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 all 12 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.4919707275390625.1	x^16 - 5x^15 + 14x^14 - 29x^13 + 50x^12 - 77x^11 + 112x^10 - 149x^9 + 176x^8 - 182x^7 + 159x^6 - 118x^5 + 73x^4 - 36x^3 + 15x^2 - 4x + 1	\( 5^{12}\cdot 67^{4} \)	$C_4\times S_4$ (as 16T181)	Trivial
16.0.38416000000000000.1	x^16 - 8x^15 + 32x^14 - 84x^13 + 164x^12 - 256x^11 + 344x^10 - 422x^9 + 478x^8 - 480x^7 + 400x^6 - 260x^5 + 127x^4 - 46x^3 + 14x^2 - 4x + 1	\( 2^{16}\cdot 5^{12}\cdot 7^{4} \)	$C_4\times S_4$ (as 16T181)	Trivial
16.0.117135062500000000.1	x^16 - 2x^15 + 3x^14 - 2x^13 + x^12 + 2x^10 - 5x^9 + 7x^8 - 5x^7 - 3x^6 + 10x^5 - 9x^4 + 2x^3 + 3x^2 - 3x + 1	\( 2^{8}\cdot 5^{12}\cdot 37^{4} \)	$C_4\times S_4$ (as 16T181)	Trivial
16.0.148333301025390625.1	x^16 - 4x^15 + 14x^14 - 36x^13 + 76x^12 - 137x^11 + 211x^10 - 281x^9 + 331x^8 - 336x^7 + 305x^6 - 244x^5 + 172x^4 - 108x^3 + 60x^2 - 24x + 11	\( 5^{12}\cdot 157^{4} \)	$C_4\times S_4$ (as 16T181)	Trivial
16.8.9349208943630483456.1	x^16 - 4x^15 - 2x^14 + 20x^13 - 5x^12 - 36x^11 + 28x^10 + 20x^9 - 62x^8 + 12x^7 + 78x^6 - 8x^5 - 54x^4 - 12x^3 + 16x^2 + 8x + 1	\( 2^{44}\cdot 3^{12} \)	$C_4\times S_4$ (as 16T181)	Trivial
16.8.9834496000000000000.1	x^16 - 4x^15 + 14x^13 - 2x^12 - 18x^11 - 26x^10 + 18x^9 + 81x^8 - 14x^7 - 98x^6 - 2x^5 + 60x^4 + 6x^3 - 16x^2 + 1	\( 2^{24}\cdot 5^{12}\cdot 7^{4} \)	$C_4\times S_4$ (as 16T181)	Trivial
16.0.78074896000000000000.1	x^16 + 4x^14 + 4x^12 - 2x^10 + 4x^8 + 16x^6 + 21x^4 + 12x^2 + 16	\( 2^{16}\cdot 5^{12}\cdot 47^{4} \)	$C_4\times S_4$ (as 16T181)	$[2]$
16.0.479785216000000000000.1	x^16 + 10x^12 + 100x^10 + 375x^8 + 500x^6 + 250x^4 + 625	\( 2^{20}\cdot 5^{12}\cdot 37^{4} \)	$C_4\times S_4$ (as 16T181)	$[2]$ (GRH)
16.0.3580992031933837890625.1	x^16 + 4x^14 - x^13 + 15x^12 + 12x^11 + 57x^10 + 34x^9 + 201x^8 + 67x^7 + 74x^6 + 33x^5 + 28x^4 - 9x^3 + 5x^2 - x + 1	\( 5^{12}\cdot 19^{4}\cdot 103^{4} \)	$C_4\times S_4$ (as 16T181)	$[5]$
16.0.6157543352187744140625.1	x^16 - 2x^15 + 7x^14 - 21x^13 + 48x^12 - 25x^11 + 66x^10 - 183x^9 + 463x^8 - 626x^7 + 649x^6 - 393x^5 + 298x^4 - 137x^3 + 43x^2 - 8x + 1	\( 3^{12}\cdot 5^{12}\cdot 83^{4} \)	$C_4\times S_4$ (as 16T181)	$[2, 2]$
16.16.175415570277650636210176.1	x^16 - 20x^14 + 158x^12 - 624x^10 + 1287x^8 - 1336x^6 + 650x^4 - 116x^2 + 1	\( 2^{52}\cdot 79^{4} \)	$C_4\times S_4$ (as 16T181)	Trivial (GRH)
16.16.248438446096000000000000.1	x^16 - 6x^15 - 7x^14 + 88x^13 - 6x^12 - 542x^11 + 166x^10 + 1764x^9 - 522x^8 - 3120x^7 + 745x^6 + 2830x^5 - 598x^4 - 1092x^3 + 256x^2 + 78x - 19	\( 2^{16}\cdot 5^{12}\cdot 353^{4} \)	$C_4\times S_4$ (as 16T181)	Trivial (GRH)