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 42936)

Label	Polynomial	Discriminant	Galois group	Class group
10.2.5441006848.1	x^10 - x^9 + x^8 - 4x^7 + 5x^6 - 5x^5 + 5x^4 - 4x^3 + 5x^2 - 5x + 1	\( 2^{8}\cdot 277^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.12119452073.1	x^10 - 3x^9 + 3x^8 + 4x^7 - 13x^6 + 7x^5 + 14x^4 - 17x^3 - 6x^2 + 6x - 1	\( 2297^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.14875426816.1	x^10 - x^9 + x^8 + 2x^7 - 5x^6 - x^5 + 9x^4 - 18x^3 + 17x^2 - 7x + 1	\( 2^{16}\cdot 61^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.18540264325.1	x^10 - 2x^8 - 5x^7 + x^6 + 6x^5 + 8x^4 + 3x^3 - 7x^2 - 7x - 2	\( 5^{2}\cdot 11^{4}\cdot 37^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.18927429625.2	x^10 - x^9 - 4x^8 + 14x^6 - 2x^5 - 21x^4 + 17x^3 - 12x^2 + 4x - 1	\( 5^{3}\cdot 13^{3}\cdot 41^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.23615200909.1	x^10 - x^9 + 3x^7 - 11x^5 + 4x^4 - 4x^2 + x - 1	\( 19^{3}\cdot 151^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.23615200909.2	x^10 - 3x^8 - 9x^7 + 11x^5 - 5x^4 - x^3 + 6x^2 - 5x + 1	\( 19^{3}\cdot 151^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.31134170368.1	x^10 - 3x^9 + 5x^8 - 2x^7 + x^6 + 3x^5 - x^4 - 2x^3 - 5x^2 - 3x - 1	\( 2^{8}\cdot 7^{4}\cdot 37^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.40355662041.1	x^10 + 3x^8 - 9x^7 - 3x^6 - 38x^5 - 11x^4 - 47x^3 - 3x^2 - 21x + 1	\( 3^{2}\cdot 17^{3}\cdot 97^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.43528754176.1	x^10 - 3x^8 - 4x^6 - 4x^5 + 10x^4 - 4x^3 - 11x^2 + 2x - 1	\( 2^{10}\cdot 349^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.45678380625.1	x^10 - 3x^9 + 3x^8 + 2x^7 - 7x^6 + 15x^5 - 26x^4 + 29x^3 - 23x^2 + 9x - 3	\( 3^{5}\cdot 5^{4}\cdot 67^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.4.50150374144.1	x^10 - 3x^9 + 3x^8 - 4x^7 + 7x^6 + 7x^5 - 21x^4 + 10x^3 + 5x^2 - 5x + 1	\( -\,2^{8}\cdot 13^{4}\cdot 19^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.54470700288.1	x^10 - 2x^9 - 3x^8 + 4x^7 + 6x^6 - 2x^5 - 7x^2 - 8x - 1	\( 2^{8}\cdot 3^{3}\cdot 199^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.58127590656.1	x^10 - x^9 + x^8 + 6x^7 - 3x^6 - 13x^5 + 21x^4 - 18x^3 + 7x^2 + x - 1	\( 2^{8}\cdot 3^{7}\cdot 47^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.59897527569.2	x^10 - x^9 + 2x^8 + 2x^7 - 4x^5 + 6x^4 - 7x^3 - 2x^2 + 5x - 1	\( 3^{8}\cdot 11^{3}\cdot 19^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.62219695104.1	x^10 - 2x^9 + x^8 - 4x^7 + 2x^6 - 8x^5 + 2x^4 - 4x^3 + x^2 - 2x + 1	\( 2^{10}\cdot 3^{11}\cdot 7^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.4.64248054784.1	x^10 - x^8 - 5x^6 + 6x^4 - 6x^2 + 1	\( -\,2^{10}\cdot 89^{4} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.66331758592.1	x^10 - x^9 - 2x^8 - 3x^7 - 2x^6 - 9x^5 - 2x^4 - 3x^3 - 2x^2 - x + 1	\( 2^{12}\cdot 11^{3}\cdot 23^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.67712875776.1	x^10 + 3x^8 - 4x^7 - 12x^5 - 4x^3 + 3x^2 + 1	\( 2^{8}\cdot 3^{3}\cdot 7^{3}\cdot 13^{4} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.0.72758649087.1	x^10 - x^9 - x^8 - x^7 + 6x^6 - 7x^5 + 3x^4 + 8x^3 - 11x^2 - x + 5	\( -\,3^{8}\cdot 223^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.4.74515853627.2	x^10 - 2x^9 - 2x^7 - x^6 + 5x^5 + 14x^4 + 2x^3 - 13x^2 - 7x - 1	\( -\,19^{4}\cdot 83^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.4.76501533375.1	x^10 - 4x^9 + 8x^8 - 16x^7 + 25x^6 - 27x^5 + 25x^4 - 16x^3 + 8x^2 - 4x + 1	\( -\,3^{7}\cdot 5^{3}\cdot 23^{4} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.87056109568.1	x^10 - 2x^9 + 2x^7 - 12x^6 + 10x^5 + 12x^4 + 14x^3 + 22x^2 + 12x + 2	\( 2^{12}\cdot 277^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.94134281149.1	x^10 - x^9 - x^8 - 7x^7 + 6x^6 + 8x^4 - 13x^3 + 4x^2 - 3x - 1	\( 4549^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.94134281149.3	x^10 - 5x^9 + 16x^8 - 29x^7 + 32x^6 - 12x^5 - 15x^4 + 24x^3 - 19x^2 + 10x - 4	\( 4549^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.4.95702452992.1	x^10 - x^8 - 4x^6 - 4x^5 - 4x^4 - x^2 + 1	\( -\,2^{8}\cdot 3^{3}\cdot 61^{4} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.97145684173.1	x^10 - 4x^9 - x^8 + 22x^7 - 20x^6 - 25x^5 + 39x^4 - 14x^3 + 15x^2 - 13x - 1	\( 4597^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.99449366848.1	x^10 - 3x^9 + 5x^8 - 3x^7 - 3x^6 + 5x^5 - 3x^4 - 6x^3 + 7x^2 - 4x - 1	\( 2^{6}\cdot 13^{3}\cdot 29^{4} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.99449366848.2	x^10 - x^9 + 5x^8 - 9x^7 + x^6 - 7x^5 + x^4 + 22x^3 + 2x^2 - 12x - 4	\( 2^{6}\cdot 13^{3}\cdot 29^{4} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.99595441125.1	x^10 - 3x^9 + 5x^8 - 12x^7 + 17x^6 - 14x^5 + 21x^4 - 10x^3 - x^2 + x - 1	\( 3^{2}\cdot 5^{3}\cdot 97^{4} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.4.107166402027.1	x^10 - 3x^9 - 4x^8 + 15x^7 + 2x^6 - 23x^5 + 2x^4 + 15x^3 - 4x^2 - 3x + 1	\( -\,3^{3}\cdot 251^{4} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.107365139712.1	x^10 - x^9 + x^8 + 2x^7 + x^6 - 7x^5 - x^4 + 2x^3 - x^2 - x - 1	\( 2^{8}\cdot 3^{4}\cdot 173^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.107646386093.2	x^10 - 2x^9 - 6x^8 + 15x^7 + 9x^6 - 36x^5 + 4x^4 + 23x^3 - 11x^2 + 7x - 8	\( 67^{3}\cdot 71^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.109075068657.1	x^10 - 3x^9 + 2x^7 + 11x^6 - 19x^5 - 3x^4 + 34x^3 + 15x^2 - 36x - 27	\( 3^{2}\cdot 2297^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.117433042273.1	x^10 - 3x^9 + 2x^8 + 4x^7 - 8x^6 + 18x^5 - 23x^4 + 7x^3 + 14x^2 - 1	\( 59^{3}\cdot 83^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.0.117865222327.1	x^10 - 2x^9 + 6x^8 - 10x^7 + 23x^6 - 34x^5 + 48x^4 - 42x^3 + 56x^2 - 30x + 25	\( -\,4903^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.126759838761.1	x^10 - 4x^8 - x^7 + 10x^6 + 7x^5 - 11x^4 - 10x^3 - x^2 - 3x + 1	\( 3^{13}\cdot 43^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.132031254528.1	x^10 - 5x^9 + 14x^8 - 26x^7 + 39x^6 - 47x^5 + 48x^4 - 38x^3 + 25x^2 - 11x + 2	\( 2^{12}\cdot 3^{8}\cdot 17^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.4.133541229312.2	x^10 - 5x^9 + 11x^8 - 14x^7 + 3x^6 + 13x^5 - 9x^4 - 8x^3 + 7x^2 + x - 1	\( -\,2^{8}\cdot 3^{8}\cdot 43^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.139975210000.1	x^10 - 4x^9 + 7x^8 - 3x^7 - 6x^6 + 10x^5 - 8x^4 + 10x^3 - 10x^2 + 5x - 1	\( 2^{4}\cdot 5^{4}\cdot 241^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.158886522112.1	x^10 - 2x^9 + x^8 + 4x^7 - 11x^6 + 26x^5 - 51x^4 + 58x^3 - 42x^2 + 10x - 2	\( 2^{8}\cdot 853^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.167595338752.1	x^10 - 2x^9 - x^8 - 2x^7 + 7x^6 + 8x^5 - 7x^4 - 6x^3 - 9x^2 + 14x - 1	\( 2^{10}\cdot 547^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.174115016704.1	x^10 - 2x^9 - x^8 + 8x^7 - 6x^6 - 10x^5 + 10x^4 - 22x^3 - 65x^2 - 46x - 13	\( 2^{12}\cdot 349^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.180649580077.1	x^10 - 4x^9 + 3x^8 + 3x^7 + 5x^6 - 11x^5 - 14x^4 + 24x^3 - 6x^2 - 4x - 1	\( 5653^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.180649580077.2	x^10 - 3x^9 + 5x^8 - 13x^7 + 26x^6 - 41x^5 + 52x^4 - 52x^3 + 40x^2 - 17x + 1	\( 5653^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.183711891456.1	x^10 - 3x^9 + 3x^8 + 2x^7 - 15x^6 + 27x^5 - 15x^4 + 2x^3 + 3x^2 - 3x + 1	\( 2^{16}\cdot 3^{3}\cdot 47^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.189852306688.1	x^10 - 5x^8 + 14x^6 - 6x^4 - 31x^2 - 37	\( 2^{8}\cdot 11^{4}\cdot 37^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.189852306688.2	x^10 + x^8 - 4x^6 - 29x^4 - 37	\( 2^{8}\cdot 11^{4}\cdot 37^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.189852306688.3	x^10 - 6x^8 + 10x^6 - 6x^4 + 22x^2 - 37	\( 2^{8}\cdot 11^{4}\cdot 37^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial
10.2.189852306688.4	x^10 - x^8 - 3x^6 - 13x^4 + 37x^2 - 37	\( 2^{8}\cdot 11^{4}\cdot 37^{3} \)	$(C_2^4:A_5) : C_2$ (as 10T38)	Trivial