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 all 36 matches)

Label	Polynomial	Discriminant	Galois group	Class group
12.4.24302560546048.1	x^12 - x^11 - 5x^10 + 13x^9 - 17x^8 + 12x^7 + 3x^6 - 14x^5 + 11x^4 + 3x^3 - 4x^2 - 2x - 1	\( 2^{8}\cdot 37^{7} \)	$A_4:C_4$ (as 12T27)	Trivial
12.4.860934420000000.1	x^12 - 6x^11 + 12x^10 - 5x^9 - 21x^8 + 48x^7 - 59x^6 + 54x^5 - 39x^4 + 21x^3 - 9x^2 + 3x + 1	\( 2^{8}\cdot 3^{16}\cdot 5^{7} \)	$A_4:C_4$ (as 12T27)	Trivial
12.0.6221455499788288.1	x^12 - 4x^11 + 14x^10 - 32x^9 + 55x^8 - 76x^7 + 76x^6 - 60x^5 + 27x^4 + 8x^3 + 6x^2 + 44x + 17	\( 2^{16}\cdot 37^{7} \)	$A_4:C_4$ (as 12T27)	$[2]$
12.0.7748409780000000.1	x^12 - 6x^11 + 24x^10 - 65x^9 + 135x^8 - 216x^7 + 261x^6 - 234x^5 + 135x^4 - 35x^3 + 3x^2 - 3x + 7	\( 2^{8}\cdot 3^{18}\cdot 5^{7} \)	$A_4:C_4$ (as 12T27)	$[2]$
12.0.694105431755676928.1	x^12 + 19x^10 + 130x^8 + 391x^6 + 518x^4 + 271x^2 + 37	\( 2^{8}\cdot 13^{4}\cdot 37^{7} \)	$A_4:C_4$ (as 12T27)	$[2]$
12.0.972102421841920000.1	x^12 - 2x^11 + 2x^10 + 37x^8 + 32x^7 - 124x^6 + 14x^5 + 311x^4 - 488x^3 + 360x^2 - 144x + 27	\( 2^{14}\cdot 5^{4}\cdot 37^{7} \)	$A_4:C_4$ (as 12T27)	$[2, 2]$
12.12.3443379683463546112.1	x^12 - 6x^11 - 8x^10 + 78x^9 - 3x^8 - 296x^7 + 129x^6 + 378x^5 - 201x^4 - 138x^3 + 56x^2 + 6x - 1	\( 2^{8}\cdot 11^{8}\cdot 13^{7} \)	$A_4:C_4$ (as 12T27)	Trivial
12.12.6370770431783206912.1	x^12 - 4x^11 - 20x^10 + 80x^9 + 122x^8 - 488x^7 - 204x^6 + 904x^5 - 8x^4 - 392x^3 - 32x^2 + 32x + 4	\( 2^{26}\cdot 37^{7} \)	$A_4:C_4$ (as 12T27)	Trivial (GRH)
12.4.16785484246943793152.2	x^12 - 6x^11 + 16x^10 - 18x^9 - 48x^8 + 114x^7 - 90x^6 - 114x^5 - 48x^4 + 18x^3 + 16x^2 + 6x + 1	\( 2^{25}\cdot 29^{8} \)	$A_4:C_4$ (as 12T27)	Trivial
12.4.16785484246943793152.7	x^12 - 5x^11 - 10x^10 + 38x^9 + 76x^8 + 60x^7 + 84x^6 - 516x^5 - 1169x^4 - 419x^3 + 434x^2 + 338x + 64	\( 2^{25}\cdot 29^{8} \)	$A_4:C_4$ (as 12T27)	Trivial (GRH)
12.0.268567747951100690432.3	x^12 + 25x^10 - 4x^9 + 234x^8 + 88x^7 + 710x^6 + 904x^5 + 938x^4 + 888x^3 + 166x^2 - 88x + 40	\( 2^{29}\cdot 29^{8} \)	$A_4:C_4$ (as 12T27)	$[2]$ (GRH)
12.0.268567747951100690432.33	x^12 + x^10 + 92x^8 + 900x^6 - 1004x^4 - 284x^2 + 512	\( 2^{29}\cdot 29^{8} \)	$A_4:C_4$ (as 12T27)	$[2]$ (GRH)
12.4.4297083967217611046912.67	x^12 - 32x^10 + 416x^8 - 2712x^6 + 8704x^4 - 12032x^2 + 2888	\( 2^{33}\cdot 29^{8} \)	$A_4:C_4$ (as 12T27)	$[4]$ (GRH)
12.0.4297083967217611046912.100	x^12 + 32x^10 + 416x^8 + 2712x^6 + 8704x^4 + 12032x^2 + 2888	\( 2^{33}\cdot 29^{8} \)	$A_4:C_4$ (as 12T27)	$[4]$ (GRH)
12.4.14116592251679730040832.6	x^12 - x^11 - 20x^10 + 9x^9 + 51x^8 + 470x^7 - 1456x^6 - 2454x^5 + 22006x^4 - 53748x^3 + 64152x^2 - 36036x + 6268	\( 2^{25}\cdot 29^{10} \)	$A_4:C_4$ (as 12T27)	$[2]$ (GRH)
12.4.14116592251679730040832.9	x^12 - x^11 + 11x^10 + 17x^9 + 194x^8 + 1050x^7 + 1042x^6 + 5030x^5 - 2703x^4 + 20679x^3 - 75901x^2 + 15209x + 14380	\( 2^{25}\cdot 29^{10} \)	$A_4:C_4$ (as 12T27)	$[2]$ (GRH)
12.4.17188335868870444187648.53	x^12 + 8x^10 - 68x^9 + 37x^8 + 256x^7 - 616x^6 + 1616x^5 - 3272x^4 + 3680x^3 - 2608x^2 + 192x + 936	\( 2^{35}\cdot 29^{8} \)	$A_4:C_4$ (as 12T27)	$[2]$ (GRH)
12.4.17188335868870444187648.69	x^12 - 8x^10 - 34x^8 + 796x^6 + 1249x^4 - 13100x^2 + 5000	\( 2^{35}\cdot 29^{8} \)	$A_4:C_4$ (as 12T27)	$[2]$ (GRH)
12.0.17188335868870444187648.70	x^12 + 12x^10 - 68x^9 + 173x^8 - 544x^7 + 904x^6 - 1728x^5 + 2808x^4 - 2176x^3 + 5312x^2 - 2352x + 3420	\( 2^{35}\cdot 29^{8} \)	$A_4:C_4$ (as 12T27)	$[2, 4]$ (GRH)
12.0.17188335868870444187648.75	x^12 + 8x^10 - 34x^8 - 796x^6 + 1249x^4 + 13100x^2 + 5000	\( 2^{35}\cdot 29^{8} \)	$A_4:C_4$ (as 12T27)	$[2, 10]$ (GRH)
12.0.68753343475481776750592.1	x^12 + 44x^10 + 240x^8 + 412x^6 + 237x^4 + 48x^2 + 2	\( 2^{37}\cdot 29^{8} \)	$A_4:C_4$ (as 12T27)	$[2, 58]$ (GRH)
12.12.68753343475481776750592.1	x^12 - 44x^10 + 240x^8 - 412x^6 + 237x^4 - 48x^2 + 2	\( 2^{37}\cdot 29^{8} \)	$A_4:C_4$ (as 12T27)	Trivial (GRH)
12.0.68753343475481776750592.77	x^12 + 8x^10 + 22x^8 + 160x^6 + 1964x^4 + 5408x^2 + 1800	\( 2^{37}\cdot 29^{8} \)	$A_4:C_4$ (as 12T27)	$[2, 4]$ (GRH)
12.4.68753343475481776750592.77	x^12 - 8x^10 + 22x^8 - 160x^6 + 1964x^4 - 5408x^2 + 1800	\( 2^{37}\cdot 29^{8} \)	$A_4:C_4$ (as 12T27)	$[2, 2]$ (GRH)
12.0.225865476026875680653312.17	x^12 - 4x^11 - 12x^10 + 168x^9 - 619x^8 + 856x^7 + 2232x^6 - 26688x^5 + 165147x^4 - 693812x^3 + 1741556x^2 - 2274088x + 1191311	\( 2^{29}\cdot 29^{10} \)	$A_4:C_4$ (as 12T27)	$[2, 2]$ (GRH)
12.0.225865476026875680653312.27	x^12 - 6x^11 + 28x^10 + 2x^9 - 483x^8 - 1916x^7 + 11800x^6 + 6772x^5 + 983x^4 - 133526x^3 - 62692x^2 - 298158x + 1956539	\( 2^{29}\cdot 29^{10} \)	$A_4:C_4$ (as 12T27)	$[2, 2]$ (GRH)
12.4.3613847616430010890452992.38	x^12 + 348x^8 - 8816x^6 - 50460x^4 - 1049568x^2 + 9715232	\( 2^{33}\cdot 29^{10} \)	$A_4:C_4$ (as 12T27)	$[2, 4]$ (GRH)
12.0.3613847616430010890452992.69	x^12 + 348x^8 + 8816x^6 - 50460x^4 + 1049568x^2 + 9715232	\( 2^{33}\cdot 29^{10} \)	$A_4:C_4$ (as 12T27)	$[2, 4]$ (GRH)
12.0.14455390465720043561811968.8	x^12 + 58x^10 + 464x^8 + 1856x^6 + 132037x^4 + 52142x^2 + 136242	\( 2^{35}\cdot 29^{10} \)	$A_4:C_4$ (as 12T27)	$[2, 2, 2]$ (GRH)
12.4.14455390465720043561811968.20	x^12 - 58x^10 + 464x^8 - 1856x^6 + 132037x^4 - 52142x^2 + 136242	\( 2^{35}\cdot 29^{10} \)	$A_4:C_4$ (as 12T27)	$[2, 2]$ (GRH)
12.0.14455390465720043561811968.48	x^12 - 4x^11 - 10x^10 - 264x^9 + 688x^8 + 224x^7 + 24180x^6 + 5384x^5 + 240035x^4 + 190308x^3 + 2102474x^2 + 1524488x + 5328774	\( 2^{35}\cdot 29^{10} \)	$A_4:C_4$ (as 12T27)	$[2, 2, 4]$ (GRH)
12.4.14455390465720043561811968.78	x^12 - 4x^11 - 10x^10 + 200x^9 - 820x^8 + 6720x^7 - 1340x^6 + 70576x^5 + 98515x^4 - 232396x^3 - 66262x^2 + 91888x + 32446	\( 2^{35}\cdot 29^{10} \)	$A_4:C_4$ (as 12T27)	$[2, 2]$ (GRH)
12.12.57821561862880174247247872.1	x^12 - 116x^10 + 4988x^8 - 98716x^6 + 899029x^4 - 3283264x^2 + 2558322	\( 2^{37}\cdot 29^{10} \)	$A_4:C_4$ (as 12T27)	$[2]$ (GRH)
12.0.57821561862880174247247872.20	x^12 + 116x^10 + 4988x^8 + 98716x^6 + 899029x^4 + 3283264x^2 + 2558322	\( 2^{37}\cdot 29^{10} \)	$A_4:C_4$ (as 12T27)	$[2, 2, 842]$ (GRH)
12.0.57821561862880174247247872.44	x^12 - 4x^11 + 6x^10 - 124x^9 + 1085x^8 + 880x^7 + 17700x^6 + 21040x^5 + 57389x^4 + 68732x^3 + 87266x^2 + 49556x + 9213	\( 2^{37}\cdot 29^{10} \)	$A_4:C_4$ (as 12T27)	$[2, 2, 4]$ (GRH)
12.4.57821561862880174247247872.65	x^12 - 4x^11 + 6x^10 - 124x^9 + 1085x^8 + 2736x^7 - 10604x^6 - 23968x^5 - 18707x^4 + 6556x^3 + 11170x^2 - 1020x + 16173	\( 2^{37}\cdot 29^{10} \)	$A_4:C_4$ (as 12T27)	$[2, 2, 2]$ (GRH)