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 898242)

Label	Polynomial	Discriminant	Galois group	Class group
10.2.4165509529.1	x^10 - x^9 - x^8 + 3x^7 - 2x^6 - x^5 + 3x^4 - x^2 - x + 1	\( 1609^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.4483962449.1	x^10 - x^7 - x^5 + x^4 - 2x^3 + x^2 - x + 1	\( 17^{3}\cdot 97^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.5441006848.2	x^10 - x^8 - 4x^7 + 2x^6 - 2x^5 + 4x^4 - 4x^3 + x^2 - 2x + 1	\( 2^{8}\cdot 277^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.5611284433.1	x^10 - x^9 + x^8 - 2x^7 + x^6 + x^5 - 4x^4 + 3x^3 - 2x + 1	\( 1777^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.10882188544.1	x^10 - x^8 - 2x^7 - 2x^6 - 4x^5 + 2x^3 + x^2 + 1	\( 2^{8}\cdot 349^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.12119452073.2	x^10 - x^9 + x^8 - x^6 - x^5 + x^3 - x^2 - x + 1	\( 2297^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.17923019113.1	x^10 - x^9 - 4x^7 + 2x^6 + 2x^5 + x^4 - x^3 - 2x + 1	\( 2617^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.18927429625.1	x^10 - x^9 - x^8 + 2x^7 - 3x^6 - x^5 + 4x^4 - x^3 + x^2 - x + 1	\( 5^{3}\cdot 13^{3}\cdot 41^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.23615200909.3	x^10 + x^8 - x^6 - 2x^5 - x^4 - x^3 + 1	\( 19^{3}\cdot 151^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.25080878336.1	x^10 - x^9 - x^8 + 2x^7 + 3x^6 + 3x^5 - 5x^4 - 12x^3 - 11x^2 - 5x - 1	\( 2^{8}\cdot 461^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.27461605913.1	x^10 - x^7 - x^6 - 2x^5 + x + 1	\( 7^{3}\cdot 431^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.29474993969.1	x^10 - x^9 - 2x^8 + 4x^7 - 4x^6 - 2x^5 + 7x^4 - x^3 - 2x^2 + 1	\( 3089^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.33608047921.1	x^10 - 3x^8 + 2x^6 - 2x^5 + 5x^4 + 4x^3 - 3x^2 - 4x - 1	\( 7^{4}\cdot 241^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.33792250337.1	x^10 - x^7 + x^6 - 2x^5 - x + 1	\( 53^{3}\cdot 61^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.38238692409.1	x^10 - x^9 + x^8 - 3x^7 - x^5 + 3x^4 - 2x^3 - x^2 - x + 1	\( 3^{3}\cdot 1123^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.54470700288.2	x^10 - 2x^6 - 4x^3 + 4x^2 - 4x + 4	\( 2^{8}\cdot 3^{3}\cdot 199^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.56409309184.1	x^10 - x^9 + 2x^8 - 7x^7 + 3x^6 + 2x^5 - 7x^4 + 5x^3 - 3x + 1	\( 2^{14}\cdot 151^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.57378463793.1	x^10 - x^9 + x^8 - 2x^7 + x^6 - 3x^5 + x^3 + x^2 + x + 1	\( 7^{3}\cdot 19^{3}\cdot 29^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.58818484369.1	x^10 - x^9 - x^8 + 2x^7 - 3x^6 - x^5 + 2x^4 - x^3 + 1	\( 3889^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.58968677632.1	x^10 - 2x^9 + 2x^8 - 2x^7 + 4x^5 - 8x^4 + 4x^3 + 4x^2 - 8x + 4	\( 2^{8}\cdot 613^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.59501707264.1	x^10 - 4x^9 + 5x^8 - 6x^6 + 4x^5 + 5x^2 - 1	\( 2^{18}\cdot 61^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.59897527569.1	x^10 - x^9 - x^8 - x^7 + 6x^6 + 5x^5 - 3x^4 - 4x^3 + x^2 + 5x - 1	\( 3^{8}\cdot 11^{3}\cdot 19^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.66331758592.2	x^10 - x^9 - 2x^8 + x^7 - 5x^6 - 2x^5 + 5x^4 - 3x^3 + x + 1	\( 2^{12}\cdot 11^{3}\cdot 23^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.72459558809.1	x^10 - 2x^9 - 2x^8 + 7x^7 - 3x^6 - 6x^5 + 4x^4 - 2x^3 + 4x^2 - x + 1	\( 11^{3}\cdot 379^{3} \)	$S_5$ (as 10T13)	Trivial
10.4.72758649087.1	x^10 - x^9 + 3x^8 - 6x^7 - 3x^6 - 3x^5 - 6x^4 + 3x^3 + 2x + 1	\( -\,3^{8}\cdot 223^{3} \)	$S_5$ (as 10T13)	Trivial
10.4.74515853627.1	x^10 - 2x^9 + 2x^8 - x^7 - 5x^6 + 3x^5 - 3x^4 + x^3 + 7x^2 + 4x + 1	\( -\,19^{4}\cdot 83^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.75049519552.1	x^10 - x^9 - 2x^8 - 3x^7 - 2x^6 + 4x^4 + x^3 + 3x^2 - 2x - 1	\( 2^{6}\cdot 7^{3}\cdot 43^{4} \)	$S_5$ (as 10T13)	Trivial
10.2.77363231581.1	x^10 + 2x^8 - 4x^7 - 2x^6 - 2x^5 + 4x^4 - 2x^3 - 2x + 1	\( 4261^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.79433915648.1	x^10 + x^8 - 4x^7 + 4x^6 - 2x^5 - 6x^4 + 4x^3 - x^2 - 2x + 1	\( 2^{8}\cdot 677^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.85707789929.1	x^10 - 2x^8 - x^7 - 2x^6 + x^5 + 3x^4 - 2x^3 - x^2 + x + 1	\( 4409^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.86175179713.1	x^10 - 2x^9 + 2x^8 + x^7 - 3x^6 - 2x^5 - 2x^4 - 2x^2 - x + 1	\( 7^{3}\cdot 631^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.86879445589.1	x^10 - 2x^9 + x^8 - 2x^7 + 4x^6 - 5x^5 + x^4 - 2x^3 + x^2 + x + 1	\( 43^{3}\cdot 103^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.89734879333.1	x^10 - x^9 - x^8 + 2x^7 - x^6 - 3x^5 + 2x^4 + x^2 + 1	\( 11^{6}\cdot 37^{3} \)	$S_5$ (as 10T13)	Trivial
10.4.91794884831.1	x^10 - x^9 + 4x^7 - 2x^6 - 2x^5 - x^4 + x^3 - 2x + 1	\( -\,13^{3}\cdot 347^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.94134281149.2	x^10 - 2x^9 + 2x^8 - 3x^7 - 3x^6 + 4x^5 + x^4 - x^2 - 2x + 1	\( 4549^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.97145684173.2	x^10 - x^9 + x^8 - 6x^7 + x^6 + x^5 + 6x^4 - 2x^3 - x^2 - 2x + 1	\( 4597^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.107365139712.2	x^10 - x^9 + x^8 + 4x^7 - 15x^6 + x^5 + 27x^4 - 14x^3 - 13x^2 + 11x - 1	\( 2^{8}\cdot 3^{4}\cdot 173^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.107646386093.1	x^10 - 2x^9 - x^8 + 6x^7 - 6x^6 - 3x^5 + 7x^4 - 4x^3 + 3x^2 - x + 1	\( 67^{3}\cdot 71^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.111771206513.1	x^10 - 2x^9 + x^7 - 3x^6 - 2x^5 + 8x^4 - 6x^3 + 2x^2 - x + 1	\( 4817^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.117433042273.2	x^10 - x^9 - x^8 + 2x^7 - 3x^6 + 5x^5 - 2x^4 + 3x^3 + x^2 + x + 1	\( 59^{3}\cdot 83^{3} \)	$S_5$ (as 10T13)	Trivial
10.4.117865222327.1	x^10 - x^9 - x^8 + 3x^6 - 3x^5 - 8x^4 + 7x^3 - 2x + 1	\( -\,4903^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.118940458033.1	x^10 - x^8 - 6x^7 - 3x^6 + x^5 - x^4 - 6x^3 - 8x^2 - 3x - 1	\( 19^{4}\cdot 97^{3} \)	$S_5$ (as 10T13)	Trivial
10.4.126237434624.1	x^10 - 3x^9 + x^8 + 2x^7 - x^6 - 3x^5 + 11x^4 - 4x^3 + x^2 + 3x - 1	\( -\,2^{8}\cdot 7^{4}\cdot 59^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.126884390625.1	x^10 - 3x^7 - 2x^6 - 3x^5 + 3x^4 + 4x^3 + x^2 + x + 1	\( 3^{3}\cdot 5^{6}\cdot 67^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.129602962688.1	x^10 - 2x^9 - 2x^7 + 8x^6 - 4x^5 - 8x^3 + 4x^2 + 4	\( 2^{8}\cdot 797^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.132031254528.2	x^10 - 2x^9 + 2x^8 - 2x^7 + 3x^6 - 8x^5 + 9x^4 + 4x^3 - 20x^2 + 16x - 4	\( 2^{12}\cdot 3^{8}\cdot 17^{3} \)	$S_5$ (as 10T13)	Trivial
10.4.133541229312.1	x^10 - 2x^9 - x^8 + 10x^7 - 6x^6 - 2x^5 + 6x^4 - 14x^3 + x^2 + 4x - 1	\( -\,2^{8}\cdot 3^{8}\cdot 43^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.137707850944.1	x^10 - x^9 - 2x^8 + 7x^7 - 8x^6 + 2x^5 + 8x^4 - 5x^3 - x^2 + 1	\( 2^{6}\cdot 1291^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.150288260544.1	x^10 - 3x^9 + 8x^8 - 6x^7 + x^6 + 9x^5 - 5x^4 + 3x^3 + 5x^2 - 3x - 2	\( 2^{6}\cdot 3^{8}\cdot 71^{3} \)	$S_5$ (as 10T13)	Trivial
10.2.160722988453.1	x^10 - 2x^9 + 4x^8 - 2x^7 - 2x^6 - 2x^5 - 2x^4 + 4x^3 - 2x^2 - 2x + 1	\( 5437^{3} \)	$S_5$ (as 10T13)	Trivial

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