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 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.1757684377967394816.1	x^16 - 6x^15 + 8x^14 + 18x^13 - 50x^12 - 6x^11 + 104x^10 - 30x^9 - 122x^8 + 30x^7 + 104x^6 + 6x^5 - 50x^4 - 18x^3 + 8x^2 + 6x + 1	\( 2^{28}\cdot 3^{14}\cdot 37^{2} \)	16T984	Trivial
16.0.31686294687883428096.1	x^16 - 2x^15 - 10x^14 + 9x^13 + 47x^12 - x^11 - 113x^10 + 6x^9 + 169x^8 + 196x^6 + 331x^5 + 98x^4 + 546x^3 + 161x^2 - 340x + 127	\( 2^{8}\cdot 3^{14}\cdot 7^{8}\cdot 67^{2} \)	16T984	Trivial
16.12.1250616032402500000000.2	x^16 - 3x^14 - 22x^12 + 82x^10 + 41x^8 - 430x^6 + 530x^4 - 225x^2 + 25	\( 2^{8}\cdot 5^{10}\cdot 29^{8} \)	16T984	Trivial (GRH)
16.4.1250616032402500000000.2	x^16 + 7x^14 - 7x^12 - 138x^10 - 319x^8 - 230x^6 + 40x^4 + 100x^2 + 25	\( 2^{8}\cdot 5^{10}\cdot 29^{8} \)	16T984	Trivial (GRH)
16.8.4051995944984100000000.1	x^16 - 2x^14 - 24x^13 + 13x^12 + 17x^11 + 144x^10 - 142x^9 - 35x^8 - 36x^7 + 396x^6 - 386x^5 - 7x^4 + 108x^3 - 18x^2 - 5x + 1	\( 2^{8}\cdot 3^{4}\cdot 5^{8}\cdot 29^{8} \)	16T984	Trivial (GRH)
16.8.4051995944984100000000.2	x^16 - 5x^15 + 4x^14 + 12x^13 - 10x^12 + 12x^11 - 203x^10 + 487x^9 - 378x^8 + 33x^7 + 22x^6 - 112x^5 + 250x^4 - 32x^3 - 71x^2 + 5x + 1	\( 2^{8}\cdot 3^{4}\cdot 5^{8}\cdot 29^{8} \)	16T984	Trivial (GRH)
16.12.42070723330020100000000.1	x^16 - 21x^14 - 6x^13 + 112x^12 - 51x^11 - 272x^10 + 345x^9 + 187x^8 - 571x^7 + 186x^6 + 283x^5 - 166x^4 - 73x^3 + 33x^2 + 13x + 1	\( 2^{8}\cdot 5^{8}\cdot 29^{10} \)	16T984	Trivial (GRH)
16.4.42070723330020100000000.1	x^16 + 5x^14 - 11x^13 - 74x^11 - 17x^10 - 147x^9 + 195x^8 - 197x^7 + 755x^6 - 727x^5 + 1518x^4 - 1255x^3 + 767x^2 - 893x + 361	\( 2^{8}\cdot 5^{8}\cdot 29^{10} \)	16T984	Trivial (GRH)
16.0.66183076013297341825024.6	x^16 - 4x^15 + 16x^14 - 42x^13 + 100x^12 - 216x^11 + 323x^10 - 412x^9 + 295x^8 - 100x^7 + 78x^6 + 838x^5 + 670x^4 + 144x^3 + 83x^2 + 8x + 2	\( 2^{32}\cdot 17^{8}\cdot 47^{2} \)	16T984	Trivial (GRH)
16.0.66183076013297341825024.7	x^16 - 2x^15 - x^14 - 2x^13 - 11x^12 + 8x^11 + 20x^10 + 124x^9 + 675x^8 + 1806x^7 + 3603x^6 + 5518x^5 + 5687x^4 + 3588x^3 + 1310x^2 + 272x + 32	\( 2^{32}\cdot 17^{8}\cdot 47^{2} \)	16T984	Trivial (GRH)
16.0.4325768496046086337890625.1	x^16 - 4x^15 + 21x^14 - 73x^13 + 257x^12 - 795x^11 + 2375x^10 - 6194x^9 + 14470x^8 - 28957x^7 + 50113x^6 - 72357x^5 + 87219x^4 - 83483x^3 + 62264x^2 - 31727x + 9931	\( 5^{10}\cdot 29^{8}\cdot 941^{2} \)	16T984	$[4, 16]$ (GRH)
16.16.4325768496046086337890625.1	x^16 - 3x^15 - 28x^14 + 89x^13 + 258x^12 - 849x^11 - 1157x^10 + 3656x^9 + 3180x^8 - 8005x^7 - 5762x^6 + 8935x^5 + 6215x^4 - 4625x^3 - 3268x^2 + 871x + 631	\( 5^{10}\cdot 29^{8}\cdot 941^{2} \)	16T984	Trivial (GRH)
16.0.2434427958226796953600000000.1	x^16 + 62x^14 + 1557x^12 + 20582x^10 + 153773x^8 + 638206x^6 + 1309128x^4 + 943504x^2 + 190096	\( 2^{20}\cdot 5^{8}\cdot 29^{8}\cdot 109^{2} \)	16T984	$[2, 2, 522]$ (GRH)
16.8.3803793684729370240000000000.1	x^16 + 17x^14 - 56x^12 - 1572x^10 + 2141x^8 + 44040x^6 - 98480x^4 - 122625x^2 + 297025	\( 2^{16}\cdot 5^{10}\cdot 29^{8}\cdot 109^{2} \)	16T984	$[2]$ (GRH)
16.8.3803793684729370240000000000.2	x^16 + 23x^14 - 146x^12 - 2998x^10 + 8106x^8 + 64955x^6 - 166890x^4 - 119900x^2 + 297025	\( 2^{16}\cdot 5^{10}\cdot 29^{8}\cdot 109^{2} \)	16T984	$[2]$ (GRH)
16.8.3888223178515238551136763904.1	x^16 + 28x^14 + 130x^12 - 1388x^10 - 8510x^8 + 7196x^6 + 37682x^4 - 35244x^2 + 7921	\( 2^{46}\cdot 17^{8}\cdot 89^{2} \)	16T984	$[2]$ (GRH)
16.12.3958890882998059417600000000.1	x^16 - 32x^14 - 14x^12 + 3913x^10 - 13901x^8 - 74902x^6 + 472796x^4 - 757272x^2 + 309136	\( 2^{20}\cdot 5^{8}\cdot 29^{8}\cdot 139^{2} \)	16T984	Trivial (GRH)
16.12.6185767004684467840000000000.1	x^16 - 37x^14 + 279x^12 + 1962x^10 - 21159x^8 + 2600x^6 + 329820x^4 - 764500x^2 + 483025	\( 2^{16}\cdot 5^{10}\cdot 29^{8}\cdot 139^{2} \)	16T984	Trivial (GRH)
16.4.6185767004684467840000000000.1	x^16 - 7x^14 - 476x^12 - 1098x^10 + 44131x^8 + 344470x^6 + 972360x^4 + 1157175x^2 + 483025	\( 2^{16}\cdot 5^{10}\cdot 29^{8}\cdot 139^{2} \)	16T984	$[2, 2]$ (GRH)
16.4.69979484620810119540570587136.1	x^16 - 8x^15 + 18x^14 - 16x^13 - 574x^12 + 1908x^11 - 8750x^10 + 8368x^9 - 23691x^8 - 53780x^7 + 145636x^6 - 567384x^5 + 1805012x^4 - 3126928x^3 + 6378576x^2 - 4249952x + 4748368	\( 2^{24}\cdot 3^{14}\cdot 11^{8}\cdot 2017^{2} \)	16T984	$[2, 2]$ (GRH)
16.8.583476490725942985079960633344.1	x^16 - 4x^15 - 18x^14 + 96x^13 - 774x^12 + 2964x^11 + 4456x^10 - 78704x^9 + 214060x^8 - 40336x^7 - 814404x^6 + 2661600x^5 - 3846476x^4 + 3226520x^3 - 2273992x^2 + 1109984x - 219964	\( 2^{42}\cdot 7^{4}\cdot 17^{8}\cdot 89^{2} \)	16T984	$[2]$ (GRH)
16.8.1397422247186214856729600000000.1	x^16 - 51x^14 + 293x^12 + 2055x^10 - 8044x^8 - 18075x^6 + 35887x^4 + 39618x^2 + 5041	\( 2^{16}\cdot 5^{8}\cdot 71^{2}\cdot 101^{8} \)	16T984	$[2]$ (GRH)
16.16.3830385813647384576561728515625.2	x^16 - 2x^15 - 147x^14 + 331x^13 + 8385x^12 - 20064x^11 - 238293x^10 + 583069x^9 + 3612524x^8 - 8792283x^7 - 28798622x^6 + 67472526x^5 + 108806388x^4 - 228249170x^3 - 147170067x^2 + 196161120x + 65392529	\( 5^{10}\cdot 29^{8}\cdot 941^{4} \)	16T984	$[2]$ (GRH)
16.8.27517209172131676143648100000000.1	x^16 + x^14 - 978x^12 + 1018x^10 + 250283x^8 - 52114x^6 - 22109826x^4 - 1789555x^2 + 635292025	\( 2^{8}\cdot 5^{8}\cdot 71^{4}\cdot 101^{8} \)	16T984	$[2]$ (GRH)