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 10865)

Label	Polynomial	Discriminant	Galois group	Class group
8.2.107171875.1	x^8 - 2x^7 + 2x^6 + x^4 + 5x^3 - 7x^2 - 6x + 1	\( -\,5^{6}\cdot 19^{3} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.143327232.1	x^8 + 6x^4 - 3	\( -\,2^{16}\cdot 3^{7} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.257298363.1	x^8 - 2x^7 + x^6 - 5x^5 + 7x^4 - 2x^3 + x^2 - 5x + 1	\( -\,3^{7}\cdot 7^{6} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.268435456.2	x^8 - 2x^4 - 1	\( -\,2^{28} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.573308928.1	x^8 - 6x^4 - 3	\( -\,2^{18}\cdot 3^{7} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.2147483648.2	x^8 - 2	\( -\,2^{31} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.3209046875.2	x^8 - x^7 - 4x^6 + 14x^5 + 6x^4 - 15x^3 + 5x^2 + 10x - 5	\( -\,5^{6}\cdot 59^{3} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.5754585088.2	x^8 + 4x^6 + 4x^4 - 4x^2 - 7	\( -\,2^{24}\cdot 7^{3} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.5754585088.3	x^8 - 4x^6 + 4x^4 + 4x^2 - 7	\( -\,2^{24}\cdot 7^{3} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.7703734375.1	x^8 - 2x^7 - x^6 + 2x^5 - 4x^4 - 20x^3 - 30x^2 - 20x - 5	\( -\,5^{6}\cdot 79^{3} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.8680921875.1	x^8 - 3x^7 - x^6 - 7x^5 + 21x^4 + 80x^3 - 45x^2 - 190x - 95	\( -\,3^{4}\cdot 5^{6}\cdot 19^{3} \)	$QD_{16}$ (as 8T8)	$[2]$
8.2.14206147659.1	x^8 - 2x^7 - x^6 - 5x^5 + 16x^4 - x^3 - 4x^2 - 28x + 16	\( -\,3^{6}\cdot 11^{7} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.15160921875.1	x^8 - 3x^7 + 7x^6 - 39x^4 + 105x^3 - 137x^2 + 96x - 29	\( -\,3^{6}\cdot 5^{6}\cdot 11^{3} \)	$QD_{16}$ (as 8T8)	$[2]$
8.2.15160921875.2	x^8 - x^7 - 4x^6 - 16x^5 - 14x^4 - 5x^3 + 5x^2 + 10x - 5	\( -\,3^{6}\cdot 5^{6}\cdot 11^{3} \)	$QD_{16}$ (as 8T8)	$[2]$
8.8.16098453125.1	x^8 - 3x^7 - 8x^6 + 35x^5 - 19x^4 - 45x^3 + 53x^2 - 14x + 1	\( 5^{6}\cdot 101^{3} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.21743271936.2	x^8 - 18x^4 - 81	\( -\,2^{28}\cdot 3^{4} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.24716870656.1	x^8 - 4x^7 + 11x^6 - 2x^5 - 15x^4 + 6x^3 - 54x^2 - 96x - 38	\( -\,2^{10}\cdot 17^{6} \)	$QD_{16}$ (as 8T8)	$[2]$
8.2.26261675072.2	x^8 - 3x^7 + 5x^6 + 9x^5 - 26x^4 + 18x^3 + 20x^2 - 24x + 16	\( -\,2^{6}\cdot 17^{7} \)	$QD_{16}$ (as 8T8)	$[4]$
8.2.27436000000.3	x^8 - 5x^6 - 35x^4 + 275x^2 - 475	\( -\,2^{8}\cdot 5^{6}\cdot 19^{3} \)	$QD_{16}$ (as 8T8)	$[2]$
8.2.36691771392.3	x^8 - 12x^4 - 12	\( -\,2^{24}\cdot 3^{7} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.36691771392.4	x^8 + 12x^4 - 12	\( -\,2^{24}\cdot 3^{7} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.41962796875.1	x^8 - x^7 + x^6 - 21x^5 - 9x^4 + 5x^3 + 10x - 5	\( -\,5^{6}\cdot 139^{3} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.58727785103.1	x^8 - x^7 - 3x^6 - 2x^5 + 9x^4 + 22x^3 - 12x^2 - 34x - 23	\( -\,13^{6}\cdot 23^{3} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.63589515264.1	x^8 - 4x^7 - 2x^6 + 8x^5 + 4x^4 - 16x^3 - 2x^2 + 8x - 23	\( -\,2^{16}\cdot 3^{6}\cdot 11^{3} \)	$QD_{16}$ (as 8T8)	$[2]$
8.2.63589515264.2	x^8 - 4x^7 + 10x^6 - 4x^5 - 20x^4 - 4x^3 + 40x^2 - 52x + 22	\( -\,2^{16}\cdot 3^{6}\cdot 11^{3} \)	$QD_{16}$ (as 8T8)	$[2]$
8.2.65536000000.1	x^8 - 10x^4 - 100	\( -\,2^{22}\cdot 5^{6} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.65536000000.2	x^8 + 10x^4 - 100	\( -\,2^{22}\cdot 5^{6} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.65868380928.1	x^8 - 42x^4 - 147x^2 - 147	\( -\,2^{8}\cdot 3^{7}\cdot 7^{6} \)	$QD_{16}$ (as 8T8)	$[2]$
8.2.69274613043.1	x^8 - 2x^7 + 2x^6 + 8x^5 - 33x^4 + 75x^3 - 126x^2 + 99x - 27	\( -\,3^{3}\cdot 37^{6} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.89579520000.3	x^8 - 4x^7 + 10x^6 - 16x^5 - 20x^4 + 32x^3 - 212x^2 - 196x - 74	\( -\,2^{16}\cdot 3^{7}\cdot 5^{4} \)	$QD_{16}$ (as 8T8)	$[2]$
8.2.89614671875.1	x^8 + 4x^6 - 25x^5 + 16x^4 - 55x^3 + 179x^2 - 80x - 29	\( -\,5^{6}\cdot 179^{3} \)	$QD_{16}$ (as 8T8)	Trivial
8.8.92652203125.1	x^8 - 3x^7 - 11x^6 + 38x^5 + 11x^4 - 115x^3 + 95x^2 - 10x - 5	\( 5^{6}\cdot 181^{3} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.97844723712.4	x^8 - 12x^6 + 18x^4 - 18	\( -\,2^{27}\cdot 3^{6} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.97844723712.5	x^8 - 12x^6 + 54x^4 - 72x^2 - 18	\( -\,2^{27}\cdot 3^{6} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.102889341747.1	x^8 - 2x^7 + 4x^6 + 10x^5 - 26x^4 - 8x^3 + 169x^2 + 136x - 356	\( -\,3^{7}\cdot 19^{6} \)	$QD_{16}$ (as 8T8)	Trivial
8.8.104963309568.1	x^8 - 4x^7 - 10x^6 + 32x^5 + 16x^4 - 68x^3 + 14x^2 + 28x - 11	\( 2^{16}\cdot 3^{6}\cdot 13^{3} \)	$QD_{16}$ (as 8T8)	Trivial
8.0.104963309568.1	x^8 - 4x^7 + 14x^6 - 16x^5 + 52x^4 - 80x^3 + 92x^2 - 140x + 118	\( 2^{16}\cdot 3^{6}\cdot 13^{3} \)	$QD_{16}$ (as 8T8)	$[2, 2]$
8.2.123134359375.1	x^8 - x^7 + 3x^6 - 20x^5 + x^4 + 20x^3 + 132x^2 - 262x + 121	\( -\,5^{6}\cdot 199^{3} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.124952510464.2	x^8 - 8x^6 + 20x^4 - 16x^2 - 124	\( -\,2^{22}\cdot 31^{3} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.124952510464.3	x^8 + 8x^6 + 20x^4 + 16x^2 - 124	\( -\,2^{22}\cdot 31^{3} \)	$QD_{16}$ (as 8T8)	$[2]$
8.2.160811476875.1	x^8 - 2x^7 + x^6 - 26x^5 - 14x^4 + 145x^3 + 169x^2 - 320x - 335	\( -\,3^{7}\cdot 5^{4}\cdot 7^{6} \)	$QD_{16}$ (as 8T8)	$[2, 2]$
8.2.167772160000.4	x^8 - 50x^4 - 625	\( -\,2^{28}\cdot 5^{4} \)	$QD_{16}$ (as 8T8)	$[2]$
8.2.173946175488.4	x^8 - 162	\( -\,2^{31}\cdot 3^{4} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.204128387072.1	x^8 - 4x^6 - 28x^4 - 44x^2 - 23	\( -\,2^{24}\cdot 23^{3} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.204128387072.4	x^8 + 4x^6 - 28x^4 + 44x^2 - 23	\( -\,2^{24}\cdot 23^{3} \)	$QD_{16}$ (as 8T8)	$[3]$
8.2.208176611328.1	x^8 - 4x^7 + 8x^6 + 4x^5 - 30x^4 + 44x^3 - 96x^2 + 276x - 227	\( -\,2^{16}\cdot 3^{3}\cdot 7^{6} \)	$QD_{16}$ (as 8T8)	$[2]$
8.2.208176611328.2	x^8 - 4x^7 + 8x^6 + 4x^5 - 72x^4 + 240x^3 - 432x^2 + 360x - 108	\( -\,2^{16}\cdot 3^{3}\cdot 7^{6} \)	$QD_{16}$ (as 8T8)	$[2]$
8.2.210093400576.2	x^8 - 17x^6 + 17x^4 + 17x^2 - 34	\( -\,2^{9}\cdot 17^{7} \)	$QD_{16}$ (as 8T8)	$[4]$
8.2.213311234375.1	x^8 - 3x^7 - x^6 - 12x^5 - 59x^4 - 60x^3 - 60x^2 - 30x - 5	\( -\,5^{6}\cdot 239^{3} \)	$QD_{16}$ (as 8T8)	Trivial
8.2.254358061056.1	x^8 - 4x^7 + 14x^6 - 16x^5 - 8x^4 + 52x^3 - 52x^2 + 40x - 26	\( -\,2^{18}\cdot 3^{6}\cdot 11^{3} \)	$QD_{16}$ (as 8T8)	$[2]$