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 2172)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.4294967296000000000000.1	x^16 + 4x^14 + 14x^12 + 48x^10 + 164x^8 + 96x^6 + 56x^4 + 32x^2 + 16	\( 2^{44}\cdot 5^{12} \)	$C_4^2$ (as 16T4)	$[5]$ (GRH)
16.0.4294967296000000000000.2	x^16 - 4x^14 + 14x^12 - 48x^10 + 164x^8 - 96x^6 + 56x^4 - 32x^2 + 16	\( 2^{44}\cdot 5^{12} \)	$C_4^2$ (as 16T4)	Trivial (GRH)
16.0.5688009063105712890625.1	x^16 - x^15 - x^14 + 7x^13 - 12x^12 + 13x^11 + 42x^10 - 137x^9 + 141x^8 + 262x^7 + 269x^6 + 182x^5 - 95x^4 + 21x^3 + 90x^2 + 108x + 81	\( 5^{12}\cdot 13^{12} \)	$C_4^2$ (as 16T4)	Trivial (GRH)
16.16.68719476736000000000000.1	x^16 - 16x^14 + 104x^12 - 352x^10 + 659x^8 - 664x^6 + 316x^4 - 48x^2 + 1	\( 2^{48}\cdot 5^{12} \)	$C_4^2$ (as 16T4)	Trivial (GRH)
16.0.68719476736000000000000.2	x^16 + 16x^14 + 104x^12 + 352x^10 + 659x^8 + 664x^6 + 316x^4 + 48x^2 + 1	\( 2^{48}\cdot 5^{12} \)	$C_4^2$ (as 16T4)	$[10]$ (GRH)
16.0.142241757136172119140625.1	x^16 - x^15 + 7x^14 - 12x^13 + 52x^12 + 55x^11 + 238x^10 + 156x^9 + 1275x^8 - 156x^7 + 238x^6 - 55x^5 + 52x^4 + 12x^3 + 7x^2 + x + 1	\( 5^{12}\cdot 17^{12} \)	$C_4^2$ (as 16T4)	$[5]$ (GRH)
16.16.28179280429056000000000000.1	x^16 - 28x^14 + 266x^12 - 1104x^10 + 2264x^8 - 2352x^6 + 1184x^4 - 256x^2 + 16	\( 2^{44}\cdot 3^{8}\cdot 5^{12} \)	$C_4^2$ (as 16T4)	Trivial (GRH)
16.16.28179280429056000000000000.2	x^16 - 4x^15 - 26x^14 + 116x^13 + 193x^12 - 1108x^11 - 316x^10 + 4348x^9 - 1044x^8 - 7132x^7 + 2894x^6 + 4760x^5 - 2020x^4 - 1036x^3 + 348x^2 + 56x + 1	\( 2^{44}\cdot 3^{8}\cdot 5^{12} \)	$C_4^2$ (as 16T4)	Trivial (GRH)
16.0.28179280429056000000000000.3	x^16 + 12x^14 + 126x^12 + 1296x^10 + 13284x^8 + 23328x^6 + 40824x^4 + 69984x^2 + 104976	\( 2^{44}\cdot 3^{8}\cdot 5^{12} \)	$C_4^2$ (as 16T4)	$[4, 8]$ (GRH)
16.0.28179280429056000000000000.4	x^16 + 28x^14 + 266x^12 + 1104x^10 + 2264x^8 + 2352x^6 + 1184x^4 + 256x^2 + 16	\( 2^{44}\cdot 3^{8}\cdot 5^{12} \)	$C_4^2$ (as 16T4)	$[10, 10]$ (GRH)
16.0.28179280429056000000000000.5	x^16 - 12x^14 + 126x^12 - 1296x^10 + 13284x^8 - 23328x^6 + 40824x^4 - 69984x^2 + 104976	\( 2^{44}\cdot 3^{8}\cdot 5^{12} \)	$C_4^2$ (as 16T4)	$[2, 10]$ (GRH)
16.0.28179280429056000000000000.6	x^16 - 4x^15 + 6x^14 + 4x^13 + 25x^12 - 180x^11 + 380x^10 - 148x^9 - 468x^8 + 932x^7 + 398x^6 - 8760x^5 + 32372x^4 - 47628x^3 + 35356x^2 - 20536x + 22801	\( 2^{44}\cdot 3^{8}\cdot 5^{12} \)	$C_4^2$ (as 16T4)	$[4, 8]$ (GRH)
16.16.37319027463036582275390625.1	x^16 - x^15 - 38x^14 + 18x^13 + 535x^12 + 24x^11 - 3437x^10 - 1638x^9 + 10110x^8 + 7313x^7 - 13981x^6 - 12302x^5 + 8419x^4 + 8699x^3 - 1399x^2 - 2083x - 179	\( 3^{8}\cdot 5^{12}\cdot 13^{12} \)	$C_4^2$ (as 16T4)	Trivial (GRH)
16.0.37319027463036582275390625.2	x^16 - 11x^14 - 12x^13 + 83x^12 - 96x^11 + 219x^10 - 294x^9 + 1304x^8 - 3846x^7 + 1788x^6 + 1980x^5 - 7933x^4 + 10752x^3 + 26944x^2 - 27624x + 15856	\( 3^{8}\cdot 5^{12}\cdot 13^{12} \)	$C_4^2$ (as 16T4)	$[2, 26]$ (GRH)
16.0.37319027463036582275390625.3	x^16 - x^15 + 12x^14 - 32x^13 + 170x^12 + 559x^11 + 1563x^10 + 3152x^9 + 8500x^8 + 10428x^7 + 13659x^6 + 15093x^5 + 15804x^4 - 3996x^3 + 1026x^2 - 243x + 81	\( 3^{8}\cdot 5^{12}\cdot 13^{12} \)	$C_4^2$ (as 16T4)	$[2, 26]$ (GRH)
16.0.86380562306022715087890625.1	x^16 - x^15 - 3x^14 - 13x^13 + 22x^12 - 241x^11 + 482x^10 + 341x^9 + 2045x^8 - 7506x^7 + 18249x^6 - 36968x^5 + 67057x^4 - 111527x^3 + 162932x^2 - 243340x + 279841	\( 5^{12}\cdot 29^{12} \)	$C_4^2$ (as 16T4)	$[2, 4]$ (GRH)
16.16.372769361959696000000000000.2	x^16 - 36x^14 + 484x^12 - 3122x^10 + 10204x^8 - 16444x^6 + 11821x^4 - 3408x^2 + 256	\( 2^{16}\cdot 5^{12}\cdot 13^{12} \)	$C_4^2$ (as 16T4)	Trivial (GRH)
16.0.372769361959696000000000000.2	x^16 - 4x^15 - 6x^14 + 58x^13 - 12x^12 - 198x^11 + 132x^10 + 62x^9 + 2251x^8 + 1998x^7 - 3846x^6 + 1288x^5 - 12245x^4 + 3244x^3 + 52255x^2 - 57018x + 26861	\( 2^{16}\cdot 5^{12}\cdot 13^{12} \)	$C_4^2$ (as 16T4)	$[4, 8]$ (GRH)
16.0.372769361959696000000000000.3	x^16 + 13x^14 + 156x^12 + 1859x^10 + 22139x^8 + 24167x^6 + 26364x^4 + 28561x^2 + 28561	\( 2^{16}\cdot 5^{12}\cdot 13^{12} \)	$C_4^2$ (as 16T4)	$[4, 8]$ (GRH)
16.0.409864247953326282266116096.1	x^16 - 4x^15 + 30x^14 - 68x^13 + 273x^12 - 468x^11 + 1236x^10 - 1660x^9 + 2356x^8 - 3756x^7 + 4134x^6 - 1280x^5 + 1444x^4 - 4436x^3 - 4652x^2 + 3912x + 4241	\( 2^{44}\cdot 13^{12} \)	$C_4^2$ (as 16T4)	$[5]$ (GRH)
16.0.409864247953326282266116096.2	x^16 - 4x^15 - 2x^14 + 44x^13 - 39x^12 - 52x^11 + 220x^10 - 108x^9 + 1364x^8 - 44x^7 + 998x^6 + 3472x^5 - 8980x^4 - 3988x^3 + 21012x^2 - 6952x + 6241	\( 2^{44}\cdot 13^{12} \)	$C_4^2$ (as 16T4)	$[5, 5]$ (GRH)
16.16.450868486864896000000000000.2	x^16 - 48x^14 + 936x^12 - 9504x^10 + 53379x^8 - 161352x^6 + 230364x^4 - 104976x^2 + 6561	\( 2^{48}\cdot 3^{8}\cdot 5^{12} \)	$C_4^2$ (as 16T4)	$[2]$ (GRH)
16.0.450868486864896000000000000.5	x^16 - 8x^14 - 4x^12 + 96x^10 + 299x^8 + 648x^6 + 2984x^4 - 656x^2 + 6241	\( 2^{48}\cdot 3^{8}\cdot 5^{12} \)	$C_4^2$ (as 16T4)	$[2, 2, 10]$ (GRH)
16.0.450868486864896000000000000.6	x^16 + 8x^14 - 4x^12 - 96x^10 + 299x^8 - 648x^6 + 2984x^4 + 656x^2 + 6241	\( 2^{48}\cdot 3^{8}\cdot 5^{12} \)	$C_4^2$ (as 16T4)	$[2, 2, 2, 10]$ (GRH)
16.0.450868486864896000000000000.7	x^16 + 48x^14 + 936x^12 + 9504x^10 + 53379x^8 + 161352x^6 + 230364x^4 + 104976x^2 + 6561	\( 2^{48}\cdot 3^{8}\cdot 5^{12} \)	$C_4^2$ (as 16T4)	$[2, 8, 40]$ (GRH)
16.0.450868486864896000000000000.12	x^16 - 24x^14 + 204x^12 - 768x^10 + 1739x^8 - 4536x^6 + 18216x^4 - 35952x^2 + 39601	\( 2^{48}\cdot 3^{8}\cdot 5^{12} \)	$C_4^2$ (as 16T4)	$[2, 2, 2]$ (GRH)
16.0.450868486864896000000000000.13	x^16 + 24x^14 + 204x^12 + 768x^10 + 1739x^8 + 4536x^6 + 18216x^4 + 35952x^2 + 39601	\( 2^{48}\cdot 3^{8}\cdot 5^{12} \)	$C_4^2$ (as 16T4)	$[2, 8, 16]$ (GRH)
16.0.933248168570425273681640625.1	x^16 - x^15 + 10x^14 + 2x^13 + 5x^12 + 206x^11 + 21x^10 + 179x^9 + 1811x^8 + 919x^7 + 18978x^6 + 10441x^5 + 59108x^4 - 125819x^3 - 212699x^2 - 102242x + 1079671	\( 3^{8}\cdot 5^{12}\cdot 17^{12} \)	$C_4^2$ (as 16T4)	$[10, 10]$ (GRH)
16.16.933248168570425273681640625.1	x^16 - 43x^14 - 16x^13 + 648x^12 + 346x^11 - 4475x^10 - 2665x^9 + 15456x^8 + 9019x^7 - 26965x^6 - 13913x^5 + 21775x^4 + 8755x^3 - 5992x^2 - 1571x - 89	\( 3^{8}\cdot 5^{12}\cdot 17^{12} \)	$C_4^2$ (as 16T4)	Trivial (GRH)
16.0.933248168570425273681640625.3	x^16 - x^15 - 10x^14 + 22x^13 + 35x^12 + 106x^11 + 51x^10 - 2326x^9 + 51x^8 + 20074x^7 - 6222x^6 - 93589x^5 + 179453x^4 - 200044x^3 - 1543984x^2 + 140608x + 7311616	\( 3^{8}\cdot 5^{12}\cdot 17^{12} \)	$C_4^2$ (as 16T4)	$[2, 10]$ (GRH)
16.0.1607166017050789863525390625.1	x^16 - x^15 - 4x^14 + 2x^13 - 24x^12 - 193x^11 + 495x^10 + 540x^9 - 488x^8 + 3780x^7 + 24255x^6 - 66199x^5 - 57624x^4 + 33614x^3 - 470596x^2 - 823543x + 5764801	\( 5^{12}\cdot 37^{12} \)	$C_4^2$ (as 16T4)	$[5, 5]$ (GRH)
16.0.5508664624112838398681640625.1	x^16 - x^15 + 16x^14 - 49x^13 + 311x^12 + 1323x^11 + 4288x^10 + 9763x^9 + 31987x^8 + 42566x^7 + 49432x^6 + 52344x^5 + 50896x^4 + 14752x^3 + 4224x^2 + 1152x + 256	\( 5^{12}\cdot 41^{12} \)	$C_4^2$ (as 16T4)	$[4, 20]$ (GRH)
16.0.6557827967253220516257857536.1	x^16 + 40x^14 + 572x^12 + 3680x^10 + 11579x^8 + 18232x^6 + 13832x^4 + 4688x^2 + 529	\( 2^{48}\cdot 13^{12} \)	$C_4^2$ (as 16T4)	$[5, 5, 10]$ (GRH)
16.16.6557827967253220516257857536.1	x^16 - 40x^14 + 572x^12 - 3680x^10 + 11579x^8 - 18232x^6 + 13832x^4 - 4688x^2 + 529	\( 2^{48}\cdot 13^{12} \)	$C_4^2$ (as 16T4)	Trivial (GRH)
16.16.9321955795676176000000000000.1	x^16 - 4x^15 - 38x^14 + 142x^13 + 512x^12 - 1790x^11 - 3022x^10 + 10314x^9 + 8440x^8 - 29394x^7 - 11572x^6 + 41790x^5 + 8077x^4 - 27422x^3 - 3558x^2 + 6564x + 956	\( 2^{16}\cdot 5^{12}\cdot 17^{12} \)	$C_4^2$ (as 16T4)	Trivial (GRH)
16.0.9321955795676176000000000000.2	x^16 - 17x^14 + 221x^12 - 2601x^10 + 29189x^8 - 176868x^6 + 1021904x^4 - 5345344x^2 + 21381376	\( 2^{16}\cdot 5^{12}\cdot 17^{12} \)	$C_4^2$ (as 16T4)	$[4, 8]$ (GRH)
16.0.9321955795676176000000000000.3	x^16 + 24x^14 + 264x^12 + 1218x^10 - 1666x^8 - 20064x^6 + 52041x^4 - 1878x^2 + 3481	\( 2^{16}\cdot 5^{12}\cdot 17^{12} \)	$C_4^2$ (as 16T4)	$[4, 40]$ (GRH)
16.16.10249598790959829536343064576.1	x^16 - 4x^15 - 34x^14 + 128x^13 + 405x^12 - 1432x^11 - 2170x^10 + 7268x^9 + 5686x^8 - 17924x^7 - 7538x^6 + 21352x^5 + 4801x^4 - 10640x^3 - 1282x^2 + 1124x + 191	\( 2^{44}\cdot 17^{12} \)	$C_4^2$ (as 16T4)	Trivial (GRH)
16.0.10249598790959829536343064576.2	x^16 - 4x^15 - 2x^14 + 16x^13 + 77x^12 - 152x^11 - 34x^10 - 444x^9 - 914x^8 + 2364x^7 + 9326x^6 + 8376x^5 + 56089x^4 - 6224x^3 + 48294x^2 - 540x + 29207	\( 2^{44}\cdot 17^{12} \)	$C_4^2$ (as 16T4)	$[4, 52]$ (GRH)
16.0.13573982477229290545823357041.2	x^16 - 19x^14 - 28x^13 + 176x^12 + 178x^11 - 389x^10 - 1671x^9 + 3890x^8 + 9181x^7 + 8065x^6 - 17091x^5 - 27083x^4 + 27781x^3 + 45006x^2 - 36777x + 23699	\( 13^{12}\cdot 17^{12} \)	$C_4^2$ (as 16T4)	$[2, 2, 10]$ (GRH)
16.16.24759631762948096000000000000.1	x^16 - 48x^14 + 696x^12 - 4184x^10 + 11384x^8 - 13472x^6 + 5864x^4 - 736x^2 + 16	\( 2^{44}\cdot 5^{12}\cdot 7^{8} \)	$C_4^2$ (as 16T4)	Trivial (GRH)
16.0.24759631762948096000000000000.2	x^16 - 4x^15 - 14x^14 + 84x^13 + 135x^12 - 1140x^11 - 100x^10 + 7832x^9 - 3713x^8 - 26568x^7 - 772x^6 + 29700x^5 + 347147x^4 - 604188x^3 - 261314x^2 + 228044x + 1113751	\( 2^{44}\cdot 5^{12}\cdot 7^{8} \)	$C_4^2$ (as 16T4)	$[2, 170]$ (GRH)
16.16.24759631762948096000000000000.2	x^16 - 4x^15 - 46x^14 + 196x^13 + 703x^12 - 3348x^11 - 4076x^10 + 25128x^9 + 4831x^8 - 86152x^7 + 29964x^6 + 123300x^5 - 83845x^4 - 47356x^3 + 50918x^2 - 10884x + 191	\( 2^{44}\cdot 5^{12}\cdot 7^{8} \)	$C_4^2$ (as 16T4)	Trivial (GRH)
16.0.24759631762948096000000000000.3	x^16 + 48x^14 + 696x^12 + 4184x^10 + 11384x^8 + 13472x^6 + 5864x^4 + 736x^2 + 16	\( 2^{44}\cdot 5^{12}\cdot 7^{8} \)	$C_4^2$ (as 16T4)	$[8, 40]$ (GRH)
16.0.24759631762948096000000000000.4	x^16 - 28x^14 + 686x^12 - 16464x^10 + 393764x^8 - 1613472x^6 + 6588344x^4 - 26353376x^2 + 92236816	\( 2^{44}\cdot 5^{12}\cdot 7^{8} \)	$C_4^2$ (as 16T4)	$[8, 8]$ (GRH)
16.0.24759631762948096000000000000.5	x^16 + 28x^14 + 686x^12 + 16464x^10 + 393764x^8 + 1613472x^6 + 6588344x^4 + 26353376x^2 + 92236816	\( 2^{44}\cdot 5^{12}\cdot 7^{8} \)	$C_4^2$ (as 16T4)	$[2, 170]$ (GRH)
16.0.32790240335000876777587890625.1	x^16 - 31x^14 - 2x^13 + 458x^12 - 376x^11 - 2816x^10 + 4356x^9 + 13769x^8 - 39196x^7 - 37967x^6 + 192150x^5 - 77783x^4 - 416788x^3 + 772584x^2 + 40056x + 250721	\( 5^{12}\cdot 7^{8}\cdot 13^{12} \)	$C_4^2$ (as 16T4)	$[4, 40]$ (GRH)
16.16.32790240335000876777587890625.1	x^16 - x^15 - 75x^14 + 29x^13 + 2024x^12 + 527x^11 - 24414x^10 - 18647x^9 + 132021x^8 + 143796x^7 - 298501x^6 - 431294x^5 + 137649x^4 + 453033x^3 + 232820x^2 + 33022x - 1889	\( 5^{12}\cdot 7^{8}\cdot 13^{12} \)	$C_4^2$ (as 16T4)	Trivial (GRH)
16.0.32790240335000876777587890625.3	x^16 - x^15 + 25x^14 - 71x^13 + 664x^12 + 2717x^11 + 14056x^10 + 38603x^9 + 219711x^8 + 318736x^7 + 672889x^6 + 1023646x^5 + 1741879x^4 - 1221277x^3 + 992380x^2 - 536558x + 707281	\( 5^{12}\cdot 7^{8}\cdot 13^{12} \)	$C_4^2$ (as 16T4)	$[4, 40]$ (GRH)
16.0.95428956661682176000000000000.1	x^16 - 4x^15 + 54x^14 - 152x^13 + 1083x^12 - 2508x^11 + 11142x^10 - 23128x^9 + 63226x^8 - 128412x^7 + 222174x^6 - 365252x^5 + 530650x^4 - 568676x^3 + 537460x^2 - 655308x + 394481	\( 2^{24}\cdot 5^{12}\cdot 13^{12} \)	$C_4^2$ (as 16T4)	$[2, 20]$ (GRH)