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 552)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.2862423051509815793.1	x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1	\( 17^{15} \)	$C_{16}$ (as 16T1)	Trivial
16.16.18780357640955901417873.1	x^16 - x^15 - 16x^14 + 16x^13 + 103x^12 - 103x^11 - 339x^10 + 339x^9 + 596x^8 - 596x^7 - 526x^6 + 526x^5 + 188x^4 - 188x^3 - 16x^2 + 16x + 1	\( 3^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	Trivial (GRH)
16.16.187591757103747287810048.1	x^16 - 17x^14 + 119x^12 - 442x^10 + 935x^8 - 1122x^6 + 714x^4 - 204x^2 + 17	\( 2^{16}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	Trivial (GRH)
16.0.604462909807314587353088.1	x^16 + 16x^14 + 104x^12 + 352x^10 + 660x^8 + 672x^6 + 336x^4 + 64x^2 + 2	\( 2^{79} \)	$C_{16}$ (as 16T1)	$[17]$ (GRH)
16.16.604462909807314587353088.1	x^16 - 16x^14 + 104x^12 - 352x^10 + 660x^8 - 672x^6 + 336x^4 - 64x^2 + 2	\( 2^{79} \)	$C_{16}$ (as 16T1)	Trivial (GRH)
16.0.1118134004496021794140625.1	x^16 - x^15 + 18x^14 - 18x^13 + 137x^12 - 137x^11 + 579x^10 - 579x^9 + 1514x^8 - 1514x^7 + 2636x^6 - 2636x^5 + 3350x^4 - 3350x^3 + 3554x^2 - 3554x + 3571	\( 5^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[34]$ (GRH)
16.16.16501299269766837593302193.1	x^16 - x^15 - 33x^14 + 33x^13 + 443x^12 - 443x^11 - 3093x^10 + 3093x^9 + 11867x^8 - 11867x^7 - 24037x^6 + 24037x^5 + 21659x^4 - 21659x^3 - 4453x^2 + 4453x - 101	\( 7^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	Trivial (GRH)
16.0.48023489818559305679372288.1	x^16 + 34x^14 + 476x^12 + 3536x^10 + 14960x^8 + 35904x^6 + 45696x^4 + 26112x^2 + 4352	\( 2^{24}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 194]$ (GRH)
16.16.48023489818559305679372288.1	x^16 - 34x^14 + 476x^12 - 3536x^10 + 14960x^8 - 35904x^6 + 45696x^4 - 26112x^2 + 4352	\( 2^{24}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	Trivial (GRH)
16.16.613585802270249473903607633.1	x^16 - x^15 - 50x^14 + 50x^13 + 1021x^12 - 1021x^11 - 10913x^10 + 10913x^9 + 64822x^8 - 64822x^7 - 207824x^6 + 207824x^5 + 312682x^4 - 312682x^3 - 133466x^2 + 133466x - 21929	\( 11^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	Trivial (GRH)
16.16.698833752810013621337890625.1	x^16 - x^15 - 33x^14 + 33x^13 + 392x^12 - 375x^11 - 2107x^10 + 1886x^9 + 5305x^8 - 4506x^7 - 5677x^6 + 5235x^5 + 1412x^4 - 2398x^3 + 732x^2 - 69x + 1	\( 5^{12}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2]$ (GRH)
16.16.698833752810013621337890625.2	x^16 - x^15 - 33x^14 + 33x^13 + 392x^12 - 375x^11 - 2107x^10 + 1886x^9 + 5305x^8 - 4506x^7 - 5677x^6 + 4810x^5 + 1837x^4 - 1463x^3 - 118x^2 + 16x + 1	\( 5^{12}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2]$ (GRH)
16.0.1230789518357685955321724928.1	x^16 + 51x^14 + 1071x^12 + 11934x^10 + 75735x^8 + 272646x^6 + 520506x^4 + 446148x^2 + 111537	\( 2^{16}\cdot 3^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2, 386]$ (GRH)
16.0.2334966419615122175401076753.2	x^16 - x^15 + 52x^14 - 52x^13 + 1123x^12 - 1123x^11 + 13057x^10 - 13057x^9 + 88792x^8 - 88792x^7 + 361438x^6 - 361438x^5 + 881944x^4 - 881944x^3 + 1328092x^2 - 1328092x + 1439629	\( 13^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2, 2, 226]$ (GRH)
16.0.3965881151245791007623610368.1	x^16 + 48x^14 + 936x^12 + 9504x^10 + 53460x^8 + 163296x^6 + 244944x^4 + 139968x^2 + 13122	\( 2^{79}\cdot 3^{8} \)	$C_{16}$ (as 16T1)	$[802]$ (GRH)
16.16.3965881151245791007623610368.1	x^16 - 48x^14 + 936x^12 - 9504x^10 + 53460x^8 - 163296x^6 + 244944x^4 - 139968x^2 + 13122	\( 2^{79}\cdot 3^{8} \)	$C_{16}$ (as 16T1)	Trivial (GRH)
16.16.7336077203498398991356640625.1	x^16 - x^15 - 67x^14 + 67x^13 + 1837x^12 - 1837x^11 - 26451x^10 + 26451x^9 + 212909x^8 - 212909x^7 - 936019x^6 + 936019x^5 + 1988525x^4 - 1988525x^3 - 1353811x^2 + 1353811x - 239699	\( 3^{8}\cdot 5^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2]$ (GRH)
16.16.48614142345328546750712906513.1	x^16 - x^15 - 84x^14 + 84x^13 + 2891x^12 - 2891x^11 - 52359x^10 + 52359x^9 + 532016x^8 - 532016x^7 - 2974234x^6 + 2974234x^5 + 8182016x^4 - 8182016x^3 - 7755484x^2 + 7755484x - 1114859	\( 17^{15}\cdot 19^{8} \)	$C_{16}$ (as 16T1)	Trivial (GRH)
16.16.73278030118651284300800000000.1	x^16 - 85x^14 + 2975x^12 - 55250x^10 + 584375x^8 - 3506250x^6 + 11156250x^4 - 15937500x^2 + 6640625	\( 2^{16}\cdot 5^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2]$ (GRH)
16.0.108265024508940221449655688273.1	x^16 - x^15 + 86x^14 - 86x^13 + 3061x^12 - 3061x^11 + 58311x^10 - 58311x^9 + 642686x^8 - 642686x^7 + 4148936x^6 - 4148936x^5 + 15305186x^4 - 15305186x^3 + 31242686x^2 - 31242686x + 37883311	\( 3^{8}\cdot 7^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 3746]$ (GRH)
16.16.224159169454780289392644342833.1	x^16 - x^15 - 101x^14 + 101x^13 + 4183x^12 - 4183x^11 - 91289x^10 + 91289x^9 + 1120471x^8 - 1120471x^7 - 7604201x^6 + 7604201x^5 + 25708183x^4 - 25708183x^3 - 31398761x^2 + 31398761x - 2845289	\( 17^{15}\cdot 23^{8} \)	$C_{16}$ (as 16T1)	Trivial (GRH)
16.0.236118324143482260684800000000.1	x^16 + 80x^14 + 2600x^12 + 44000x^10 + 412500x^8 + 2100000x^6 + 5250000x^4 + 5000000x^2 + 781250	\( 2^{79}\cdot 5^{8} \)	$C_{16}$ (as 16T1)	$[11458]$ (GRH)
16.16.236118324143482260684800000000.1	x^16 - 80x^14 + 2600x^12 - 44000x^10 + 412500x^8 - 2100000x^6 + 5250000x^4 - 5000000x^2 + 781250	\( 2^{79}\cdot 5^{8} \)	$C_{16}$ (as 16T1)	$[2]$ (GRH)
16.0.315082116699567604562361581568.1	x^16 + 102x^14 + 4284x^12 + 95472x^10 + 1211760x^8 + 8724672x^6 + 33312384x^4 + 57106944x^2 + 28553472	\( 2^{24}\cdot 3^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2, 4162]$ (GRH)
16.16.315082116699567604562361581568.1	x^16 - 102x^14 + 4284x^12 - 95472x^10 + 1211760x^8 - 8724672x^6 + 33312384x^4 - 57106944x^2 + 28553472	\( 2^{24}\cdot 3^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2]$ (GRH)
16.16.633251189136789386043275954593.1	x^16 - x^15 - 45x^14 + 98x^13 + 650x^12 - 2183x^11 - 2576x^10 + 17205x^9 - 9748x^8 - 44003x^7 + 63779x^6 + 18576x^5 - 86644x^4 + 43324x^3 + 15475x^2 - 17690x + 3721	\( 97^{15} \)	$C_{16}$ (as 16T1)	Trivial (GRH)
16.0.1081429148943439468514652520448.1	x^16 + 119x^14 + 5831x^12 + 151606x^10 + 2244935x^8 + 18857454x^6 + 84001386x^4 + 168002772x^2 + 98001617	\( 2^{16}\cdot 7^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2, 13666]$ (GRH)
16.0.1431916863894665085730117693073.1	x^16 - x^15 + 120x^14 - 120x^13 + 5951x^12 - 5951x^11 + 157557x^10 - 157557x^9 + 2402492x^8 - 2402492x^7 + 21259946x^6 - 21259946x^5 + 105261332x^4 - 105261332x^3 + 273264104x^2 - 273264104x + 371265721	\( 17^{15}\cdot 29^{8} \)	$C_{16}$ (as 16T1)	$[40834]$ (GRH)
16.16.2441334965997239773086576105713.1	x^16 - x^15 - 135x^14 + 135x^13 + 7481x^12 - 7481x^11 - 218823x^10 + 218823x^9 + 3610937x^8 - 3610937x^7 - 33154759x^6 + 33154759x^5 + 154016057x^4 - 154016057x^3 - 273802951x^2 + 273802951x + 11409721	\( 17^{15}\cdot 31^{8} \)	$C_{16}$ (as 16T1)	Trivial (GRH)
16.0.3484608386920116940487669055488.4	x^16 + 112x^14 + 5096x^12 + 120736x^10 + 1584660x^8 + 11294304x^6 + 39530064x^4 + 52706752x^2 + 11529602	\( 2^{79}\cdot 7^{8} \)	$C_{16}$ (as 16T1)	$[2, 27394]$ (GRH)
16.16.3484608386920116940487669055488.4	x^16 - 112x^14 + 5096x^12 - 120736x^10 + 1584660x^8 - 11294304x^6 + 39530064x^4 - 52706752x^2 + 11529602	\( 2^{79}\cdot 7^{8} \)	$C_{16}$ (as 16T1)	Trivial (GRH)
16.0.4025736448695106798281569680113.1	x^16 - x^15 + 137x^14 - 137x^13 + 7753x^12 - 7753x^11 + 234057x^10 - 234057x^9 + 4063817x^8 - 4063817x^7 + 40829513x^6 - 40829513x^5 + 228000329x^4 - 228000329x^3 + 655819337x^2 - 655819337x + 941032009	\( 3^{8}\cdot 11^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 28066]$ (GRH)
16.0.4585048252186499369597900390625.1	x^16 - x^15 + 52x^14 - 52x^13 + 1072x^12 - 375x^11 + 10728x^10 + 4776x^9 + 67695x^8 + 76584x^7 + 217448x^6 + 420375x^5 + 129932x^4 - 901018x^3 + 2686052x^2 - 2023749x + 459511	\( 3^{8}\cdot 5^{12}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 7556]$ (GRH)
16.0.4585048252186499369597900390625.2	x^16 - x^15 + 52x^14 - 52x^13 + 1072x^12 - 1395x^11 + 11748x^10 - 13839x^9 + 86310x^8 - 83556x^7 + 540278x^6 - 463965x^5 + 1553597x^4 - 771733x^3 + 3292187x^2 - 1949034x + 2213401	\( 3^{8}\cdot 5^{12}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 1412]$ (GRH)
16.0.6254270377697284219642783674257.1	x^16 - x^15 + 4x^14 - 20x^13 + 110x^12 - 525x^11 + 325x^10 + 425x^9 + 12062x^8 + 21729x^7 + 64244x^6 + 119403x^5 + 154492x^4 + 132177x^3 + 210865x^2 + 281708x + 132937	\( 113^{15} \)	$C_{16}$ (as 16T1)	$[17]$ (GRH)
16.16.6445820027252670934883669140625.1	x^16 - x^15 - 152x^14 + 152x^13 + 9487x^12 - 9487x^11 - 312731x^10 + 312731x^9 + 5821804x^8 - 5821804x^7 - 60431174x^6 + 60431174x^5 + 319017700x^4 - 319017700x^3 - 656707976x^2 + 656707976x + 75086281	\( 5^{8}\cdot 7^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2]$ (GRH)
16.0.10054202156858080231167941574353.1	x^16 - x^15 + 154x^14 - 154x^13 + 9793x^12 - 9793x^11 + 332011x^10 - 332011x^9 + 6466546x^8 - 6466546x^7 + 72719524x^6 - 72719524x^5 + 452168398x^4 - 452168398x^3 + 1427894074x^2 - 1427894074x + 2159688331	\( 17^{15}\cdot 37^{8} \)	$C_{16}$ (as 16T1)	$[83234]$ (GRH)
16.16.15319714679094816592806464576433.1	x^16 - x^15 - 169x^14 + 169x^13 + 11731x^12 - 11731x^11 - 430269x^10 + 430269x^9 + 8919731x^8 - 8919731x^7 - 103280269x^6 + 103280269x^5 + 610719731x^4 - 610719731x^3 - 1429280269x^2 + 1429280269x + 270719731	\( 3^{8}\cdot 13^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2]$ (GRH)
16.0.18759175710374728781004800000000.1	x^16 + 170x^14 + 11900x^12 + 442000x^10 + 9350000x^8 + 112200000x^6 + 714000000x^4 + 2040000000x^2 + 1700000000	\( 2^{24}\cdot 5^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2, 38978]$ (GRH)
16.16.18759175710374728781004800000000.1	x^16 - 170x^14 + 11900x^12 - 442000x^10 + 9350000x^8 - 112200000x^6 + 714000000x^4 - 2040000000x^2 + 1700000000	\( 2^{24}\cdot 5^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2]$ (GRH)
16.0.22856234040418247855901029307953.1	x^16 - x^15 + 171x^14 - 171x^13 + 12071x^12 - 12071x^11 + 454071x^10 - 454071x^9 + 9804071x^8 - 9804071x^7 + 122004071x^6 - 122004071x^5 + 836004071x^4 - 836004071x^3 + 2876004071x^2 - 2876004071x + 4576004071	\( 17^{15}\cdot 41^{8} \)	$C_{16}$ (as 16T1)	$[220354]$ (GRH)
16.16.33456573905268530473918973952593.1	x^16 - x^15 - 186x^14 + 186x^13 + 14213x^12 - 14213x^11 - 574089x^10 + 574089x^9 + 13115246x^8 - 13115246x^7 - 167583976x^6 + 167583976x^5 + 1097310578x^4 - 1097310578x^3 - 2878072306x^2 + 2878072306x + 766028671	\( 17^{15}\cdot 43^{8} \)	$C_{16}$ (as 16T1)	Trivial (GRH)
16.0.40211959137583069521746829836288.1	x^16 + 187x^14 + 14399x^12 + 588302x^10 + 13689335x^8 + 180699222x^6 + 1264894554x^4 + 3975382884x^2 + 3644100977	\( 2^{16}\cdot 11^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 94, 1598]$ (GRH)
16.0.45798768824157052688000000000000.1	x^16 + 85x^14 + 2720x^12 + 42075x^10 + 341275x^8 + 1510875x^6 + 3604000x^4 + 4218125x^2 + 1795625	\( 2^{16}\cdot 5^{12}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2, 2372]$ (GRH)
16.0.45798768824157052688000000000000.2	x^16 + 85x^14 + 2720x^12 + 42075x^10 + 329375x^8 + 1213375x^6 + 1632000x^4 + 690625x^2 + 10625	\( 2^{16}\cdot 5^{12}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2, 12868]$ (GRH)
16.0.50356278859985642512053476261888.1	x^16 + 68x^14 + 1802x^12 + 24072x^10 + 172720x^8 + 643824x^6 + 1067464x^4 + 493408x^2 + 45968	\( 2^{44}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2308]$ (GRH)
16.16.50356278859985642512053476261888.1	x^16 - 68x^14 + 1802x^12 - 24072x^10 + 176528x^8 - 719984x^6 + 1532040x^4 - 1337696x^2 + 45968	\( 2^{44}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[4]$ (GRH)
16.0.50356278859985642512053476261888.2	x^16 + 68x^14 + 1802x^12 + 24072x^10 + 176528x^8 + 719984x^6 + 1532040x^4 + 1337696x^2 + 45968	\( 2^{44}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 6404]$ (GRH)
16.16.50356278859985642512053476261888.2	x^16 - 68x^14 + 1802x^12 - 24072x^10 + 172720x^8 - 643824x^6 + 1067464x^4 - 493408x^2 + 45968	\( 2^{44}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[4]$ (GRH)
16.16.66688975910627504451630153142433.1	x^16 - x^15 - 84x^14 + 84x^13 + 2738x^12 - 2245x^11 - 45100x^10 + 20127x^9 + 417368x^8 + 13038x^7 - 2183632x^6 - 1155899x^5 + 5808017x^4 + 5988419x^3 - 5013027x^2 - 9372458x - 3484829	\( 13^{12}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[4]$ (GRH)