$	$2$	$7$	$2507.3594667$
8.0.1680747204608.1	$x^{8} + 34 x^{6} + 272 x^{4} + 680 x^{2} + 272$	$8$	[0,4]	$2^{12}\cdot 17^{7}$	$2$	$33.7433191593$	$33.74331915933294$	✓	✓		$C_8$ (as 8T1)	$[6, 6]$	$2$	$3$	$27.6959098582$
8.8.1680747204608.1	$x^{8} - 34 x^{6} + 272 x^{4} - 680 x^{2} + 272$	$8$	[8,0]	$2^{12}\cdot 17^{7}$	$2$	$33.7433191593$	$33.74331915933294$		✓		$C_8$ (as 8T1)	$[2]$	$2$	$7$	$2413.01102399$
8.8.5156108238848.1	$x^{8} - 56 x^{6} + 980 x^{4} - 5488 x^{2} + 4802$	$8$	[8,0]	$2^{31}\cdot 7^{4}$	$2$	$38.818634393$	$38.81863439296463$		✓	?	$C_8$ (as 8T1)	trivial	$2$	$7$	$9687.95863021$
8.0.5156108238848.1	$x^{8} + 56 x^{6} + 980 x^{4} + 5488 x^{2} + 4802$	$8$	[0,4]	$2^{31}\cdot 7^{4}$	$2$	$38.818634393$	$38.81863439296463$	✓	✓	?	$C_8$ (as 8T1)	$[2, 34]$	$2$	$3$	$19.534360053$
8.0.6007768511393.1	$x^{8} - x^{7} + 44 x^{6} - 45 x^{5} + 423 x^{4} - 877 x^{3} + 1826 x^{2} - 3515 x + 4591$	$8$	[0,4]	$11^{4}\cdot 17^{7}$	$2$	$39.5675489934$	$39.56754899342178$	✓	✓	?	$C_8$ (as 8T1)	$[34]$	$2$	$3$	$27.6959098582$
8.0.6411541765625.1	$x^{8} - x^{7} + 10 x^{6} - 79 x^{5} + 134 x^{4} + 41 x^{3} + 245 x^{2} - 846 x + 596$	$8$	[0,4]	$5^{6}\cdot 17^{7}$	$2$	$39.8905761936$	$39.89057619356904$	✓	✓		$C_8$ (as 8T1)	$[4]$	$2$	$3$	$489.802404202$
8.0.6411541765625.2	$x^{8} - x^{7} + 10 x^{6} + 6 x^{5} + 49 x^{4} - 129 x^{3} + 500 x^{2} + 2044 x + 1616$	$8$	[0,4]	$5^{6}\cdot 17^{7}$	$2$	$39.8905761936$	$39.89057619356904$	✓	✓		$C_8$ (as 8T1)	$[292]$	$2$	$3$	$489.802404202$
8.8.8508782723328.1	$x^{8} - 51 x^{6} + 612 x^{4} - 2295 x^{2} + 1377$	$8$	[8,0]	$2^{8}\cdot 3^{4}\cdot 17^{7}$	$3$	$41.3269570841$	$41.32695708412257$		✓		$C_8$ (as 8T1)	$[2]$	$2$	$7$	$2744.12339498$
8.0.11047398519097.1	$x^{8} - x^{7} + 5 x^{6} + 17 x^{5} - 46 x^{4} + 136 x^{3} + 320 x^{2} - 512 x + 4096$	$8$	[0,4]	$73^{7}$	$1$	$42.6979970229$	$42.69799702286967$	✓	✓		$C_8$ (as 8T1)	$[89]$	$2$	$3$	$2046.25577237$
8.8.11719682839553.1	$x^{8} - x^{7} - 58 x^{6} + 57 x^{5} + 831 x^{4} - 1285 x^{3} - 3070 x^{2} + 6889 x - 2753$	$8$	[8,0]	$13^{4}\cdot 17^{7}$	$2$	$43.0144607117$	$43.014460711706995$		✓	?	$C_8$ (as 8T1)	$[2]$	$2$	$7$	$3630.8787207$
8.8.15775096184361.1	$x^{8} - x^{7} - 38 x^{6} + 30 x^{5} + 331 x^{4} - 152 x^{3} - 708 x^{2} - 291 x - 23$	$8$	[8,0]	$3^{4}\cdot 41^{7}$	$2$	$44.6422938687$	$44.64229386869556$		✓	?	$C_8$ (as 8T1)	trivial	$2$	$7$	$8457.57651835$
8.0.20773395320625.1	$x^{8} - x^{7} + 61 x^{6} - 62 x^{5} + 831 x^{4} - 1642 x^{3} + 4546 x^{2} - 9176 x + 12241$	$8$	[0,4]	$3^{4}\cdot 5^{4}\cdot 17^{7}$	$3$	$46.2049426717$	$46.20494267165728$	✓	✓	?	$C_8$ (as 8T1)	$[2, 34]$	$2$	$3$	$27.6959098582$
8.8.31441308090368.1	$x^{8} - 88 x^{6} + 2420 x^{4} - 21296 x^{2} + 29282$	$8$	[8,0]	$2^{31}\cdot 11^{4}$	$2$	$48.6617334808$	$48.66173348077995$		✓	?	$C_8$ (as 8T1)	trivial	$2$	$7$	$21339.8618782$
8.0.31441308090368.8	$x^{8} + 88 x^{6} + 2420 x^{4} + 21296 x^{2} + 29282$	$8$	[0,4]	$2^{31}\cdot 11^{4}$	$2$	$48.6617334808$	$48.66173348077995$	✓	✓	?	$C_8$ (as 8T1)	$[226]$	$2$	$3$	$19.534360053$
8.0.33554432000000.1	$x^{8} + 40 x^{6} + 500 x^{4} + 2000 x^{2} + 50$	$8$	[0,4]	$2^{31}\cdot 5^{6}$	$2$	$49.0590050814$	$49.05900508138431$	✓	✓	?	$C_8$ (as 8T1)	$[3, 12]$	$2$	$3$	$78.6242549932$
8.8.33554432000000.1	$x^{8} - 40 x^{6} + 500 x^{4} - 2000 x^{2} + 50$	$8$	[8,0]	$2^{31}\cdot 5^{6}$	$2$	$49.0590050814$	$49.05900508138431$		✓		$C_8$ (as 8T1)	$[2]$	$2$	$7$	$26385.2551796$
8.0.33554432000000.2	$x^{8} + 40 x^{6} + 500 x^{4} + 2000 x^{2} + 2450$	$8$	[0,4]	$2^{31}\cdot 5^{6}$	$2$	$49.0590050814$	$49.05900508138431$	✓	✓		$C_8$ (as 8T1)	$[164]$	$2$	$3$	$78.6242549932$
8.8.33554432000000.2	$x^{8} - 40 x^{6} + 500 x^{4} - 2000 x^{2} + 2450$	$8$	[8,0]	$2^{31}\cdot 5^{6}$	$2$	$49.0590050814$	$49.05900508138431$		✓	?	$C_8$ (as 8T1)	$[2]$	$2$	$7$	$6237.2438059$
8.0.44231334895529.1	$x^{8} - x^{7} + 6 x^{6} - 46 x^{5} - 143 x^{4} + 575 x^{3} + 1160 x^{2} - 16 x + 512$	$8$	[0,4]	$89^{7}$	$1$	$50.7827547495$	$50.78275474951909$	✓	✓		$C_8$ (as 8T1)	$[113]$	$2$	$3$	$2970.52387144$
8.8.49857094113536.1	$x^{8} - 41 x^{6} + 533 x^{4} - 2296 x^{2} + 656$	$8$	[8,0]	$2^{8}\cdot 41^{7}$	$2$	$51.5484807647$	$51.548480764667524$		✓		$C_8$ (as 8T1)	trivial	$2$	$7$	$27148.8915251$
8.0.53475746204033.2	$x^{8} - x^{7} + 78 x^{6} - 79 x^{5} + 1375 x^{4} - 2645 x^{3} + 9170 x^{2} - 18951 x + 26351$	$8$	[0,4]	$17^{7}\cdot 19^{4}$	$2$	$52.0019472831$	$52.00194728311084$	✓	✓	?	$C_8$ (as 8T1)	$[10, 10]$	$2$	$3$	$27.6959098582$
8.8.61334280470528.1	$x^{8} - 104 x^{6} + 3380 x^{4} - 35152 x^{2} + 57122$	$8$	[8,0]	$2^{31}\cdot 13^{4}$	$2$	$52.9008815613$	$52.9008815613158$		✓	?	$C_8$ (as 8T1)	$[2]$	$2$	$7$	$8398.03205033$
8.0.61334280470528.11	$x^{8} + 104 x^{6} + 3380 x^{4} + 35152 x^{2} + 57122$	$8$	[0,4]	$2^{31}\cdot 13^{4}$	$2$	$52.9008815613$	$52.9008815613158$	✓	✓	?	$C_8$ (as 8T1)	$[9, 18]$	$2$	$3$	$19.534360053$
8.0.65654187680000.2	$x^{8} + 85 x^{6} + 1700 x^{4} + 10625 x^{2} + 10625$	$8$	[0,4]	$2^{8}\cdot 5^{4}\cdot 17^{7}$	$3$	$53.3528721787$	$53.352872178745116$	✓	✓		$C_8$ (as 8T1)	$[2, 10, 10]$	$2$	$3$	$27.6959098582$
8.8.79803075463713.1	$x^{8} - x^{7} - 92 x^{6} + 91 x^{5} + 2055 x^{4} - 3325 x^{3} - 12590 x^{2} + 28309 x - 7649$	$8$	[8,0]	$3^{4}\cdot 7^{4}\cdot 17^{7}$	$3$	$54.6704254438$	$54.67042544381368$		✓	?	$C_8$ (as 8T1)	$[2]$	$2$	$7$	$11333.9362425$
8.8.80798284478113.1	$x^{8} - x^{7} - 42 x^{6} + 59 x^{5} + 497 x^{4} - 719 x^{3} - 1792 x^{2} + 2295 x + 193$	$8$	[8,0]	$97^{7}$	$1$	$54.7551871235$	$54.755187123491936$		✓	?	$C_8$ (as 8T1)	trivial	$2$	$7$	$13092.2724361$
8.8.108716359680000.1	$x^{8} - 120 x^{6} + 4500 x^{4} - 54000 x^{2} + 101250$	$8$	[8,0]	$2^{31}\cdot 3^{4}\cdot 5^{4}$	$3$	$56.8246622038$	$56.82466220378493$		✓	?	$C_8$ (as 8T1)	$[2]$	$2$	$7$	$12922.0093704$
8.0.108716359680000.13	$x^{8} + 120 x^{6} + 4500 x^{4} + 54000 x^{2} + 101250$	$8$	[0,4]	$2^{31}\cdot 3^{4}\cdot 5^{4}$	$3$	$56.8246622038$	$56.82466220378493$	✓	✓	?	$C_8$ (as 8T1)	$[14, 14]$	$2$	$3$	$19.534360053$
8.0.114829584590993.1	$x^{8} - x^{7} + 95 x^{6} - 96 x^{5} + 2055 x^{4} - 3886 x^{3} + 16208 x^{2} - 33962 x + 49573$	$8$	[0,4]	$17^{7}\cdot 23^{4}$	$2$	$57.2145813161$	$57.21458131612729$	✓	✓	?	$C_8$ (as 8T1)	$[7, 14]$	$2$	$3$	$27.6959098582$
8.0.121721421175625.1	$x^{8} - x^{7} + 44 x^{6} - 52 x^{5} + 823 x^{4} + 94 x^{3} + 6016 x^{2} + 6843 x + 4651$	$8$	[0,4]	$5^{4}\cdot 41^{7}$	$2$	$57.6329535633$	$57.632953563318466$	✓	✓	?	$C_8$ (as 8T1)	$[6, 6]$	$2$	$3$	$108.197795509$
8.8.136140523573248.1	$x^{8} - 102 x^{6} + 2448 x^{4} - 18360 x^{2} + 22032$	$8$	[8,0]	$2^{12}\cdot 3^{4}\cdot 17^{7}$	$3$	$58.4451432$	$58.445143199977$		✓		$C_8$ (as 8T1)	$[2]$	$2$	$7$	$24393.5787616$
8.0.136140523573248.5	$x^{8} + 102 x^{6} + 2448 x^{4} + 18360 x^{2} + 22032$	$8$	[0,4]	$2^{12}\cdot 3^{4}\cdot 17^{7}$	$3$	$58.4451432$	$58.445143199977$	✓	✓		$C_8$ (as 8T1)	$[2, 2, 82]$	$2$	$3$	$27.6959098582$
8.8.179359981764608.1	$x^{8} - 136 x^{6} + 5780 x^{4} - 78608 x^{2} + 167042$	$8$	[8,0]	$2^{31}\cdot 17^{4}$	$2$	$60.494472468$	$60.49447246802112$		✓	?	$C_8$ (as 8T1)	$[2]$	$2$	$7$	$19415.8257216$
8.0.179359981764608.32	$x^{8} + 136 x^{6} + 5780 x^{4} + 78608 x^{2} + 167042$	$8$	[0,4]	$2^{31}\cdot 17^{4}$	$2$	$60.494472468$	$60.49447246802112$	✓	✓	?	$C_8$ (as 8T1)	$[2, 2, 10, 10]$	$2$	$3$	$19.534360053$
8.8.235260548044817.1	$x^{8} - x^{7} - 49 x^{6} - 16 x^{5} + 511 x^{4} + 367 x^{3} - 1499 x^{2} - 798 x + 1372$	$8$	[8,0]	$113^{7}$	$1$	$62.5811641949$	$62.58116419486453$		✓		$C_8$ (as 8T1)	trivial	$2$	$7$	$172951.810041$
8.8.252217127391488.1	$x^{8} - 119 x^{6} + 3332 x^{4} - 29155 x^{2} + 40817$	$8$	[8,0]	$2^{8}\cdot 7^{4}\cdot 17^{7}$	$3$	$63.1279696934$	$63.127969693394384$		✓		$C_8$ (as 8T1)	$[2]$	$2$	$7$	$31560.7919293$
8.8.279862216491008.1	$x^{8} - 152 x^{6} + 7220 x^{4} - 109744 x^{2} + 260642$	$8$	[8,0]	$2^{31}\cdot 19^{4}$	$2$	$63.9540472824$	$63.954047282357884$		✓	?	$C_8$ (as 8T1)	trivial	$2$	$7$	$54291.5640611$
8.0.279862216491008.16	$x^{8} + 152 x^{6} + 7220 x^{4} + 109744 x^{2} + 260642$	$8$	[0,4]	$2^{31}\cdot 19^{4}$	$2$	$63.9540472824$	$63.954047282357884$	✓	✓	?	$C_8$ (as 8T1)	$[274]$	$2$	$3$	$19.534360053$