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 64259)

Label	Polynomial	Discriminant	Galois group	Class group
6.2.242000.2	x^6 - 2x^5 + 2x^4 - 4x^3 + 2x^2 - 4x + 1	\( 2^{4}\cdot 5^{3}\cdot 11^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.0.309123.2	x^6 - 3x^5 + x^4 - 2x^3 + 7x^2 + 2x + 1	\( -\,3^{3}\cdot 107^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.2.406125.1	x^6 - x^5 + 3x^4 + 3x^2 + 4x + 1	\( 3^{2}\cdot 5^{3}\cdot 19^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.2.739328.4	x^6 - 2x^5 + 3x^4 - 4x^3 + x^2 - 2x + 1	\( 2^{11}\cdot 19^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.2.836352.2	x^6 - 2x^5 + 4x^4 - 2x^3 + 2x^2 - 2	\( 2^{8}\cdot 3^{3}\cdot 11^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.0.861184.1	x^6 - 2x^5 - 3x^4 + 9x^2 + 6x + 5	\( -\,2^{10}\cdot 29^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.2.903168.1	x^6 - 2x^5 + 3x^4 - 3x^2 + 2x + 1	\( 2^{11}\cdot 3^{2}\cdot 7^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.0.906304.1	x^6 - 2x^5 + 6x^4 - 10x^3 + 15x^2 - 6x + 1	\( -\,2^{6}\cdot 7^{2}\cdot 17^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.0.1000188.1	x^6 - x^3 + 2	\( -\,2^{2}\cdot 3^{6}\cdot 7^{3} \)	$S_3^2$ (as 6T9)	Trivial
6.2.1058000.2	x^6 - 2x^5 + 5x^4 - 6x^3 + x^2 - 4x + 1	\( 2^{4}\cdot 5^{3}\cdot 23^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.0.1081600.1	x^6 - 2x^5 + 6x^4 - 2x^3 + 4x^2 + 4x + 2	\( -\,2^{8}\cdot 5^{2}\cdot 13^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.2.1083392.1	x^6 - 2x^5 - x^4 + 4x^3 - 8x + 2	\( 2^{11}\cdot 23^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.0.1156923.2	x^6 - 3x^5 + 2x^3 + 6x + 7	\( -\,3^{7}\cdot 23^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.0.1166400.3	x^6 - 4x^3 + 5	\( -\,2^{6}\cdot 3^{6}\cdot 5^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.2.1168128.1	x^6 - x^4 - 2x^3 + x^2 - 2x + 1	\( 2^{8}\cdot 3^{3}\cdot 13^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.2.1331712.1	x^6 - 2x^5 + 5x^4 - 6x^3 + 7x^2 - 8x + 2	\( 2^{9}\cdot 3^{2}\cdot 17^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.2.1382400.1	x^6 - 2x^4 - 4x^3 - 8x^2 - 8x - 2	\( 2^{11}\cdot 3^{3}\cdot 5^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.0.1415907.2	x^6 - x^5 + x^4 - 2x^3 - 2x^2 + 9x + 7	\( -\,3^{3}\cdot 229^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.2.1453248.5	x^6 - 2x^5 + 2x^4 + 3x^2 - 4x + 1	\( 2^{6}\cdot 3^{3}\cdot 29^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.2.1458000.1	x^6 - 2x^3 - 4	\( 2^{4}\cdot 3^{6}\cdot 5^{3} \)	$S_3^2$ (as 6T9)	Trivial
6.0.1492992.5	x^6 - 2x^5 + x^4 + 4x^3 + x^2 - 2x + 3	\( -\,2^{11}\cdot 3^{6} \)	$S_3^2$ (as 6T9)	Trivial
6.2.1492992.5	x^6 - 4x^3 + 2	\( 2^{11}\cdot 3^{6} \)	$S_3^2$ (as 6T9)	Trivial
6.0.1494108.1	x^6 - 2x^5 + 5x^4 - 9x^3 + 16x^2 - 17x + 8	\( -\,2^{2}\cdot 3^{2}\cdot 7^{3}\cdot 11^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.2.1601613.1	x^6 - x^5 + 3x^4 - 2x^3 + 2x^2 + 3x - 3	\( 3^{6}\cdot 13^{3} \)	$S_3^2$ (as 6T9)	Trivial
6.0.1617984.1	x^6 - 3x^4 - 6x^3 + 9x^2 + 12x + 4	\( -\,2^{6}\cdot 3^{2}\cdot 53^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.2.1778112.1	x^6 - 2x^5 + 2x^4 + 2x^3 - x^2 - 2x - 3	\( 2^{6}\cdot 3^{4}\cdot 7^{3} \)	$S_3^2$ (as 6T9)	Trivial
6.2.1782272.2	x^6 - 2x^5 - x^4 + 2x^3 - x^2 - 4x - 2	\( 2^{9}\cdot 59^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.0.1783323.1	x^6 - 2x^5 + 2x^3 + 6x^2 + 13x + 7	\( -\,3^{3}\cdot 257^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.0.1849600.1	x^6 - 2x^5 + 6x^4 - 18x^3 + 28x^2 - 20x + 10	\( -\,2^{8}\cdot 5^{2}\cdot 17^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.0.1878268.1	x^6 - x^5 + 4x^4 - 6x^3 + 14x^2 - 12x + 8	\( -\,2^{2}\cdot 7^{3}\cdot 37^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.2.1922000.2	x^6 - x^5 + 6x^4 - 5x^3 + 8x^2 - 9x - 1	\( 2^{4}\cdot 5^{3}\cdot 31^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.0.2101707.1	x^6 - 3x^4 - 10x^3 + 6x^2 + 18x + 7	\( -\,3^{7}\cdot 31^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.2.2178000.1	x^6 - 3x^5 + 4x^4 - 3x^3 - 9x + 9	\( 2^{4}\cdot 3^{2}\cdot 5^{3}\cdot 11^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.2.2278125.2	x^6 - 5x^3 + 5	\( 3^{6}\cdot 5^{5} \)	$S_3^2$ (as 6T9)	Trivial
6.2.2365632.1	x^6 - x^4 - 2x^3 - 5x^2 - 2x - 2	\( 2^{6}\cdot 3^{3}\cdot 37^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.2.2377892.1	x^6 - x^5 + 2x^4 - 4x^3 + x^2 - 3x - 4	\( 2^{2}\cdot 11^{2}\cdot 17^{3} \)	$S_3^2$ (as 6T9)	Trivial
6.2.2415125.3	x^6 - x^5 - x^4 + 2x^3 - 6x^2 + 5x + 11	\( 5^{3}\cdot 139^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.0.2433600.1	x^6 - 2x^5 + 4x^4 + 4x^3 + 8x^2 - 6x + 1	\( -\,2^{6}\cdot 3^{2}\cdot 5^{2}\cdot 13^{2} \)	$S_3^2$ (as 6T9)	$[3]$
6.2.2450000.1	x^6 - x^5 + 5x^3 - 10x^2 - x + 11	\( 2^{4}\cdot 5^{5}\cdot 7^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.2.2508800.2	x^6 - 2x^4 - 4x^3 + 6x^2 + 8x - 8	\( 2^{11}\cdot 5^{2}\cdot 7^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.0.2592000.1	x^6 - 2x^5 + 6x^4 - 4x^3 + 4x^2 + 4	\( -\,2^{8}\cdot 3^{4}\cdot 5^{3} \)	$S_3^2$ (as 6T9)	$[2]$
6.2.2676429.1	x^6 - 3x^5 + 2x^4 - 2x^3 - 2x^2 - 2x + 1	\( 3^{3}\cdot 7^{3}\cdot 17^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.0.2695275.1	x^6 - 3x^3 + 5	\( -\,3^{4}\cdot 5^{2}\cdot 11^{3} \)	$S_3^2$ (as 6T9)	Trivial
6.0.2696112.2	x^6 - 3x^5 - 5x^4 + 10x^3 + 13x^2 + 5x + 7	\( -\,2^{4}\cdot 3^{3}\cdot 79^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.2.2847312.1	x^6 - x^5 + 2x^4 - 7x^3 + 2x^2 + 5x + 1	\( 2^{4}\cdot 3^{4}\cdot 13^{3} \)	$S_3^2$ (as 6T9)	Trivial
6.2.2847312.2	x^6 - x^5 - 3x^4 + 4x^3 - 2x^2 + 4	\( 2^{4}\cdot 3^{4}\cdot 13^{3} \)	$S_3^2$ (as 6T9)	Trivial
6.2.2888000.2	x^6 - x^5 - 3x^4 + 8x^3 - 5x^2 - 7x + 11	\( 2^{6}\cdot 5^{3}\cdot 19^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.0.2958147.3	x^6 - x^5 + 11x^4 - 8x^3 + 34x^2 - 15x + 21	\( -\,3^{3}\cdot 331^{2} \)	$S_3^2$ (as 6T9)	Trivial
6.0.3359232.3	x^6 - 2x^3 + 3	\( -\,2^{9}\cdot 3^{8} \)	$S_3^2$ (as 6T9)	Trivial
6.2.3403125.1	x^6 - x^5 + 5x^4 + 9x - 9	\( 3^{2}\cdot 5^{5}\cdot 11^{2} \)	$S_3^2$ (as 6T9)	Trivial