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 468)

Label	Polynomial	Discriminant	Galois group	Class group
12.2.659081523200.1	x^12 - 2x^11 + 5x^10 - 2x^9 + 6x^8 - 2x^7 + 11x^6 + 2x^5 - x^4 + 2x^3 + 4x - 1	\( -\,2^{12}\cdot 5^{2}\cdot 23^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.1055385022464.1	x^12 - 6x^11 + 20x^10 - 44x^9 + 66x^8 - 64x^7 + 30x^6 + 12x^5 - 34x^4 + 30x^3 - 17x^2 + 6x - 1	\( -\,2^{12}\cdot 3^{2}\cdot 31^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.4.28028872326425.1	x^12 - 5x^11 + 5x^10 + 13x^9 - 36x^8 + 33x^7 + 8x^6 - 66x^5 + 79x^4 - 47x^3 + 21x^2 - 6x + 1	\( 5^{2}\cdot 257^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.4.28403284787200.1	x^12 - 2x^11 - 2x^10 + 6x^9 + 9x^8 - 14x^7 - 18x^6 + 14x^5 + 9x^4 - 6x^3 - 2x^2 + 2x + 1	\( 2^{14}\cdot 5^{2}\cdot 37^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.4.161219428390144.1	x^12 - x^11 - 5x^10 + x^9 - 6x^8 + 11x^7 - 55x^6 - 29x^5 - 32x^4 + 45x^3 + 41x^2 - 9x + 1	\( 2^{8}\cdot 229^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.0.290849636220928.1	x^12 + 4x^10 + 11x^8 + 4x^6 - 41x^4 - 8x^2 + 37	\( 2^{22}\cdot 37^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.0.410143432327168.1	x^12 - 4x^11 + 4x^10 - 2x^8 + 6x^7 + 24x^6 + 12x^5 + 48x^4 + 46x^3 + 44x^2 + 56x + 58	\( 2^{14}\cdot 19^{2}\cdot 37^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	$[2]$
12.0.494429307838137.1	x^12 - 2x^11 + 12x^10 - 24x^9 + 61x^8 - 117x^7 + 187x^6 - 293x^5 + 350x^4 - 383x^3 + 442x^2 - 336x + 103	\( 3^{2}\cdot 7^{2}\cdot 257^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	$[2]$
12.4.601013506097152.1	x^12 - 4x^11 + 2x^10 + 2x^9 + 8x^8 + 30x^7 - 90x^6 - 22x^5 + 84x^4 + 34x^3 - 12x^2 - 8x + 2	\( 2^{14}\cdot 23^{2}\cdot 37^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.685529707511808.1	x^12 - 3x^11 + 3x^10 + 5x^9 - 9x^8 + 12x^6 - 18x^5 - 18x^4 + 4x^3 - 12x^2 + 12x - 4	\( -\,2^{16}\cdot 3^{21} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.685529707511808.2	x^12 + 6x^10 + 12x^8 - 16x^6 - 36x^4 - 18x^2 - 3	\( -\,2^{16}\cdot 3^{21} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.892554561978368.2	x^12 - 2x^11 + 4x^10 + 12x^9 - 11x^8 + 24x^7 + 94x^6 + 32x^5 - 56x^4 + 382x^3 + 150x^2 - 326x - 167	\( -\,2^{18}\cdot 23^{7} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.0.955486500241408.1	x^12 - 2x^11 + 8x^10 - 14x^9 + 24x^8 - 38x^7 + 78x^6 - 136x^5 + 232x^4 - 274x^3 + 276x^2 - 200x + 74	\( 2^{14}\cdot 29^{2}\cdot 37^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	$[2]$
12.2.1307761908383744.17	x^12 - 4x^11 + 10x^10 - 16x^9 - x^8 + 8x^7 - 88x^6 + 104x^5 - 35x^4 - 96x^3 + 166x^2 - 132x + 61	\( -\,2^{26}\cdot 11^{7} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.1376479908724736.2	x^12 - 8x^10 + 9x^8 - 13x^4 + 8x^2 - 29	\( -\,2^{26}\cdot 29^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.2742118830047232.5	x^12 + 3x^10 - 12x^9 - 12x^8 + 18x^7 + 22x^6 + 18x^5 - 12x^4 - 12x^3 + 3x^2 + 1	\( -\,2^{18}\cdot 3^{21} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.5231047633534976.1	x^12 - 10x^10 - 8x^9 + 34x^8 + 56x^7 - 52x^6 - 268x^5 - 464x^4 - 648x^3 - 756x^2 - 536x - 158	\( -\,2^{28}\cdot 11^{7} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.5231047633534976.4	x^12 + 6x^10 - 8x^9 + 14x^8 - 32x^7 + 16x^6 - 92x^5 - 2x^4 - 472x^3 - 196x^2 - 96x - 22	\( -\,2^{28}\cdot 11^{7} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.5505919634898944.1	x^12 + 4x^10 - 10x^8 - 84x^6 - 207x^4 - 256x^2 - 116	\( -\,2^{28}\cdot 29^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.5505919634898944.2	x^12 - 4x^10 - 10x^8 + 84x^6 - 207x^4 + 256x^2 - 116	\( -\,2^{28}\cdot 29^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.7212266713513984.1	x^12 - 2x^11 + 14x^10 - 18x^9 + 18x^8 + 38x^7 - 222x^6 - 68x^5 + 389x^4 + 70x^3 + 84x^2 - 308x - 223	\( -\,2^{18}\cdot 31^{7} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.9889949432152064.4	x^12 + 4x^10 - 5x^8 + 4x^6 + 23x^4 + 88x^2 - 11	\( -\,2^{22}\cdot 11^{9} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.8.10318043416969216.1	x^12 - 12x^10 - 20x^9 + 36x^8 + 130x^7 + 34x^6 - 220x^5 - 174x^4 + 120x^3 + 154x^2 - 10x - 41	\( 2^{14}\cdot 229^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.10968475320188928.4	x^12 + 3x^10 + 3x^8 - 14x^6 - 9x^4 + 27x^2 - 27	\( -\,2^{20}\cdot 3^{21} \)	$C_2\times C_2^2:S_4$ (as 12T100)	$[2]$
12.2.10968475320188928.10	x^12 - 6x^10 + 12x^8 + 16x^6 - 36x^4 + 18x^2 - 3	\( -\,2^{20}\cdot 3^{21} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.11555266180939776.4	x^12 - 6x^10 + 18x^8 - 12x^6 + 105x^4 - 78x^2 - 4	\( -\,2^{28}\cdot 3^{16} \)	$C_2\times C_2^2:S_4$ (as 12T100)	$[2]$
12.2.12757530337869824.1	x^12 + 8x^10 + 26x^8 + 12x^6 - 103x^4 - 196x^2 - 104	\( -\,2^{35}\cdot 13^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.12757530337869824.4	x^12 - 8x^10 + 26x^8 - 12x^6 - 103x^4 + 196x^2 - 104	\( -\,2^{35}\cdot 13^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	$[2]$
12.2.12757530337869824.10	x^12 + 2x^10 + 12x^8 + 24x^6 + 13x^4 - 18x^2 - 26	\( -\,2^{35}\cdot 13^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.13421772800000000.8	x^12 + 6x^10 + 8x^8 - 8x^6 - 19x^4 - 6x^2 - 2	\( -\,2^{35}\cdot 5^{8} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.18087806300585984.1	x^12 - 6x^11 + 10x^10 + 4x^9 - 41x^8 + 94x^7 - 42x^6 - 320x^5 + 669x^4 - 474x^3 - 64x^2 + 580x - 524	\( -\,2^{20}\cdot 29^{7} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.18087806300585984.18	x^12 + 3x^10 - 6x^9 + 34x^8 - 48x^7 + 51x^6 + 30x^5 + 273x^4 + 156x^3 + 244x^2 + 1296x + 568	\( -\,2^{20}\cdot 29^{7} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.20528754925502464.1	x^12 + 4x^10 - 10x^9 + 14x^8 - 42x^7 + 6x^6 - 4x^5 - 2x^4 + 58x^3 + 78x^2 + 50x - 17	\( -\,2^{18}\cdot 23^{8} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.22023678539595776.8	x^12 + 6x^10 + 5x^8 - 100x^6 + 135x^4 - 10x^2 - 29	\( -\,2^{30}\cdot 29^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.22023678539595776.11	x^12 - 8x^10 - 4x^9 + 3x^8 - 24x^7 - 14x^6 + 20x^5 - 22x^4 - 32x^3 + 4x^2 - 8x - 14	\( -\,2^{30}\cdot 29^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.25999348907114496.6	x^12 - 9x^10 + 45x^8 - 126x^6 + 171x^4 - 81x^2 - 9	\( -\,2^{26}\cdot 3^{18} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.33687853548437504.2	x^12 - 4x^11 + 8x^10 + 4x^9 - 33x^8 - 24x^7 + 356x^6 - 940x^5 + 1221x^4 - 644x^3 - 266x^2 + 488x - 166	\( -\,2^{29}\cdot 13^{7} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.39559797728608256.3	x^12 + 2x^10 - 15x^8 - 60x^6 - 79x^4 - 44x^2 - 11	\( -\,2^{24}\cdot 11^{9} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.39559797728608256.6	x^12 - 2x^10 - 15x^8 + 60x^6 - 79x^4 + 44x^2 - 11	\( -\,2^{24}\cdot 11^{9} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.8.41272173667876864.1	x^12 - 4x^11 + 2x^10 - 18x^9 + 48x^8 + 64x^7 - 73x^6 - 108x^5 + 41x^4 + 64x^3 - 4x^2 - 12x - 2	\( 2^{16}\cdot 229^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.43873901280755712.2	x^12 - 6x^10 + 15x^8 - 62x^6 - 180x^5 - 372x^4 - 552x^3 - 564x^2 - 360x - 116	\( -\,2^{22}\cdot 3^{21} \)	$C_2\times C_2^2:S_4$ (as 12T100)	$[2]$
12.2.43873901280755712.15	x^12 + 12x^10 + 48x^8 - 26x^6 - 72x^4 - 3	\( -\,2^{22}\cdot 3^{21} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.43873901280755712.16	x^12 - 6x^10 + 12x^8 - 8x^6 - 3	\( -\,2^{22}\cdot 3^{21} \)	$C_2\times C_2^2:S_4$ (as 12T100)	$[2]$
12.2.51030121351479296.11	x^12 - 4x^11 + 10x^10 - 4x^9 - 3x^8 + 16x^7 - 20x^6 + 24x^5 - 18x^4 - 16x^3 + 36x^2 - 72x - 54	\( -\,2^{37}\cdot 13^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.51030121351479296.12	x^12 - 4x^10 - 4x^8 + 12x^6 - 43x^4 - 112x^2 - 26	\( -\,2^{37}\cdot 13^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.51030121351479296.14	x^12 - 8x^10 + 12x^8 + 36x^6 + 5x^4 - 4x^2 - 26	\( -\,2^{37}\cdot 13^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	$[2]$
12.2.51030121351479296.18	x^12 - 4x^11 + 14x^10 - 28x^9 + 47x^8 - 64x^7 + 108x^6 - 160x^5 + 129x^4 + 108x^3 - 30x^2 - 92x - 13	\( -\,2^{37}\cdot 13^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.51030121351479296.19	x^12 - 4x^11 + 14x^10 - 44x^9 + 99x^8 - 176x^7 + 212x^6 - 112x^5 - 59x^4 + 172x^3 - 158x^2 + 52x - 13	\( -\,2^{37}\cdot 13^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	$[2]$
12.2.51030121351479296.20	x^12 - 4x^11 + 10x^10 - 20x^9 + x^8 + 32x^7 - 140x^6 + 328x^5 - 370x^4 + 224x^3 - 76x^2 + 8x - 2	\( -\,2^{37}\cdot 13^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.53687091200000000.12	x^12 - 4x^11 + 10x^10 - 20x^9 + 53x^8 - 112x^7 + 124x^6 - 128x^5 + 161x^4 - 164x^3 + 118x^2 - 20x + 1	\( -\,2^{37}\cdot 5^{8} \)	$C_2\times C_2^2:S_4$ (as 12T100)	$[2]$