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 2097)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.1792160394037.1	x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1	\( 13^{11} \)	$C_{12}$ (as 12T1)	Trivial
12.0.11259376953125.1	x^12 - x^11 + 3x^10 - 4x^9 + 9x^8 + 2x^7 + 12x^6 + x^5 + 25x^4 - 11x^3 + 5x^2 - 2x + 1	\( 5^{9}\cdot 7^{8} \)	$C_{12}$ (as 12T1)	Trivial
12.0.84075626953125.1	x^12 + 3x^10 - x^9 + 9x^8 + 9x^7 + 28x^6 + 18x^5 + 75x^4 + 26x^3 + 9x^2 + 3x + 1	\( 3^{16}\cdot 5^{9} \)	$C_{12}$ (as 12T1)	Trivial
12.12.551709470703125.1	x^12 - x^11 - 12x^10 + 11x^9 + 54x^8 - 43x^7 - 113x^6 + 71x^5 + 110x^4 - 46x^3 - 40x^2 + 8x + 1	\( 5^{9}\cdot 7^{10} \)	$C_{12}$ (as 12T1)	Trivial
12.12.756680642578125.1	x^12 - 12x^10 - x^9 + 54x^8 + 9x^7 - 112x^6 - 27x^5 + 105x^4 + 31x^3 - 36x^2 - 12x + 1	\( 3^{18}\cdot 5^{9} \)	$C_{12}$ (as 12T1)	Trivial
12.12.1306484927252973.1	x^12 - x^11 - 12x^10 + 12x^9 + 53x^8 - 53x^7 - 103x^6 + 103x^5 + 79x^4 - 79x^3 - 12x^2 + 12x + 1	\( 3^{6}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	Trivial
12.0.1593224064453125.1	x^12 - x^11 + 5x^10 - 10x^9 + 31x^8 + 50x^7 + 84x^6 + 85x^5 + 201x^4 + 55x^3 + 15x^2 + 4x + 1	\( 5^{9}\cdot 13^{8} \)	$C_{12}$ (as 12T1)	$[2, 2]$
12.12.7340688973975552.1	x^12 - 13x^10 + 65x^8 - 156x^6 + 182x^4 - 91x^2 + 13	\( 2^{12}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	Trivial
12.12.8208085798828125.1	x^12 - x^11 - 22x^10 + 14x^9 + 153x^8 - 62x^7 - 396x^6 + 84x^5 + 361x^4 - 87x^3 - 112x^2 + 37x + 1	\( 3^{6}\cdot 5^{9}\cdot 7^{8} \)	$C_{12}$ (as 12T1)	Trivial
12.0.28002506156828125.1	x^12 - x^11 + 14x^10 - 14x^9 + 79x^8 - 79x^7 + 235x^6 - 235x^5 + 417x^4 - 417x^3 + 508x^2 - 508x + 521	\( 5^{6}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[2, 2, 2]$
12.0.33171021564453125.1	x^12 - x^11 + 7x^10 - 6x^9 + 41x^8 - 62x^7 + 266x^6 - 351x^5 + 1513x^4 - 1757x^3 + 2107x^2 - 2058x + 2401	\( 5^{9}\cdot 19^{8} \)	$C_{12}$ (as 12T1)	$[13]$
12.12.46118408000000000.1	x^12 - 4x^11 - 17x^10 + 74x^9 + 74x^8 - 412x^7 - 23x^6 + 734x^5 - 175x^4 - 324x^3 + 90x^2 + 22x + 1	\( 2^{12}\cdot 5^{9}\cdot 7^{8} \)	$C_{12}$ (as 12T1)	Trivial
12.0.49519263525896192.1	x^12 + 20x^10 + 122x^8 + 280x^6 + 264x^4 + 96x^2 + 8	\( 2^{33}\cdot 7^{8} \)	$C_{12}$ (as 12T1)	$[3, 3]$
12.12.49519263525896192.1	x^12 - 20x^10 + 122x^8 - 280x^6 + 264x^4 - 96x^2 + 8	\( 2^{33}\cdot 7^{8} \)	$C_{12}$ (as 12T1)	Trivial
12.0.61132828589969773.1	x^12 - x^11 - 4x^10 - 10x^9 + 39x^8 - 78x^7 + 214x^6 - 280x^5 + 693x^4 - 573x^3 - 222x^2 + 123x + 601	\( 7^{8}\cdot 13^{9} \)	$C_{12}$ (as 12T1)	$[2, 2]$
12.0.177917621779460413.1	x^12 - x^11 + 2x^10 + 20x^9 - 13x^8 + 19x^7 + 85x^6 - 51x^5 + 94x^4 + 2x^3 - 13x^2 + 77x + 47	\( 37^{11} \)	$C_{12}$ (as 12T1)	Trivial
12.12.210845878198059013.1	x^12 - x^11 - 25x^10 + 25x^9 + 235x^8 - 235x^7 - 1013x^6 + 1013x^5 + 1899x^4 - 1899x^3 - 1013x^2 + 1013x - 181	\( 7^{6}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	Trivial
12.0.269254866892578125.1	x^12 - x^11 + 10x^10 - 15x^9 + x^8 - 55x^7 + 24x^6 + 155x^5 + 471x^4 + 505x^3 + 415x^2 + 309x + 521	\( 5^{9}\cdot 13^{10} \)	$C_{12}$ (as 12T1)	$[2, 2, 2]$
12.12.344373768000000000.1	x^12 - 27x^10 - 4x^9 + 234x^8 + 36x^7 - 737x^6 + 72x^5 + 795x^4 - 336x^3 - 96x^2 + 42x + 1	\( 2^{12}\cdot 3^{16}\cdot 5^{9} \)	$C_{12}$ (as 12T1)	Trivial (GRH)
12.0.369768517790072832.1	x^12 + 24x^10 + 180x^8 + 472x^6 + 468x^4 + 144x^2 + 8	\( 2^{33}\cdot 3^{16} \)	$C_{12}$ (as 12T1)	$[13]$
12.12.369768517790072832.1	x^12 - 24x^10 - 4x^9 + 180x^8 + 36x^7 - 502x^6 - 36x^5 + 501x^4 - 32x^3 - 138x^2 + 36x - 1	\( 2^{33}\cdot 3^{16} \)	$C_{12}$ (as 12T1)	Trivial
12.0.402196204142578125.1	x^12 - x^11 + 23x^10 - 24x^9 + 194x^8 - 218x^7 + 832x^6 - 1084x^5 + 2455x^4 - 2566x^3 + 5315x^2 - 1567x + 6931	\( 3^{6}\cdot 5^{9}\cdot 7^{10} \)	$C_{12}$ (as 12T1)	$[2, 26]$
12.0.456488925854205933.1	x^12 - 3x^11 - 3x^10 + 25x^9 + 3x^8 + 30x^7 + 140x^6 - 60x^5 + 348x^4 - 286x^3 - 822x^2 + 567x + 1569	\( 3^{16}\cdot 13^{9} \)	$C_{12}$ (as 12T1)	$[3, 3]$
12.0.469804094334435328.1	x^12 + 26x^10 + 260x^8 + 1248x^6 + 2912x^4 + 2912x^2 + 832	\( 2^{18}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[26]$
12.12.469804094334435328.1	x^12 - 26x^10 + 260x^8 - 1248x^6 + 2912x^4 - 2912x^2 + 832	\( 2^{18}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	Trivial
12.12.683635509017782097.1	x^12 - x^11 - 28x^10 + 31x^9 + 232x^8 - 249x^7 - 742x^6 + 716x^5 + 925x^4 - 785x^3 - 388x^2 + 288x + 13	\( 7^{8}\cdot 17^{9} \)	$C_{12}$ (as 12T1)	Trivial (GRH)
12.12.1161460342986328125.1	x^12 - x^11 - 30x^10 + 10x^9 + 291x^8 - 20x^7 - 1136x^6 + 90x^5 + 1881x^4 - 395x^3 - 1100x^2 + 409x + 31	\( 3^{6}\cdot 5^{9}\cdot 13^{8} \)	$C_{12}$ (as 12T1)	Trivial (GRH)
12.0.1665802807501953125.1	x^12 - x^11 + 11x^10 - 13x^9 + 115x^8 - 46x^7 + 1092x^6 - 632x^5 + 11184x^4 - 8768x^3 + 6912x^2 - 5120x + 4096	\( 5^{9}\cdot 31^{8} \)	$C_{12}$ (as 12T1)	$[3, 3]$
12.0.2259801992000000000.1	x^12 + 35x^10 + 455x^8 + 2800x^6 + 8575x^4 + 12250x^2 + 6125	\( 2^{12}\cdot 5^{9}\cdot 7^{10} \)	$C_{12}$ (as 12T1)	$[2, 26]$
12.0.2426443912768913408.1	x^12 + 28x^10 + 266x^8 + 1064x^6 + 1960x^4 + 1568x^2 + 392	\( 2^{33}\cdot 7^{10} \)	$C_{12}$ (as 12T1)	$[2, 26]$
12.12.2426443912768913408.1	x^12 - 28x^10 + 266x^8 - 1064x^6 + 1960x^4 - 1568x^2 + 392	\( 2^{33}\cdot 7^{10} \)	$C_{12}$ (as 12T1)	Trivial (GRH)
12.0.2951578112000000000.1	x^12 - 4x^11 + 28x^10 - 76x^9 + 359x^8 - 772x^7 + 2662x^6 - 4216x^5 + 11540x^4 - 13284x^3 + 37260x^2 - 26468x + 52681	\( 2^{18}\cdot 5^{9}\cdot 7^{8} \)	$C_{12}$ (as 12T1)	$[146]$
12.12.2951578112000000000.1	x^12 - 4x^11 - 32x^10 + 124x^9 + 339x^8 - 1252x^7 - 1458x^6 + 4864x^5 + 2480x^4 - 6484x^3 - 1580x^2 + 2052x - 239	\( 2^{18}\cdot 5^{9}\cdot 7^{8} \)	$C_{12}$ (as 12T1)	Trivial (GRH)
12.12.2995508600908518877.1	x^12 - x^11 - 31x^10 + 28x^9 + 292x^8 - 208x^7 - 946x^6 + 596x^5 + 1123x^4 - 672x^3 - 369x^2 + 215x + 1	\( 7^{10}\cdot 13^{9} \)	$C_{12}$ (as 12T1)	Trivial (GRH)
12.0.3099363912000000000.1	x^12 + 30x^10 + 315x^8 + 1500x^6 + 3375x^4 + 3375x^2 + 1125	\( 2^{12}\cdot 3^{18}\cdot 5^{9} \)	$C_{12}$ (as 12T1)	$[10, 10]$
12.12.3174921459820581757.1	x^12 - x^11 - 38x^10 + 38x^9 + 547x^8 - 547x^7 - 3665x^6 + 3665x^5 + 11077x^4 - 11077x^3 - 11036x^2 + 11036x - 1559	\( 11^{6}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	Trivial (GRH)
12.0.3327916660110655488.1	x^12 + 24x^10 + 180x^8 + 552x^6 + 756x^4 + 432x^2 + 72	\( 2^{33}\cdot 3^{18} \)	$C_{12}$ (as 12T1)	$[26]$
12.12.3327916660110655488.1	x^12 - 24x^10 + 180x^8 - 552x^6 + 756x^4 - 432x^2 + 72	\( 2^{33}\cdot 3^{18} \)	$C_{12}$ (as 12T1)	Trivial
12.12.3500313269603515625.1	x^12 - x^11 - 25x^10 + 25x^9 + 196x^8 - 170x^7 - 571x^6 + 350x^5 + 586x^4 - 105x^3 - 155x^2 - x + 1	\( 5^{9}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[2]$
12.12.3500313269603515625.2	x^12 - x^11 - 25x^10 + 25x^9 + 196x^8 - 170x^7 - 571x^6 + 350x^5 + 586x^4 - 170x^3 - 90x^2 - x + 1	\( 5^{9}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[2]$
12.12.4108400332687853397.1	x^12 - 30x^10 - 17x^9 + 279x^8 + 285x^7 - 752x^6 - 909x^5 + 600x^4 + 858x^3 - 72x^2 - 243x - 51	\( 3^{18}\cdot 13^{9} \)	$C_{12}$ (as 12T1)	Trivial (GRH)
12.12.5104819233548816337.1	x^12 - 3x^11 - 27x^10 + 64x^9 + 231x^8 - 435x^7 - 819x^6 + 1107x^5 + 1245x^4 - 867x^3 - 765x^2 + 17	\( 3^{16}\cdot 17^{9} \)	$C_{12}$ (as 12T1)	Trivial
12.0.5351362262028177408.1	x^12 + 39x^10 + 585x^8 + 4212x^6 + 14742x^4 + 22113x^2 + 9477	\( 2^{12}\cdot 3^{6}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[2, 2, 26]$
12.12.6525845768000000000.1	x^12 - 4x^11 - 25x^10 + 90x^9 + 206x^8 - 660x^7 - 511x^6 + 2010x^5 - 219x^4 - 2040x^3 + 1290x^2 - 54x - 79	\( 2^{12}\cdot 5^{9}\cdot 13^{8} \)	$C_{12}$ (as 12T1)	Trivial (GRH)
12.0.6860311433439453125.1	x^12 - x^11 + 13x^10 - 36x^9 + 203x^8 + 718x^7 + 2114x^6 + 4269x^5 + 13201x^4 + 14773x^3 + 16093x^2 + 15972x + 14641	\( 5^{9}\cdot 37^{8} \)	$C_{12}$ (as 12T1)	$[7, 7]$
12.0.7007073538075000832.1	x^12 - 4x^11 + 2x^10 + 71x^8 - 60x^7 - 166x^6 - 468x^5 + 234x^4 + 2196x^3 + 5160x^2 + 3408x + 2417	\( 2^{33}\cdot 13^{8} \)	$C_{12}$ (as 12T1)	$[13]$
12.12.7007073538075000832.1	x^12 - 4x^11 - 22x^10 + 80x^9 + 159x^8 - 508x^7 - 406x^6 + 1276x^5 + 194x^4 - 1100x^3 + 184x^2 + 256x - 79	\( 2^{33}\cdot 13^{8} \)	$C_{12}$ (as 12T1)	Trivial
12.12.9891413435408203125.1	x^12 - 3x^11 - 36x^10 + 106x^9 + 393x^8 - 1164x^7 - 1350x^6 + 4794x^5 + 441x^4 - 6643x^3 + 1926x^2 + 2865x - 1349	\( 3^{16}\cdot 5^{9}\cdot 7^{6} \)	$C_{12}$ (as 12T1)	Trivial (GRH)
12.0.10331448031704891637.1	x^12 - x^11 + x^10 - 27x^9 + 27x^8 + 90x^7 + 53x^6 - 1353x^5 + 768x^4 + 3886x^3 + 1600x^2 - 5409x + 1847	\( 7^{8}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[3]$
12.0.10331448031704891637.2	x^12 - x^11 + x^10 - 27x^9 + 27x^8 - 183x^7 + 326x^6 + 649x^5 + 131x^4 - 573x^3 + 1782x^2 - 2133x + 4941	\( 7^{8}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[111]$