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 16 matches)

Label	Polynomial	Discriminant	Galois group	Class group
12.6.2611367412498432.2	x^12 - 10x^10 - 4x^9 + 23x^8 + 8x^7 - 38x^6 - 20x^5 + 50x^4 + 24x^3 - 48x^2 + 12x + 1	\( -\,2^{24}\cdot 3^{3}\cdot 7^{8} \)	12T205	Trivial
12.6.3382973020957376.1	x^12 - 5x^11 + 7x^10 + x^9 - 22x^8 + 56x^7 - 45x^6 - 20x^5 + 76x^4 - 122x^3 + 46x^2 + 27x + 13	\( -\,2^{6}\cdot 7^{8}\cdot 11^{3}\cdot 83^{2} \)	12T205	Trivial
12.8.3515376756641792.1	x^12 - 9x^10 - 8x^9 + 29x^8 + 62x^7 - 48x^6 - 162x^5 + 51x^4 + 166x^3 - 24x^2 - 58x - 1	\( 2^{12}\cdot 7^{8}\cdot 53^{3} \)	12T205	Trivial
12.0.4326419489802557.1	x^12 - 6x^11 + 18x^10 - 30x^9 + 22x^8 + 23x^7 - 99x^6 + 120x^5 + 51x^4 - 314x^3 + 348x^2 - 153x + 27	\( 7^{8}\cdot 53^{3}\cdot 71^{2} \)	12T205	$[2]$
12.8.4326419489802557.1	x^12 - 3x^11 + 17x^9 - 50x^8 + 51x^7 - x^6 - 79x^5 + 112x^4 + 7x^3 - 58x^2 + 17x - 1	\( 7^{8}\cdot 53^{3}\cdot 71^{2} \)	12T205	Trivial
12.0.8075239234190093.1	x^12 - 3x^11 + 5x^10 - x^9 - 13x^8 + 20x^7 - x^6 - 38x^5 + 39x^4 + 16x^3 - 12x^2 + 9x + 27	\( 7^{8}\cdot 53^{3}\cdot 97^{2} \)	12T205	$[2]$
12.4.8075239234190093.1	x^12 - x^11 - 8x^10 + 5x^9 + 15x^8 - 8x^7 - 43x^6 - 76x^5 - 6x^4 + 129x^3 + 172x^2 + 154x + 43	\( 7^{8}\cdot 53^{3}\cdot 97^{2} \)	12T205	Trivial
12.0.16582176346454117.1	x^12 - 5x^11 + 22x^10 - 65x^9 + 156x^8 - 296x^7 + 463x^6 - 557x^5 + 519x^4 - 351x^3 + 168x^2 - 49x + 7	\( 7^{8}\cdot 53^{3}\cdot 139^{2} \)	12T205	$[2]$
12.4.16582176346454117.1	x^12 - 3x^11 - 8x^10 + 28x^9 + 25x^8 - 104x^7 - 47x^6 + 207x^5 + 60x^4 - 230x^3 - 36x^2 + 126x - 27	\( 7^{8}\cdot 53^{3}\cdot 139^{2} \)	12T205	Trivial
12.0.49712627311169536.1	x^12 + 5x^10 - 4x^9 + 17x^8 - 18x^7 + 8x^6 - 28x^5 + 44x^4 - 72x^3 - 5x^2 - 228x + 419	\( 2^{12}\cdot 7^{9}\cdot 67^{3} \)	12T205	$[2]$
12.4.224984112425074688.1	x^12 - 2x^11 - 6x^10 + 10x^9 + 7x^8 + 42x^7 - 130x^6 + 12x^5 + 172x^4 - 156x^3 + 128x^2 - 98x + 13	\( 2^{18}\cdot 7^{8}\cdot 53^{3} \)	12T205	Trivial
12.4.224984112425074688.2	x^12 - 6x^11 + 4x^10 + 26x^9 - 15x^8 - 60x^7 + 32x^6 - 156x^5 + 431x^4 - 86x^3 - 468x^2 - 6x + 71	\( 2^{18}\cdot 7^{8}\cdot 53^{3} \)	12T205	$[2]$
12.12.7370704507157871853568.1	x^12 - 4x^11 - 58x^10 + 172x^9 + 1386x^8 - 2246x^7 - 16998x^6 + 5452x^5 + 100217x^4 + 67246x^3 - 203954x^2 - 313842x - 122123	\( 2^{18}\cdot 7^{8}\cdot 53^{3}\cdot 181^{2} \)	12T205	$[2]$ (GRH)
12.12.7998466419337746972672.1	x^12 - 54x^10 - 60x^9 + 831x^8 + 1032x^7 - 5290x^6 - 4428x^5 + 17112x^4 + 2936x^3 - 23700x^2 + 10860x + 703	\( 2^{24}\cdot 3^{16}\cdot 13^{3}\cdot 71^{2} \)	12T205	Trivial (GRH)
12.0.62341666127720981987328000.1	x^12 + 72x^10 - 48x^9 + 2242x^8 - 3672x^7 + 30790x^6 - 90228x^5 + 112045x^4 - 559968x^3 + 2659010x^2 - 930600x + 1618375	\( 2^{24}\cdot 3^{6}\cdot 5^{3}\cdot 7^{4}\cdot 19^{8} \)	12T205	$[2, 2, 2]$ (GRH)
12.0.1917688793698627249096001323008000.1	x^12 - 24x^10 - 3036x^9 + 19956x^8 - 12144x^7 - 438096x^6 + 31301160x^5 + 361635132x^4 - 15275047040x^3 + 65875535760x^2 + 293930060688x + 1130499648312	\( 2^{24}\cdot 3^{20}\cdot 5^{3}\cdot 11^{6}\cdot 23^{6} \)	12T205	$[2, 2, 4]$ (GRH)