Global number field search results

Degree	Signature	Galois group	Class number	Class group structure
Regulator	Number of ramified primes	Ram. primes	Unramified primes	CM field
Discriminant	Root discriminant

Results (displaying matches 1-50 of )

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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