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 235091)

Label	Polynomial	Discriminant	Galois group	Class group
9.1.29510281.1	x^9 - 2x^8 + 2x^7 - 3x^5 + 7x^4 - 8x^3 + 6x^2 - 3x + 1	\( 101\cdot 292181 \)	$S_9$ (as 9T34)	Trivial
9.1.30073129.1	x^9 - 2x^8 + 2x^7 - x^5 + x^3 + x^2 - 2x + 1	\( 353\cdot 85193 \)	$S_9$ (as 9T34)	Trivial
9.1.30626693.1	x^9 - x^6 - 2x^5 - x^4 + 2x^2 + x + 1	\( 30626693 \)	$S_9$ (as 9T34)	Trivial
9.1.32029433.1	x^9 - 2x^8 + 3x^6 - x^5 - 3x^4 + 3x^3 + x^2 - 2x + 1	\( 32029433 \)	$S_9$ (as 9T34)	Trivial
9.1.32206049.1	x^9 - 2x^8 + 4x^7 - 5x^6 + 6x^5 - 6x^4 + 5x^3 - 4x^2 + 3x - 1	\( 23^{3}\cdot 2647 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.32344469.1	x^9 - x^7 - x^6 + 2x^5 + 2x^4 - x^3 - 2x^2 + 1	\( 53\cdot 89\cdot 6857 \)	$S_9$ (as 9T34)	Trivial
9.1.33860761.1	x^9 - 2x^8 + 2x^7 - 2x^5 + 2x^4 - x + 1	\( 11^{2}\cdot 23^{4} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30)	Trivial
9.1.35028793.1	x^9 - 2x^8 + 4x^7 - 7x^6 + 10x^5 - 11x^4 + 11x^3 - 8x^2 + 4x - 1	\( 23^{3}\cdot 2879 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.35050633.1	x^9 - x^8 + x^7 - 3x^6 + 3x^5 - 2x^4 + 4x^3 - 2x^2 + x - 1	\( 43\cdot 311\cdot 2621 \)	$S_9$ (as 9T34)	Trivial
9.1.38817673.1	x^9 - x^7 - 2x^4 - 2x^3 + x^2 + 3x + 1	\( 31^{3}\cdot 1303 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.43302353.1	x^9 - 2x^7 + 2x^5 - x^4 + 2x^3 - 2x + 1	\( 23^{3}\cdot 3559 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.44555813.1	x^9 - x^8 + 2x^7 - 2x^5 + 2x^4 - 2x^3 - x^2 + x - 1	\( 44555813 \)	$S_9$ (as 9T34)	Trivial
9.1.44656709.1	x^9 - 3x^8 + 6x^7 - 10x^6 + 13x^5 - 13x^4 + 10x^3 - 7x^2 + 3x - 1	\( 31^{3}\cdot 1499 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.44908397.1	x^9 + x^7 - x^6 + 3x^5 + 2x^3 + x + 1	\( 23^{3}\cdot 3691 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.47159153.1	x^9 - x^8 - 2x^7 + x^6 + 2x^5 + x^3 - 2x - 1	\( 31^{3}\cdot 1583 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.49483189.1	x^9 - 2x^8 + 2x^7 - 2x^6 + 3x^5 - 4x^4 + 2x^3 - x^2 + x - 1	\( 7^{2}\cdot 23^{3}\cdot 83 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.50797225.1	x^9 - 2x^8 + x^7 + 2x^6 - 4x^5 + x^4 + 3x^3 - 2x^2 + 1	\( 5^{2}\cdot 23^{3}\cdot 167 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.51478577.1	x^9 - x^8 + 3x^7 - 5x^6 + 6x^5 - 7x^4 + 6x^3 - 5x^2 + 2x - 1	\( 23^{3}\cdot 4231 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.53628353.1	x^9 - 3x^8 + 4x^7 - 3x^6 + 3x^5 - 2x^4 - x^3 + 4x^2 - 3x + 1	\( 17\cdot 43\cdot 73363 \)	$S_9$ (as 9T34)	Trivial
9.1.53814641.1	x^9 - 3x^8 + 5x^7 - 6x^6 + 4x^5 - 2x^4 + x^2 + 1	\( 23^{3}\cdot 4423 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.54982673.1	x^9 - 2x^8 + 3x^7 - 4x^6 + 4x^5 - 3x^4 + 3x^3 - 2x^2 - 1	\( 23^{3}\cdot 4519 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.56491381.1	x^9 - 4x^8 + 9x^7 - 15x^6 + 20x^5 - 20x^4 + 16x^3 - 10x^2 + 5x - 1	\( 23^{3}\cdot 4643 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.58778777.1	x^9 - 2x^8 + 3x^7 - 3x^6 + x^5 + x^4 - 2x^3 + x^2 - 1	\( 23^{3}\cdot 4831 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.58956389.1	x^9 - 2x^8 + 2x^7 - 2x^5 + 4x^4 - 5x^3 + 4x^2 - 2x + 1	\( 31^{3}\cdot 1979 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.59552209.1	x^9 - 2x^8 + 4x^7 - 6x^6 + 8x^5 - 9x^4 + 8x^3 - 5x^2 + 3x - 1	\( 31^{3}\cdot 1999 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.59849473.1	x^9 - 3x^8 + 5x^7 - 6x^6 + 8x^5 - 10x^4 + 11x^3 - 9x^2 + 5x - 1	\( 23^{3}\cdot 4919 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.66078977.1	x^9 - x^8 - x^7 + x^6 + 2x^4 - x^3 - 2x^2 + x + 1	\( 23^{3}\cdot 5431 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.66711661.1	x^9 - 3x^8 + 5x^7 - 8x^6 + 11x^5 - 11x^4 + 10x^3 - 6x^2 + 3x - 1	\( 23^{3}\cdot 5483 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.67149673.1	x^9 - 3x^8 + 4x^7 - 5x^5 + 5x^4 + x^3 - 4x^2 + 3x - 1	\( 23^{3}\cdot 5519 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.68755717.1	x^9 - x^8 + 3x^7 - 2x^6 + 3x^5 + x^4 + x^2 + x + 1	\( 23^{3}\cdot 5651 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.72503153.1	x^9 - 3x^8 + 7x^7 - 12x^6 + 17x^5 - 19x^4 + 17x^3 - 12x^2 + 6x - 1	\( 23^{3}\cdot 59\cdot 101 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.73513792.1	x^9 - 3x^8 + 3x^7 - 4x^5 + 7x^4 - 7x^3 + 5x^2 - 2x + 1	\( 2^{6}\cdot 11^{3}\cdot 863 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.74566873.1	x^9 - x^8 - x^7 + 2x^6 - 2x^5 + x^3 - x^2 + x - 1	\( 31^{3}\cdot 2503 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.74839217.1	x^9 - 3x^8 + 2x^7 + 2x^4 - 2x^2 - 1	\( 23^{3}\cdot 6151 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.75401021.1	x^9 - x^8 + 3x^7 - 3x^6 + 4x^5 - 5x^4 + 5x^3 - 5x^2 + 3x - 1	\( 31^{3}\cdot 2531 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.75909913.1	x^9 - 2x^8 + 2x^7 - x^6 + x^5 - 3x^4 + 6x^3 - 3x^2 - x + 1	\( 17\cdot 23^{3}\cdot 367 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.76639933.1	x^9 - x^8 + 4x^7 - 2x^6 + 4x^5 + 2x^4 - x^3 + 5x^2 - 2x + 1	\( 23^{3}\cdot 6299 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.76931941.1	x^9 - 2x^8 + x^7 - x^6 + 3x^5 - 4x^4 + x^3 + 3x^2 - 2x + 1	\( 23^{3}\cdot 6323 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.78284096.1	x^9 - x^8 - x^7 + 2x^6 - 3x^4 + x^3 + 3x^2 - 1	\( 2^{6}\cdot 11^{3}\cdot 919 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.79073333.1	x^9 - x^8 - 2x^7 + x^6 + x^4 + 4x^3 - x^2 - 3x - 1	\( 23^{3}\cdot 67\cdot 97 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.80387369.1	x^9 - x^8 + 4x^7 - 5x^6 + 6x^5 - 6x^4 + 3x^3 - x^2 - x + 1	\( 23^{3}\cdot 6607 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.81117389.1	x^9 - x^8 + x^7 + x^6 - x^5 + 2x^4 + x^3 + x^2 + x + 1	\( 23^{3}\cdot 59\cdot 113 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.82042081.1	x^9 - 3x^8 + 7x^7 - 12x^6 + 15x^5 - 16x^4 + 12x^3 - 8x^2 + 4x - 1	\( 11\cdot 23^{3}\cdot 613 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.82334089.1	x^9 - 2x^8 + x^7 - x^6 + 3x^5 - x^4 - x^3 + 1	\( 23^{3}\cdot 67\cdot 101 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.82431425.1	x^9 - 2x^8 + 2x^7 + x^6 - 2x^5 + 3x^3 - 2x^2 - x + 1	\( 5^{2}\cdot 23^{3}\cdot 271 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.83319616.1	x^9 - 4x^8 + 9x^7 - 15x^6 + 17x^5 - 14x^4 + 8x^3 - x^2 - x + 1	\( 2^{6}\cdot 23^{3}\cdot 107 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.89611328.1	x^9 - 2x^8 + 2x^7 + x^6 - x^5 - x^4 + x^3 + 2x^2 - 3x + 1	\( 2^{6}\cdot 31^{3}\cdot 47 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.90161381.1	x^9 - 3x^8 + 5x^7 - 8x^6 + 10x^5 - 11x^4 + 10x^3 - 8x^2 + 4x - 1	\( 59^{3}\cdot 439 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.1.92371321.1	x^9 - 2x^8 + 5x^7 - 7x^6 + 8x^5 - 9x^4 + 7x^3 - 4x^2 + 3x - 1	\( 7^{2}\cdot 1373^{2} \)	$A_9$ (as 9T33)	Trivial
9.1.92943713.1	x^9 - 3x^8 + 6x^7 - 7x^6 + 5x^5 - 4x^3 + 6x^2 - 4x + 1	\( 23^{3}\cdot 7639 \)	$S_3\wr S_3$ (as 9T31)	Trivial

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