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 18 matches)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.722204136308736.2	x^12 + 3x^10 - 3x^9 + 9x^8 + 2x^6 - 18x^5 + 45x^4 - 56x^3 + 33x^2 - 9x + 1	\( 2^{24}\cdot 3^{16} \)	12T206	$[3]$
12.0.855355656503296.1	x^12 - 7x^10 - 7x^9 + 13x^8 + 24x^7 + 24x^6 + 28x^5 + 37x^4 + 16x^3 + 9x^2 + 5x + 1	\( 2^{20}\cdot 13^{8} \)	12T206	$[3]$
12.0.2911171376593984.1	x^12 + 6x^10 - x^9 + 15x^8 - 4x^7 + 11x^6 - 6x^5 - 3x^4 + 4x^3 - 3x^2 - x + 1	\( 2^{6}\cdot 7^{8}\cdot 53^{4} \)	12T206	$[6]$
12.0.6938632771983936.1	x^12 - 3x^11 - x^9 + 24x^8 - 33x^7 + 21x^6 - 36x^5 + 36x^4 - 24x^3 + 27x^2 - 9x + 3	\( 2^{6}\cdot 3^{18}\cdot 23^{4} \)	12T206	Trivial
12.4.186314968102014976.1	x^12 - 6x^11 + 21x^10 - 47x^9 + 59x^8 - 20x^7 - 108x^6 + 268x^5 - 305x^4 + 174x^3 + 23x^2 - 13x + 1	\( 2^{12}\cdot 7^{8}\cdot 53^{4} \)	12T206	$[3]$
12.4.186314968102014976.2	x^12 - x^11 - 4x^10 - 8x^9 + 14x^8 + 38x^7 + 20x^6 - 124x^5 - 27x^4 - 33x^3 + 464x^2 - 452x + 120	\( 2^{12}\cdot 7^{8}\cdot 53^{4} \)	12T206	$[3]$
12.4.4606941747037077504.1	x^12 - 2x^11 - 6x^10 + 22x^9 - 120x^8 + 328x^7 - 318x^6 + 320x^5 - 492x^4 + 96x^3 + 108x + 162	\( 2^{20}\cdot 3^{4}\cdot 7^{8}\cdot 97^{2} \)	12T206	$[3]$
12.4.4606941747037077504.2	x^12 - 2x^11 + 2x^10 + 24x^9 - 74x^8 - 32x^7 + 328x^6 - 496x^5 - 1068x^4 + 824x^3 + 504x^2 - 800x + 216	\( 2^{20}\cdot 3^{4}\cdot 7^{8}\cdot 97^{2} \)	12T206	$[3]$
12.8.11924157958528958464.1	x^12 - 4x^11 - 4x^10 + 44x^9 - 34x^8 - 190x^7 + 256x^6 + 436x^5 - 600x^4 - 556x^3 + 514x^2 + 242x - 167	\( 2^{18}\cdot 7^{8}\cdot 53^{4} \)	12T206	$[3]$
12.8.11924157958528958464.2	x^12 - 2x^11 - 22x^10 + 36x^9 + 198x^8 - 152x^7 - 836x^6 - 448x^5 + 188x^4 + 192x^3 + 224x^2 - 64	\( 2^{18}\cdot 7^{8}\cdot 53^{4} \)	12T206	$[3]$
12.4.37488192928956714905856.1	x^12 - 3x^11 + 9x^10 + 12x^9 - 78x^8 - 69x^7 + 3x^6 + 399x^5 + 750x^4 - 739x^3 - 2640x^2 - 2256x - 672	\( 2^{8}\cdot 3^{18}\cdot 7^{4}\cdot 12547^{2} \)	12T206	$[2]$
12.12.42265191567128002560000.1	x^12 - 54x^10 - 96x^9 + 630x^8 + 1476x^7 - 1608x^6 - 3852x^5 + 1620x^4 + 1036x^3 - 324x^2 - 72x + 18	\( 2^{26}\cdot 3^{20}\cdot 5^{4}\cdot 17^{2} \)	12T206	Trivial (GRH)
12.4.172908068640615127056384.1	x^12 - 18x^10 - 36x^9 - 249x^8 + 2616x^7 - 8632x^6 + 13488x^5 + 17715x^4 - 40144x^3 - 43302x^2 - 10500x + 3633	\( 2^{26}\cdot 3^{12}\cdot 7^{8}\cdot 29^{2} \)	12T206	$[2]$ (GRH)
12.12.390647338879367208239104.1	x^12 - 2x^11 - 64x^10 + 120x^9 + 1340x^8 - 2202x^7 - 11432x^6 + 17570x^5 + 40302x^4 - 58564x^3 - 48286x^2 + 58814x + 12951	\( 2^{18}\cdot 7^{8}\cdot 53^{4}\cdot 181^{2} \)	12T206	$[3]$ (GRH)
12.0.2033481475843686400000000.1	x^12 + 36x^10 - 216x^9 + 578x^8 - 2944x^7 + 10844x^6 - 23008x^5 + 43265x^4 - 75616x^3 + 93128x^2 - 73384x + 29828	\( 2^{30}\cdot 5^{8}\cdot 7^{8}\cdot 29^{2} \)	12T206	$[3, 6]$ (GRH)
12.0.4048192313897753640960000.1	x^12 - 6x^11 + 24x^10 - 26x^9 + 750x^8 - 5964x^7 + 26166x^6 - 68820x^5 + 118560x^4 - 130312x^3 + 85716x^2 - 30000x + 4250	\( 2^{20}\cdot 3^{20}\cdot 5^{4}\cdot 11^{6} \)	12T206	$[2]$ (GRH)
12.0.4048192313897753640960000.2	x^12 - 6x^11 + 36x^10 - 72x^9 + 153x^8 + 792x^7 + 3270x^6 + 252x^5 + 59823x^4 - 60058x^3 + 258990x^2 - 156744x + 232125	\( 2^{20}\cdot 3^{20}\cdot 5^{4}\cdot 11^{6} \)	12T206	$[2]$ (GRH)
12.0.110824488078449614816055296.1	x^12 - 4x^11 - 9x^10 + 153x^9 + 374x^8 + 1756x^7 + 19085x^6 + 62587x^5 + 138762x^4 + 703184x^3 + 1772939x^2 + 617071x + 12414703	\( 2^{12}\cdot 7^{8}\cdot 29^{6}\cdot 53^{4} \)	12T206	$[2, 6]$ (GRH)