Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying matches 1-50 of 6206)

Label	Polynomial	Discriminant	Galois group	Class group
8.8.410338673.1	x^8 - x^7 - 7x^6 + 6x^5 + 15x^4 - 10x^3 - 10x^2 + 4x + 1	\( 17^{7} \)	$C_8$ (as 8T1)	Trivial
8.0.2147483648.1	x^8 + 8x^6 + 20x^4 + 16x^2 + 2	\( 2^{31} \)	$C_8$ (as 8T1)	Trivial
8.8.2147483648.1	x^8 - 8x^6 + 20x^4 - 16x^2 + 2	\( 2^{31} \)	$C_8$ (as 8T1)	Trivial
8.0.33237432513.1	x^8 - x^7 + 10x^6 - 11x^5 + 15x^4 - 61x^3 + 58x^2 - 47x + 103	\( 3^{4}\cdot 17^{7} \)	$C_8$ (as 8T1)	$[2]$
8.0.105046700288.1	x^8 + 17x^6 + 68x^4 + 85x^2 + 17	\( 2^{8}\cdot 17^{7} \)	$C_8$ (as 8T1)	$[2, 2]$
8.0.173946175488.1	x^8 + 24x^6 + 180x^4 + 432x^2 + 162	\( 2^{31}\cdot 3^{4} \)	$C_8$ (as 8T1)	$[3, 6]$
8.8.173946175488.1	x^8 - 24x^6 + 180x^4 - 432x^2 + 162	\( 2^{31}\cdot 3^{4} \)	$C_8$ (as 8T1)	Trivial
8.0.194754273881.1	x^8 - x^7 + 3x^6 - 11x^5 + 44x^4 + 53x^3 + 153x^2 + 160x + 59	\( 41^{7} \)	$C_8$ (as 8T1)	Trivial
8.8.256461670625.1	x^8 - x^7 - 24x^6 + 23x^5 + 151x^4 - 197x^3 - 214x^2 + 429x - 169	\( 5^{4}\cdot 17^{7} \)	$C_8$ (as 8T1)	$[2]$
8.0.985223153873.1	x^8 - x^7 + 27x^6 - 28x^5 + 151x^4 - 350x^3 + 500x^2 - 846x + 1157	\( 7^{4}\cdot 17^{7} \)	$C_8$ (as 8T1)	$[3, 6]$
8.0.1342177280000.1	x^8 + 40x^6 + 500x^4 + 2000x^2 + 1250	\( 2^{31}\cdot 5^{4} \)	$C_8$ (as 8T1)	$[34]$
8.8.1342177280000.1	x^8 - 40x^6 + 500x^4 - 2000x^2 + 1250	\( 2^{31}\cdot 5^{4} \)	$C_8$ (as 8T1)	$[2]$
8.0.1680747204608.1	x^8 + 34x^6 + 272x^4 + 680x^2 + 272	\( 2^{12}\cdot 17^{7} \)	$C_8$ (as 8T1)	$[6, 6]$
8.8.1680747204608.1	x^8 - 34x^6 + 272x^4 - 680x^2 + 272	\( 2^{12}\cdot 17^{7} \)	$C_8$ (as 8T1)	$[2]$
8.0.5156108238848.1	x^8 + 56x^6 + 980x^4 + 5488x^2 + 4802	\( 2^{31}\cdot 7^{4} \)	$C_8$ (as 8T1)	$[2, 34]$
8.8.5156108238848.1	x^8 - 56x^6 + 980x^4 - 5488x^2 + 4802	\( 2^{31}\cdot 7^{4} \)	$C_8$ (as 8T1)	Trivial
8.0.6007768511393.1	x^8 - x^7 + 44x^6 - 45x^5 + 423x^4 - 877x^3 + 1826x^2 - 3515x + 4591	\( 11^{4}\cdot 17^{7} \)	$C_8$ (as 8T1)	$[34]$
8.0.6411541765625.1	x^8 - x^7 + 10x^6 - 79x^5 + 134x^4 + 41x^3 + 245x^2 - 846x + 596	\( 5^{6}\cdot 17^{7} \)	$C_8$ (as 8T1)	$[4]$
8.0.6411541765625.2	x^8 - x^7 + 10x^6 + 6x^5 + 49x^4 - 129x^3 + 500x^2 + 2044x + 1616	\( 5^{6}\cdot 17^{7} \)	$C_8$ (as 8T1)	$[292]$
8.8.8508782723328.1	x^8 - 51x^6 + 612x^4 - 2295x^2 + 1377	\( 2^{8}\cdot 3^{4}\cdot 17^{7} \)	$C_8$ (as 8T1)	$[2]$
8.0.11047398519097.1	x^8 - x^7 + 5x^6 + 17x^5 - 46x^4 + 136x^3 + 320x^2 - 512x + 4096	\( 73^{7} \)	$C_8$ (as 8T1)	$[89]$
8.8.11719682839553.1	x^8 - x^7 - 58x^6 + 57x^5 + 831x^4 - 1285x^3 - 3070x^2 + 6889x - 2753	\( 13^{4}\cdot 17^{7} \)	$C_8$ (as 8T1)	$[2]$
8.8.15775096184361.1	x^8 - x^7 - 38x^6 + 30x^5 + 331x^4 - 152x^3 - 708x^2 - 291x - 23	\( 3^{4}\cdot 41^{7} \)	$C_8$ (as 8T1)	Trivial
8.0.20773395320625.1	x^8 - x^7 + 61x^6 - 62x^5 + 831x^4 - 1642x^3 + 4546x^2 - 9176x + 12241	\( 3^{4}\cdot 5^{4}\cdot 17^{7} \)	$C_8$ (as 8T1)	$[2, 34]$
8.8.31441308090368.1	x^8 - 88x^6 + 2420x^4 - 21296x^2 + 29282	\( 2^{31}\cdot 11^{4} \)	$C_8$ (as 8T1)	Trivial
8.0.31441308090368.8	x^8 + 88x^6 + 2420x^4 + 21296x^2 + 29282	\( 2^{31}\cdot 11^{4} \)	$C_8$ (as 8T1)	$[226]$
8.0.33554432000000.1	x^8 + 40x^6 + 500x^4 + 2000x^2 + 50	\( 2^{31}\cdot 5^{6} \)	$C_8$ (as 8T1)	$[3, 12]$
8.8.33554432000000.1	x^8 - 40x^6 + 500x^4 - 2000x^2 + 50	\( 2^{31}\cdot 5^{6} \)	$C_8$ (as 8T1)	$[2]$
8.0.33554432000000.2	x^8 + 40x^6 + 500x^4 + 2000x^2 + 2450	\( 2^{31}\cdot 5^{6} \)	$C_8$ (as 8T1)	$[164]$
8.8.33554432000000.2	x^8 - 40x^6 + 500x^4 - 2000x^2 + 2450	\( 2^{31}\cdot 5^{6} \)	$C_8$ (as 8T1)	$[2]$
8.0.44231334895529.1	x^8 - x^7 + 6x^6 - 46x^5 - 143x^4 + 575x^3 + 1160x^2 - 16x + 512	\( 89^{7} \)	$C_8$ (as 8T1)	$[113]$
8.8.49857094113536.1	x^8 - 41x^6 + 533x^4 - 2296x^2 + 656	\( 2^{8}\cdot 41^{7} \)	$C_8$ (as 8T1)	Trivial
8.0.53475746204033.2	x^8 - x^7 + 78x^6 - 79x^5 + 1375x^4 - 2645x^3 + 9170x^2 - 18951x + 26351	\( 17^{7}\cdot 19^{4} \)	$C_8$ (as 8T1)	$[10, 10]$
8.8.61334280470528.1	x^8 - 104x^6 + 3380x^4 - 35152x^2 + 57122	\( 2^{31}\cdot 13^{4} \)	$C_8$ (as 8T1)	$[2]$
8.0.61334280470528.11	x^8 + 104x^6 + 3380x^4 + 35152x^2 + 57122	\( 2^{31}\cdot 13^{4} \)	$C_8$ (as 8T1)	$[9, 18]$
8.0.65654187680000.2	x^8 + 85x^6 + 1700x^4 + 10625x^2 + 10625	\( 2^{8}\cdot 5^{4}\cdot 17^{7} \)	$C_8$ (as 8T1)	$[2, 10, 10]$
8.8.79803075463713.1	x^8 - x^7 - 92x^6 + 91x^5 + 2055x^4 - 3325x^3 - 12590x^2 + 28309x - 7649	\( 3^{4}\cdot 7^{4}\cdot 17^{7} \)	$C_8$ (as 8T1)	$[2]$
8.8.80798284478113.1	x^8 - x^7 - 42x^6 + 59x^5 + 497x^4 - 719x^3 - 1792x^2 + 2295x + 193	\( 97^{7} \)	$C_8$ (as 8T1)	Trivial
8.8.108716359680000.1	x^8 - 120x^6 + 4500x^4 - 54000x^2 + 101250	\( 2^{31}\cdot 3^{4}\cdot 5^{4} \)	$C_8$ (as 8T1)	$[2]$
8.0.108716359680000.13	x^8 + 120x^6 + 4500x^4 + 54000x^2 + 101250	\( 2^{31}\cdot 3^{4}\cdot 5^{4} \)	$C_8$ (as 8T1)	$[14, 14]$
8.0.114829584590993.1	x^8 - x^7 + 95x^6 - 96x^5 + 2055x^4 - 3886x^3 + 16208x^2 - 33962x + 49573	\( 17^{7}\cdot 23^{4} \)	$C_8$ (as 8T1)	$[7, 14]$
8.0.121721421175625.1	x^8 - x^7 + 44x^6 - 52x^5 + 823x^4 + 94x^3 + 6016x^2 + 6843x + 4651	\( 5^{4}\cdot 41^{7} \)	$C_8$ (as 8T1)	$[6, 6]$
8.8.136140523573248.1	x^8 - 102x^6 + 2448x^4 - 18360x^2 + 22032	\( 2^{12}\cdot 3^{4}\cdot 17^{7} \)	$C_8$ (as 8T1)	$[2]$
8.0.136140523573248.5	x^8 + 102x^6 + 2448x^4 + 18360x^2 + 22032	\( 2^{12}\cdot 3^{4}\cdot 17^{7} \)	$C_8$ (as 8T1)	$[2, 2, 82]$
8.8.179359981764608.1	x^8 - 136x^6 + 5780x^4 - 78608x^2 + 167042	\( 2^{31}\cdot 17^{4} \)	$C_8$ (as 8T1)	$[2]$
8.0.179359981764608.32	x^8 + 136x^6 + 5780x^4 + 78608x^2 + 167042	\( 2^{31}\cdot 17^{4} \)	$C_8$ (as 8T1)	$[2, 2, 10, 10]$
8.8.235260548044817.1	x^8 - x^7 - 49x^6 - 16x^5 + 511x^4 + 367x^3 - 1499x^2 - 798x + 1372	\( 113^{7} \)	$C_8$ (as 8T1)	Trivial
8.8.252217127391488.1	x^8 - 119x^6 + 3332x^4 - 29155x^2 + 40817	\( 2^{8}\cdot 7^{4}\cdot 17^{7} \)	$C_8$ (as 8T1)	$[2]$
8.8.279862216491008.1	x^8 - 152x^6 + 7220x^4 - 109744x^2 + 260642	\( 2^{31}\cdot 19^{4} \)	$C_8$ (as 8T1)	Trivial
8.0.279862216491008.16	x^8 + 152x^6 + 7220x^4 + 109744x^2 + 260642	\( 2^{31}\cdot 19^{4} \)	$C_8$ (as 8T1)	$[274]$