Global number field search results

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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 690)

Label	Polynomial	Discriminant	Galois group	Class group
8.0.1817487424.1	x^8 - x^7 + 6x^6 - 2x^5 + 12x^4 + 4x^3 + 14x^2 + 2	\( 2^{6}\cdot 73^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	Trivial
8.0.9597924961.1	x^8 - x^7 + x^6 + 3x^5 + 5x^4 - 5x^3 + 7x + 9	\( 313^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2]$
8.0.9597924961.2	x^8 - x^7 - x^6 - 4x^5 + x^4 + 11x^3 + 16x^2 + 5x + 1	\( 313^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2]$
8.0.18078415936.1	x^8 - x^7 + 7x^6 + 7x^5 + 7x^4 + 7x^3 + 7x^2 + 5x + 2	\( 2^{6}\cdot 7^{10} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	Trivial
8.0.29079798784.1	x^8 - 2x^7 + 8x^6 - 2x^5 + 14x^4 + 10x^3 + 28x^2 + 10x + 1	\( 2^{10}\cdot 73^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2]$
8.0.72313663744.1	x^8 - 4x^7 + 14x^6 - 14x^5 + 14x^4 + 28x^3 + 14x^2 - 2x + 1	\( 2^{8}\cdot 7^{10} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2]$
8.0.100367308864.1	x^8 - 3x^7 + 4x^6 - 16x^5 + 46x^4 - 70x^3 + 82x^2 - 48x + 22	\( 2^{6}\cdot 199^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	Trivial
8.0.116319195136.1	x^8 - 2x^7 - 4x^6 - 8x^5 + 56x^4 - 54x^3 + 20x^2 - 4x + 1	\( 2^{12}\cdot 73^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2]$
8.0.116319195136.3	x^8 - 2x^7 + 10x^6 - 6x^5 + 2x^4 + 8x^3 - 16x^2 + 16x + 26	\( 2^{12}\cdot 73^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2]$
8.0.272225149504.1	x^8 - x^7 - 9x^6 - x^5 + 41x^4 + 21x^3 - 67x^2 - 35x + 66	\( 2^{6}\cdot 7^{4}\cdot 11^{6} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2]$
8.0.272225149504.2	x^8 - 3x^7 + 9x^6 - 21x^5 + 33x^4 - 69x^3 + 7x^2 - 7x + 238	\( 2^{6}\cdot 7^{4}\cdot 11^{6} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2]$
8.0.387790161984.1	x^8 + 4x^6 - 14x^5 + 6x^4 + 16x^3 + 32x^2 + 18x + 8	\( 2^{6}\cdot 3^{8}\cdot 31^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	Trivial
8.0.401469235456.1	x^8 - 2x^7 + 4x^6 - 4x^5 - 8x^4 + 4x^3 + 16x^2 - 14x + 6	\( 2^{8}\cdot 199^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	Trivial
8.0.401469235456.2	x^8 - 2x^7 - 4x^6 + 4x^5 + 12x^4 - 16x^3 + 68x + 52	\( 2^{8}\cdot 199^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	Trivial
8.0.525346636864.3	x^8 - 2x^7 + 2x^6 + 20x^5 + 20x^4 + 56x^2 + 52x + 40	\( 2^{6}\cdot 7^{4}\cdot 43^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	Trivial
8.0.525346636864.4	x^8 - 2x^7 + 2x^6 - 12x^5 + 64x^4 - 184x^3 + 296x^2 - 280x + 128	\( 2^{6}\cdot 7^{4}\cdot 43^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	Trivial
8.0.525346636864.5	x^8 - 2x^7 + 14x^6 - 38x^5 + 100x^4 - 198x^3 + 338x^2 - 322x + 139	\( 2^{6}\cdot 7^{4}\cdot 43^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	Trivial
8.0.591559418641.1	x^8 - x^7 + 11x^6 - 13x^5 + 16x^4 - 10x^3 + 17x^2 - 7x + 4	\( 877^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2]$
8.0.591559418641.2	x^8 - 2x^7 - 2x^6 + 7x^5 + 3x^4 - 34x^3 + 93x^2 - 29x + 39	\( 877^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2]$
8.0.777431921841.1	x^8 - 9x^6 - 4x^5 + 24x^4 + 21x^3 + 22x^2 - 3x + 3	\( 3^{4}\cdot 313^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2]$
8.0.777431921841.2	x^8 - 3x^7 + 9x^6 - 19x^5 + 35x^4 - 39x^3 + 19x^2 - 4x + 4	\( 3^{4}\cdot 313^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2]$
8.0.1135929640000.1	x^8 - 2x^7 + 16x^6 - 20x^5 + 56x^4 - 56x^3 + 80x^2 - 80x + 64	\( 2^{6}\cdot 5^{4}\cdot 73^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2, 2]$
8.0.1157018619904.1	x^8 - 4x^7 + 14x^6 - 14x^5 + 14x^4 + 28x^3 + 14x^2 - 18x + 23	\( 2^{12}\cdot 7^{10} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	Trivial
8.0.1157018619904.2	x^8 - 2x^7 + 28x^4 - 14x^3 - 56x^2 + 40x + 53	\( 2^{12}\cdot 7^{10} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	Trivial
8.0.1464351690816.1	x^8 - 4x^7 + 14x^6 - 14x^5 + 14x^4 + 28x^3 + 14x^2 - 30x + 64	\( 2^{6}\cdot 3^{4}\cdot 7^{10} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2, 2]$
8.0.1605876941824.1	x^8 - 2x^6 - 12x^5 + 40x^4 - 76x^3 + 74x^2 - 24x + 19	\( 2^{10}\cdot 199^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2]$
8.0.1624709678881.2	x^8 - x^7 - 5x^6 + 11x^5 + 3x^4 - 27x^3 + 29x^2 - 11x + 3	\( 1129^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	Trivial
8.0.1688107729984.5	x^8 - x^7 + 4x^6 - 2x^5 + 4x^4 - 60x^3 + 120x^2 - 88x + 24	\( 2^{6}\cdot 13^{4}\cdot 31^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2]$
8.0.1688107729984.6	x^8 - x^7 + 4x^6 + 16x^4 - 20x^3 + 24x^2 + 20x + 4	\( 2^{6}\cdot 13^{4}\cdot 31^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2]$
8.0.1861107122176.20	x^8 + 4x^6 - 12x^5 + 16x^4 - 40x^3 + 72x^2 - 52x + 202	\( 2^{16}\cdot 73^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	Trivial
8.0.1861107122176.22	x^8 - 4x^7 + 12x^6 - 8x^5 - 4x^4 - 40x^3 + 344x^2 - 608x + 612	\( 2^{16}\cdot 73^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	Trivial
8.0.2101386547456.12	x^8 - 2x^7 + 2x^6 - 16x^5 + 34x^4 + 4x^3 - 94x^2 + 16x + 153	\( 2^{8}\cdot 7^{4}\cdot 43^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2, 2]$
8.0.2420662999104.2	x^8 - 3x^7 - 7x^6 + 35x^5 - 21x^4 - 77x^3 + 189x^2 - 171x + 72	\( 2^{6}\cdot 3^{8}\cdot 7^{8} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	Trivial (GRH)
8.0.2528484794641.1	x^8 - 2x^7 + x^6 + 19x^5 + 31x^4 + 17x^3 + 9x^2 + 13x + 9	\( 13^{4}\cdot 97^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2]$
8.0.2528484794641.2	x^8 - x^7 + 12x^6 + 2x^5 + 49x^4 + 87x^3 + 148x^2 + 87x + 31	\( 13^{4}\cdot 97^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2]$
8.0.2528484794641.3	x^8 - x^7 - 7x^6 + 10x^5 - 15x^4 + 5x^3 + 111x^2 - 171x + 134	\( 13^{4}\cdot 97^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2, 2]$
8.0.2528484794641.4	x^8 + 7x^6 - 11x^5 + 65x^4 + 43x^3 + 191x^2 + 137x + 240	\( 13^{4}\cdot 97^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2]$
8.0.3490111457856.2	x^8 + 18x^6 - 6x^5 + 54x^4 - 108x^3 + 66x^2 - 18x + 9	\( 2^{6}\cdot 3^{10}\cdot 31^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[4]$
8.0.3490111457856.4	x^8 - 2x^7 + 4x^6 + 4x^5 + 10x^4 + 142x^3 + 196x^2 + 58x + 136	\( 2^{6}\cdot 3^{10}\cdot 31^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[4]$
8.0.3490111457856.5	x^8 - 3x^7 + 6x^6 + 30x^5 - 18x^4 - 90x^3 + 198x^2 - 162x + 54	\( 2^{6}\cdot 3^{10}\cdot 31^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2]$
8.0.4355602392064.2	x^8 - 4x^7 + 12x^6 - 20x^5 + 46x^4 - 94x^3 + 126x^2 - 110x + 49	\( 2^{10}\cdot 7^{4}\cdot 11^{6} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2]$
8.0.4355602392064.4	x^8 - 2x^7 + 2x^6 - 8x^5 + 60x^4 - 60x^3 - 52x^2 + 166x + 235	\( 2^{10}\cdot 7^{4}\cdot 11^{6} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2]$
8.0.4543718560000.9	x^8 + 4x^6 - 2x^5 + 52x^4 - 124x^3 + 352x^2 - 58x + 91	\( 2^{8}\cdot 5^{4}\cdot 73^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[4]$
8.0.4543718560000.10	x^8 - 2x^6 - 8x^5 - 16x^4 - 2x^3 + 58x^2 + 88x + 171	\( 2^{8}\cdot 5^{4}\cdot 73^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[4]$
8.0.5323914784321.1	x^8 + 14x^6 + 98x^4 + 280x^2 - 31x + 252	\( 7^{8}\cdot 31^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	Trivial (GRH)
8.0.5482378736704.1	x^8 - 3x^7 + 11x^6 - 37x^5 + 73x^4 - 79x^3 + 51x^2 - 23x + 12	\( 2^{6}\cdot 541^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	Trivial (GRH)
8.0.5482378736704.2	x^8 - x^7 + 5x^6 + x^5 - 23x^4 + 9x^3 + 27x^2 - 9x + 14	\( 2^{6}\cdot 541^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	Trivial (GRH)
8.0.5482378736704.3	x^8 - x^7 - 4x^6 + 18x^5 - 4x^4 - 36x^3 + 50x^2 - 28x + 6	\( 2^{6}\cdot 541^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	Trivial (GRH)
8.0.5857406763264.1	x^8 - 4x^7 + 14x^6 - 14x^5 + 14x^4 + 28x^3 + 14x^2 - 18x + 121	\( 2^{8}\cdot 3^{4}\cdot 7^{10} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2, 2]$
8.0.6029426229121.1	x^8 - 3x^7 + 17x^6 - 25x^5 + 50x^4 + 118x^3 - 75x^2 + 113x + 228	\( 1567^{4} \)	$C_2^3:(C_7: C_3)$ (as 8T36)	Trivial (GRH)