Global number field search results

Further refine search

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 9982)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.70516271401.1	x^12 - 3x^11 + 4x^10 - x^9 - 3x^8 + 4x^7 - 3x^6 + 4x^5 - 3x^4 - x^3 + 4x^2 - 3x + 1	\( 37^{2}\cdot 7177^{2} \)	12T285	Trivial
12.0.90534190321.1	x^12 - 2x^11 + 5x^10 - 7x^9 + 8x^8 - 10x^7 + 8x^6 - 8x^5 + 5x^4 - 2x^3 + 2x^2 + 1	\( 300889^{2} \)	12T285	Trivial
12.0.201018619201.1	x^12 - x^11 + x^10 - x^8 + x^7 - x^6 + x^5 - x^4 + x^2 - x + 1	\( 448351^{2} \)	12T285	Trivial
12.0.236681277001.1	x^12 - 5x^11 + 10x^10 - 10x^9 + 2x^8 + 10x^7 - 15x^6 + 7x^5 + 6x^4 - 10x^3 + 5x^2 - x + 1	\( 13^{2}\cdot 37423^{2} \)	12T285	Trivial
12.0.242978013184.1	x^12 - 2x^10 + 2x^8 - 2x^6 + 2x^4 + 2x^2 + 1	\( 2^{14}\cdot 3851^{2} \)	12T285	Trivial
12.0.316981386121.1	x^12 - x^9 - x^8 + x^7 + x^6 + x^5 - x^4 - x^3 + 1	\( 563011^{2} \)	12T285	Trivial
12.4.949704822784.1	x^12 - 2x^11 + 4x^10 - 2x^9 - 4x^8 + 10x^7 - 15x^6 + 10x^5 - 4x^4 - 2x^3 + 4x^2 - 2x + 1	\( 2^{12}\cdot 15227^{2} \)	12T285	Trivial
12.4.1085603537929.1	x^12 - 6x^11 + 15x^10 - 20x^9 + 16x^8 - 10x^7 + 11x^6 - 16x^5 + 12x^4 - 2x^3 - 6x^2 + 5x - 1	\( 23^{2}\cdot 89^{2}\cdot 509^{2} \)	12T285	Trivial
12.4.1167128033569.1	x^12 - 3x^11 + 3x^10 + 3x^9 - 9x^8 + 8x^7 - 8x^6 - x^5 + 3x^3 + 4x^2 - x - 1	\( 29^{2}\cdot 37253^{2} \)	12T285	Trivial
12.4.1270162810225.1	x^12 - x^11 - 3x^10 + 5x^9 + 3x^8 - 6x^7 - 4x^6 - 3x^5 + 4x^4 + 7x^3 - 3x - 1	\( 5^{2}\cdot 17^{2}\cdot 13259^{2} \)	12T285	Trivial
12.4.1286838403321.1	x^12 - 2x^11 + 3x^9 - 3x^8 - x^7 + 3x^6 - x^5 - 3x^4 + 3x^3 - 2x + 1	\( 1134389^{2} \)	12T285	Trivial
12.4.3493045122961.1	x^12 - 3x^10 - x^9 + 3x^8 + x^7 - 3x^6 + x^5 + 3x^4 - x^3 - 3x^2 + 1	\( 107^{2}\cdot 17467^{2} \)	12T285	Trivial
12.8.35258133876736.1	x^12 - 3x^10 + x^8 - 6x^6 + 11x^4 - 6x^2 + 1	\( 2^{12}\cdot 92779^{2} \)	12T285	Trivial
12.8.36472323149824.1	x^12 - 6x^10 + 13x^8 - 15x^6 + 14x^4 - 9x^2 + 1	\( 2^{12}\cdot 197^{2}\cdot 479^{2} \)	12T285	Trivial
12.8.116284756498681.1	x^12 - 4x^10 + 13x^6 - 8x^4 - 4x^2 + 1	\( 10783541^{2} \)	12T285	Trivial
12.8.123068382517161.1	x^12 - 3x^11 - 3x^10 + 15x^9 - 7x^8 - 10x^7 + 13x^6 - 10x^5 - 7x^4 + 15x^3 - 3x^2 - 3x + 1	\( 3^{2}\cdot 997^{2}\cdot 3709^{2} \)	12T285	Trivial
12.4.623717458640896.2	x^12 - 4x^11 + 2x^10 + 12x^9 - 26x^8 + 24x^7 - 4x^6 - 24x^5 + 60x^4 - 80x^3 + 60x^2 - 24x + 4	\( 2^{20}\cdot 29^{6} \)	12T285	Trivial
12.0.632773018800400.1	x^12 - 4x^11 + 12x^10 - 29x^9 + 58x^8 - 101x^7 + 151x^6 - 202x^5 + 232x^4 - 232x^3 + 192x^2 - 128x + 64	\( 2^{4}\cdot 5^{2}\cdot 1257749^{2} \)	12T285	Trivial
12.0.676934710884961.1	x^12 - 4x^11 + 8x^10 - 9x^9 + 7x^8 - 8x^7 + 13x^6 - 16x^5 + 28x^4 - 72x^3 + 128x^2 - 128x + 64	\( 3203^{2}\cdot 8123^{2} \)	12T285	Trivial
12.0.700350123728641.1	x^12 - 4x^11 + 5x^10 + 3x^9 - 14x^8 + 10x^7 + x^6 + 20x^5 - 56x^4 + 24x^3 + 80x^2 - 128x + 64	\( 67^{2}\cdot 394987^{2} \)	12T285	Trivial
12.0.855355656503296.5	x^12 + 2x^10 + 25x^8 + 20x^6 + 12x^4 + 16x^2 + 4	\( 2^{20}\cdot 13^{8} \)	12T285	Trivial
12.0.1014454095446016.1	x^12 + 6x^10 + 17x^8 + 28x^6 + 27x^4 + 10x^2 + 1	\( 2^{34}\cdot 3^{10} \)	12T285	Trivial
12.4.1014454095446016.1	x^12 - 6x^10 + 17x^8 - 28x^6 + 27x^4 - 10x^2 + 1	\( 2^{34}\cdot 3^{10} \)	12T285	Trivial
12.4.1014454095446016.2	x^12 - 6x^10 + 17x^8 - 28x^6 + 27x^4 - 18x^2 + 9	\( 2^{34}\cdot 3^{10} \)	12T285	Trivial
12.0.1014454095446016.3	x^12 + 6x^10 + 17x^8 + 28x^6 + 27x^4 + 18x^2 + 9	\( 2^{34}\cdot 3^{10} \)	12T285	Trivial
12.0.1080396404539456.1	x^12 - 3x^11 + 4x^10 - 4x^9 - 4x^8 + 19x^7 - 29x^6 + 38x^5 - 16x^4 - 32x^3 + 64x^2 - 96x + 64	\( 2^{6}\cdot 4108673^{2} \)	12T285	Trivial
12.0.1092378979038649.1	x^12 - 5x^11 + 10x^10 - 8x^9 - 7x^8 + 30x^7 - 51x^6 + 60x^5 - 28x^4 - 64x^3 + 160x^2 - 160x + 64	\( 373^{2}\cdot 88609^{2} \)	12T285	Trivial
12.0.1230402733947409.1	x^12 - 5x^11 + 10x^10 - 9x^9 + x^8 + 3x^7 - x^6 + 6x^5 + 4x^4 - 72x^3 + 160x^2 - 160x + 64	\( 11^{2}\cdot 19^{2}\cdot 157^{2}\cdot 1069^{2} \)	12T285	Trivial
12.0.1434791671278736.1	x^12 - x^11 - 5x^9 - 2x^8 + 8x^7 + 9x^6 + 16x^5 - 8x^4 - 40x^3 - 32x + 64	\( 2^{4}\cdot 9469661^{2} \)	12T285	Trivial
12.0.1498332179223616.1	x^12 - x^10 - 3x^9 - 2x^8 + 6x^7 + 8x^6 + 12x^5 - 8x^4 - 24x^3 - 16x^2 + 64	\( 2^{6}\cdot 11^{2}\cdot 439867^{2} \)	12T285	$[2]$
12.0.1640218977146689.1	x^12 - 2x^11 + 2x^10 - 5x^9 + 3x^8 - 2x^7 + 13x^6 - 4x^5 + 12x^4 - 40x^3 + 32x^2 - 64x + 64	\( 40499617^{2} \)	12T285	Trivial
12.0.1831614793322161.1	x^12 - 2x^11 - 2x^10 + 12x^9 - 11x^8 - 15x^7 + 47x^6 - 30x^5 - 44x^4 + 96x^3 - 32x^2 - 64x + 64	\( 42797369^{2} \)	12T285	Trivial
12.0.2044021590674449.1	x^12 - x^11 + x^10 - 4x^9 - 2x^8 + 6x^7 + x^6 + 12x^5 - 8x^4 - 32x^3 + 16x^2 - 32x + 64	\( 127^{2}\cdot 317^{2}\cdot 1123^{2} \)	12T285	Trivial
12.0.2534583582243904.1	x^12 - x^11 + x^10 - x^9 - 2x^8 + 6x^7 - 8x^6 + 12x^5 - 8x^4 - 8x^3 + 16x^2 - 32x + 64	\( 2^{6}\cdot 6293081^{2} \)	12T285	$[2]$
12.0.2621440000000000.17	x^12 - x^11 + x^10 - 10x^9 + 20x^8 - 32x^7 + 32x^6 + 8x^5 + 10x^4 + 30x^3 + 18x^2 + 12x + 8	\( 2^{28}\cdot 5^{10} \)	12T285	Trivial
12.0.2836942055754304.1	x^12 - x^11 - 2x^10 - x^9 + 2x^8 + 9x^6 + 8x^4 - 8x^3 - 32x^2 - 32x + 64	\( 2^{6}\cdot 569^{2}\cdot 11701^{2} \)	12T285	$[2]$
12.0.3090737867304025.1	x^12 - 4x^11 + 6x^10 - 4x^9 + 2x^8 - 11x^7 + 27x^6 - 22x^5 + 8x^4 - 32x^3 + 96x^2 - 128x + 64	\( 5^{2}\cdot 691^{2}\cdot 16091^{2} \)	12T285	Trivial
12.0.3109398971140225.1	x^12 - 4x^11 + 9x^10 - 12x^9 + 11x^8 - 5x^7 + 3x^6 - 10x^5 + 44x^4 - 96x^3 + 144x^2 - 128x + 64	\( 5^{2}\cdot 859^{2}\cdot 12983^{2} \)	12T285	Trivial
12.12.3185030335661329.1	x^12 - 4x^11 - 6x^10 + 38x^9 + 2x^8 - 134x^7 + 49x^6 + 213x^5 - 104x^4 - 146x^3 + 60x^2 + 33x - 1	\( 17^{2}\cdot 101^{2}\cdot 32869^{2} \)	12T285	Trivial
12.0.3280129749021889.1	x^12 - 4x^11 + 6x^10 - 3x^9 - 5x^8 + 22x^7 - 43x^6 + 44x^5 - 20x^4 - 24x^3 + 96x^2 - 128x + 64	\( 293^{2}\cdot 195469^{2} \)	12T285	Trivial
12.0.3576878205912064.1	x^12 + 12x^10 + 50x^8 + 90x^6 + 67x^4 + 15x^2 + 1	\( 2^{10}\cdot 107^{2}\cdot 17467^{2} \)	12T285	$[2]$
12.0.3666051221805625.1	x^12 - x^10 - 3x^9 - 4x^8 + 7x^7 + 11x^6 + 14x^5 - 16x^4 - 24x^3 - 16x^2 + 64	\( 5^{4}\cdot 2421917^{2} \)	12T285	Trivial
12.0.4109555773237489.1	x^12 - 5x^11 + 11x^10 - 12x^9 + 24x^7 - 47x^6 + 48x^5 - 96x^3 + 176x^2 - 160x + 64	\( 64105817^{2} \)	12T285	Trivial
12.0.4296772084853824.1	x^12 - 5x^11 + 9x^10 - 4x^9 - 9x^8 + 16x^7 - 18x^6 + 32x^5 - 36x^4 - 32x^3 + 144x^2 - 160x + 64	\( 2^{6}\cdot 599^{2}\cdot 13679^{2} \)	12T285	Trivial
12.0.4516319686337761.1	x^12 - 4x^11 + 8x^10 - 15x^9 + 27x^8 - 42x^7 + 61x^6 - 84x^5 + 108x^4 - 120x^3 + 128x^2 - 128x + 64	\( 137^{2}\cdot 490537^{2} \)	12T285	Trivial
12.0.4700446861638025.1	x^12 - x^11 + 5x^9 - 3x^8 + 13x^6 - 12x^4 + 40x^3 - 32x + 64	\( 5^{2}\cdot 1453^{2}\cdot 9437^{2} \)	12T285	Trivial
12.0.4736522879404801.1	x^12 - 4x^11 + 8x^10 - 11x^9 + 11x^8 - 4x^7 - 3x^6 - 8x^5 + 44x^4 - 88x^3 + 128x^2 - 128x + 64	\( 68822401^{2} \)	12T285	Trivial
12.0.4803019327984761.1	x^12 - 5x^11 + 11x^10 - 17x^9 + 28x^8 - 51x^7 + 81x^6 - 102x^5 + 112x^4 - 136x^3 + 176x^2 - 160x + 64	\( 3^{2}\cdot 13^{2}\cdot 59^{2}\cdot 30119^{2} \)	12T285	Trivial
12.0.4857016121751616.1	x^12 - 4x^11 + 6x^10 - 3x^9 - 2x^8 - 2x^7 + 12x^6 - 4x^5 - 8x^4 - 24x^3 + 96x^2 - 128x + 64	\( 2^{6}\cdot 197^{2}\cdot 44221^{2} \)	12T285	$[2]$
12.0.5213530976896225.1	x^12 - x^11 - 2x^10 + 4x^9 - 2x^8 - 4x^7 + 13x^6 - 8x^5 - 8x^4 + 32x^3 - 32x^2 - 32x + 64	\( 5^{2}\cdot 61^{2}\cdot 236737^{2} \)	12T285	Trivial