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 87)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.689675577587306205184.2	x^16 - 3x^15 + 11x^14 - 11x^13 + 8x^12 + 45x^11 - 57x^10 + 47x^9 + 172x^8 - 377x^7 + 615x^6 - 631x^5 + 563x^4 - 358x^3 + 192x^2 - 64x + 16	\( 2^{12}\cdot 17^{14} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[2]$
16.4.1180591620717411303424.3	x^16 + 4x^12 - 16x^11 + 16x^10 - 64x^9 + 206x^8 - 528x^7 + 1152x^6 - 1904x^5 + 2140x^4 - 1472x^3 + 544x^2 - 80x - 1	\( 2^{70} \)	$C_2^5.C_2.C_2$ (as 16T257)	Trivial (GRH)
16.8.1180591620717411303424.3	x^16 - 16x^14 - 16x^13 + 84x^12 + 160x^11 - 80x^10 - 400x^9 - 286x^8 + 48x^7 + 224x^6 + 320x^5 + 300x^4 + 144x^3 + 32x^2 - 1	\( 2^{70} \)	$C_2^5.C_2.C_2$ (as 16T257)	Trivial (GRH)
16.4.1180591620717411303424.4	x^16 - 8x^14 + 24x^12 - 16x^11 - 48x^10 + 112x^9 + 8x^8 - 496x^7 + 1024x^6 - 864x^5 + 8x^4 + 640x^3 - 576x^2 + 224x - 34	\( 2^{70} \)	$C_2^5.C_2.C_2$ (as 16T257)	Trivial (GRH)
16.0.1180591620717411303424.5	x^16 + 8x^14 - 16x^13 + 24x^12 - 64x^11 + 128x^10 - 64x^9 + 156x^8 - 240x^7 + 128x^6 - 96x^5 + 160x^4 - 64x^3 + 96x^2 - 64x + 34	\( 2^{70} \)	$C_2^5.C_2.C_2$ (as 16T257)	Trivial
16.0.4809039104363049933169.1	x^16 - x^15 + 12x^14 - 17x^13 + 70x^12 - 92x^11 + 249x^10 - 246x^9 + 504x^8 - 359x^7 + 550x^6 - 266x^5 + 257x^4 - 68x^3 + 22x^2 - 4x + 1	\( 13^{4}\cdot 17^{14} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[4]$
16.8.176556947862350388527104.1	x^16 - 13x^14 + 75x^12 - 299x^10 + 814x^8 - 1405x^6 + 1285x^4 - 290x^2 + 1	\( 2^{20}\cdot 17^{14} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[2]$ (GRH)
16.8.385172627945073865129984.2	x^16 - 24x^14 + 212x^12 - 1024x^10 + 3046x^8 - 5760x^6 + 6728x^4 - 4352x^2 + 1156	\( 2^{62}\cdot 17^{4} \)	$C_2^5.C_2.C_2$ (as 16T257)	Trivial (GRH)
16.0.385172627945073865129984.3	x^16 + 24x^14 + 212x^12 + 1024x^10 + 3046x^8 + 5760x^6 + 6728x^4 + 4352x^2 + 1156	\( 2^{62}\cdot 17^{4} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[20]$ (GRH)
16.0.812727608637355438705561.1	x^16 - 6x^15 + 25x^14 - 35x^13 + 45x^12 + 33x^11 + 335x^10 - 152x^9 + 557x^8 + 1282x^7 + 3818x^6 + 3737x^5 + 3189x^4 + 1060x^3 + 344x^2 - 72x + 16	\( 13^{6}\cdot 17^{14} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[2, 2]$ (GRH)
16.0.812727608637355438705561.3	x^16 - 7x^15 + 37x^14 - 125x^13 + 364x^12 - 853x^11 + 1800x^10 - 3145x^9 + 5181x^8 - 7004x^7 + 9317x^6 - 9844x^5 + 10325x^4 - 6153x^3 + 7724x^2 - 988x + 169	\( 13^{6}\cdot 17^{14} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[2, 2]$ (GRH)
16.0.821630081083204084623649.4	x^16 - x^15 + 6x^14 - 16x^13 - 25x^12 + 42x^11 + 203x^10 + 219x^9 + 117x^8 - 169x^7 - 421x^6 - 290x^5 + 365x^4 + 740x^3 + 704x^2 + 512x + 256	\( 17^{14}\cdot 47^{4} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[2]$ (GRH)
16.0.3393001956715501807791409.5	x^16 - 2x^15 + 12x^14 - 56x^13 + 83x^12 - 238x^11 + 490x^10 + 33x^9 + 2212x^8 + 488x^7 + 2305x^6 + 1156x^5 + 1640x^4 - 155x^3 + 1690x^2 - 479x + 611	\( 17^{14}\cdot 67^{4} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[2, 4]$ (GRH)
16.0.10564402173046133902941889.1	x^16 - x^15 + 23x^14 - 16x^13 + 196x^12 - 43x^11 + 798x^10 - 2x^9 + 1953x^8 - 594x^7 + 2622x^6 - 817x^5 + 1368x^4 - 144x^3 + 143x^2 - 15x + 1	\( 17^{14}\cdot 89^{4} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[20]$ (GRH)
16.16.24651048188484727368318976.3	x^16 - 32x^14 + 364x^12 - 48x^11 - 1904x^10 + 528x^9 + 4762x^8 - 1792x^7 - 5440x^6 + 2368x^5 + 2260x^4 - 1072x^3 - 80x^2 + 16x + 1	\( 2^{68}\cdot 17^{4} \)	$C_2^5.C_2.C_2$ (as 16T257)	Trivial (GRH)
16.8.24651048188484727368318976.3	x^16 - 24x^14 - 48x^13 + 8x^12 + 464x^11 + 1056x^10 + 512x^9 - 2236x^8 - 5664x^7 - 4240x^6 + 2656x^5 + 7168x^4 + 5024x^3 + 1248x^2 - 128x - 68	\( 2^{68}\cdot 17^{4} \)	$C_2^5.C_2.C_2$ (as 16T257)	Trivial (GRH)
16.8.24651048188484727368318976.4	x^16 + 16x^14 - 48x^13 - 92x^12 - 176x^11 + 336x^10 + 1472x^9 + 954x^8 - 1792x^7 - 3664x^6 - 752x^5 + 2748x^4 + 1872x^3 - 336x^2 - 448x + 97	\( 2^{68}\cdot 17^{4} \)	$C_2^5.C_2.C_2$ (as 16T257)	Trivial (GRH)
16.0.24651048188484727368318976.7	x^16 - 24x^14 - 16x^13 + 264x^12 + 304x^11 - 1472x^10 - 2496x^9 + 4004x^8 + 10016x^7 - 2448x^6 - 11360x^5 + 23040x^4 + 57952x^3 + 37920x^2 + 13184x + 12028	\( 2^{68}\cdot 17^{4} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[2, 10]$ (GRH)
16.0.24651048188484727368318976.8	x^16 + 24x^14 + 224x^12 - 48x^11 + 896x^10 - 384x^9 + 1724x^8 - 608x^7 + 912x^6 - 1664x^5 + 2192x^4 - 608x^3 - 352x^2 - 1344x + 956	\( 2^{68}\cdot 17^{4} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[2, 6]$ (GRH)
16.0.24651048188484727368318976.9	x^16 - 8x^14 + 64x^12 - 48x^11 - 128x^10 + 480x^9 + 316x^8 - 32x^7 + 1808x^6 + 2432x^5 + 5232x^4 + 6688x^3 + 6816x^2 - 10496x + 7292	\( 2^{68}\cdot 17^{4} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[2, 10]$ (GRH)
16.0.24651048188484727368318976.10	x^16 - 16x^14 - 16x^13 + 196x^12 + 464x^11 - 304x^10 - 2048x^9 - 1190x^8 + 3392x^7 + 8592x^6 + 11440x^5 + 13820x^4 + 11024x^3 + 12016x^2 + 7552x + 5729	\( 2^{68}\cdot 17^{4} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[2, 10]$ (GRH)
16.0.24651048188484727368318976.11	x^16 + 44x^12 - 48x^11 + 176x^10 - 336x^9 + 794x^8 - 320x^7 + 3360x^6 + 320x^5 + 10996x^4 + 12048x^3 + 26960x^2 + 19120x + 16097	\( 2^{68}\cdot 17^{4} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[2, 30]$ (GRH)
16.8.111314889476126347022565376.3	x^16 - 40x^14 + 588x^12 - 4800x^10 + 25518x^8 - 97920x^6 + 275128x^4 - 471648x^2 + 334084	\( 2^{62}\cdot 17^{6} \)	$C_2^5.C_2.C_2$ (as 16T257)	Trivial (GRH)
16.0.137350965859713069141239809.5	x^16 - 4x^15 + 30x^14 - 96x^13 + 449x^12 - 1142x^11 + 3458x^10 - 5841x^9 + 11802x^8 - 9944x^7 + 12789x^6 + 5932x^5 + 8336x^4 + 8839x^3 + 11450x^2 + 4329x + 611	\( 13^{8}\cdot 17^{14} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[2, 2, 2]$ (GRH)
16.16.1090301154156564404349435904.1	x^16 - 40x^14 - 16x^13 + 576x^12 + 336x^11 - 3712x^10 - 1744x^9 + 12144x^8 + 1712x^7 - 20336x^6 + 6048x^5 + 13240x^4 - 10208x^3 + 1920x^2 + 160x - 34	\( 2^{70}\cdot 31^{4} \)	$C_2^5.C_2.C_2$ (as 16T257)	Trivial (GRH)
16.4.1814980849112797822933640641.6	x^16 - 3x^15 + 15x^14 + 21x^13 + 153x^12 - 38x^11 + 277x^10 - 1675x^9 - 4624x^8 + 14970x^7 + 32600x^6 + 7129x^5 - 16915x^4 - 6310x^3 - 744x^2 + 16x + 16	\( 17^{14}\cdot 47^{6} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[2]$ (GRH)
16.4.1814980849112797822933640641.14	x^16 - 2x^15 + 26x^14 - 106x^13 + 233x^12 - 586x^11 - 92x^10 + 9959x^9 - 40766x^8 + 109192x^7 - 229565x^6 + 140380x^5 + 63696x^4 - 524065x^3 + 680616x^2 - 283821x + 66469	\( 17^{14}\cdot 47^{6} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[2]$ (GRH)
16.0.7124152926472086209444184064.1	x^16 - 24x^14 - 16x^13 + 244x^12 + 368x^11 - 1152x^10 - 3088x^9 + 2486x^8 + 15392x^7 + 10952x^6 - 31424x^5 - 57820x^4 - 4272x^3 + 100336x^2 + 120768x + 60911	\( 2^{68}\cdot 17^{6} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[2, 2, 24]$ (GRH)
16.4.10614152867452364890755536401.3	x^16 - 8x^15 + 32x^14 - 84x^13 + 448x^12 - 1960x^11 + 7209x^10 - 19127x^9 + 40660x^8 - 67722x^7 + 80553x^6 - 65189x^5 + 13517x^4 + 30978x^3 - 34132x^2 + 14824x - 1808	\( 23^{4}\cdot 41^{14} \)	$C_2^5.C_2.C_2$ (as 16T257)	Trivial (GRH)
16.4.15231185783695887615175635001.14	x^16 - 3x^15 - 10x^14 + 110x^13 - 225x^12 - 354x^11 - 299x^10 + 3942x^9 + 57x^8 - 10770x^7 + 6980x^6 - 7723x^5 - 25504x^4 + 21643x^3 + 19611x^2 - 16757x - 10267	\( 17^{14}\cdot 67^{6} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[2, 4]$ (GRH)
16.4.15231185783695887615175635001.28	x^16 - 43x^14 + 147x^12 + 3847x^10 - 16998x^8 - 53987x^6 + 275241x^4 + 624962x^2 + 28561	\( 17^{14}\cdot 67^{6} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[2, 4]$ (GRH)
16.4.35028437828275611780530528881.2	x^16 - 5x^15 - 5x^14 + 41x^13 + 11x^12 - 108x^11 - 135x^10 + 235x^9 + 746x^8 - 1038x^7 - 1282x^6 + 621x^5 + 4835x^4 + 2542x^3 + 196x^2 + 8x + 16	\( 31^{4}\cdot 41^{14} \)	$C_2^5.C_2.C_2$ (as 16T257)	Trivial (GRH)
16.8.71085478368850138600216861921.1	x^16 - 8x^15 - 2x^14 + 154x^13 - 525x^12 + 784x^11 + 942x^10 - 7273x^9 + 13980x^8 - 11666x^7 - 12455x^6 + 47452x^5 - 58720x^4 + 39343x^3 - 11990x^2 - 17x + 1231	\( 37^{4}\cdot 41^{14} \)	$C_2^5.C_2.C_2$ (as 16T257)	Trivial (GRH)
16.0.83680629612698426645202702769.5	x^16 - 2x^15 + 52x^14 - 160x^13 + 1377x^12 - 4670x^11 + 22994x^10 - 70205x^9 + 236402x^8 - 628712x^7 + 1574231x^6 - 3303540x^5 + 5538260x^4 - 7740329x^3 + 7719080x^2 - 5374135x + 2660159	\( 17^{14}\cdot 89^{6} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[2, 10]$ (GRH)
16.0.83680629612698426645202702769.6	x^16 + 51x^14 + 714x^12 + 4471x^10 + 31042x^8 + 218195x^6 + 727413x^4 + 2901560x^2 + 10214416	\( 17^{14}\cdot 89^{6} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[2, 10]$ (GRH)
16.4.459602138371809190522512417121.9	x^16 - 2x^15 + 4x^14 - 74x^13 + 86x^12 - 366x^11 + 2016x^10 - 2228x^9 + 9414x^8 - 20076x^7 + 51954x^6 - 57772x^5 + 221773x^4 - 366712x^3 + 226816x^2 - 695194x + 652721	\( 41^{14}\cdot 59^{4} \)	$C_2^5.C_2.C_2$ (as 16T257)	Trivial (GRH)
16.4.1800057439498232157527332231681.1	x^16 - 6x^15 - 32x^14 + 286x^13 - 66x^12 - 4798x^11 + 18244x^10 - 22288x^9 - 40093x^8 + 192420x^7 - 279342x^6 + 2310x^5 + 661683x^4 - 1123766x^3 + 902493x^2 - 322426x - 23369	\( 41^{14}\cdot 83^{4} \)	$C_2^5.C_2.C_2$ (as 16T257)	Trivial (GRH)
16.8.4009292695690170390860412175969.4	x^16 - 5x^15 + 15x^14 - 77x^13 + 397x^12 - 1838x^11 + 2349x^10 - 298x^9 + 33979x^8 - 88601x^7 - 53000x^6 + 380450x^5 - 477557x^4 + 244778x^3 - 15384x^2 - 34848x + 9808	\( 17^{14}\cdot 47^{8} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[2]$ (GRH)
16.0.5614886866882301027209678756129.2	x^16 - x^14 - 284x^12 + 3843x^10 - 61087x^8 + 514808x^6 - 882864x^4 + 717824x^2 + 65536	\( 23^{6}\cdot 41^{14} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[4, 4]$ (GRH)
16.8.5614886866882301027209678756129.8	x^16 - 2x^15 - 30x^14 + 88x^13 + 124x^12 + 332x^11 - 2430x^10 - 16974x^9 + 102421x^8 - 131446x^7 - 365052x^6 + 1430580x^5 - 1448971x^4 - 1074064x^3 + 4472119x^2 - 5491088x + 2822581	\( 23^{6}\cdot 41^{14} \)	$C_2^5.C_2.C_2$ (as 16T257)	Trivial (GRH)
16.4.28643813255402702732772283462081.1	x^16 + 44x^14 + 580x^12 + 4422x^10 + 24772x^8 - 101684x^6 - 1604663x^4 + 147840x^2 + 4096	\( 11^{4}\cdot 89^{14} \)	$C_2^5.C_2.C_2$ (as 16T257)	Trivial (GRH)
16.8.33662328752972862921089838254641.2	x^16 - 4x^15 - 44x^14 + 274x^13 - 358x^12 - 1104x^11 + 11216x^10 - 63054x^9 + 236931x^8 - 647354x^7 + 1418618x^6 - 2710906x^5 + 4072213x^4 - 4514914x^3 + 2713383x^2 + 802816x - 1270343	\( 31^{6}\cdot 41^{14} \)	$C_2^5.C_2.C_2$ (as 16T257)	Trivial (GRH)
16.0.33662328752972862921089838254641.9	x^16 - 8x^15 + 30x^14 - 70x^13 - 245x^12 + 2016x^11 - 3898x^10 + 295x^9 + 87100x^8 - 326850x^7 + 1209077x^6 - 2505376x^5 + 5675872x^4 - 7546349x^3 + 18066458x^2 - 14658053x + 6958823	\( 31^{6}\cdot 41^{14} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[2, 2]$ (GRH)
16.8.68372792983010839504523425519489.15	x^16 - 4x^15 - 20x^14 + 215x^13 - 2055x^12 + 4318x^11 - 583x^10 - 110764x^9 + 671213x^8 - 1272579x^7 + 2452222x^6 + 6911503x^5 - 13031290x^4 + 10060145x^3 + 218575x^2 - 19306519x + 9916201	\( 17^{14}\cdot 67^{8} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[2, 4]$ (GRH)
16.8.97316019886955839743696883969849.1	x^16 - x^15 - 33x^14 - 82x^13 + 325x^12 + 3104x^11 + 817x^10 - 22856x^9 - 138288x^8 + 96456x^7 + 1535051x^6 - 156613x^5 - 2487647x^4 - 16596185x^3 + 11317276x^2 + 36447801x - 7493779	\( 37^{6}\cdot 41^{14} \)	$C_2^5.C_2.C_2$ (as 16T257)	Trivial (GRH)
16.8.97316019886955839743696883969849.3	x^16 - 6x^15 - 50x^14 + 401x^13 + 259x^12 - 9892x^11 + 16521x^10 + 88546x^9 - 288843x^8 - 212247x^7 + 1225576x^6 + 396097x^5 - 2021904x^4 - 624129x^3 + 1131549x^2 + 261657x - 155333	\( 37^{6}\cdot 41^{14} \)	$C_2^5.C_2.C_2$ (as 16T257)	Trivial (GRH)
16.8.228732005557745506375281661426849.1	x^16 - x^15 - 28x^14 - 91x^13 + 147x^12 + 2372x^11 + 4771x^10 - 11007x^9 - 72564x^8 - 113581x^7 + 312141x^6 + 994380x^5 + 247876x^4 - 507536x^3 - 289456x^2 - 35712x + 1024	\( 37^{4}\cdot 73^{14} \)	$C_2^5.C_2.C_2$ (as 16T257)	Trivial (GRH)
16.8.344870040917968360157170212631249.1	x^16 - x^15 - 66x^14 - 3x^13 + 2135x^12 + 1730x^11 - 42649x^10 - 54891x^9 + 628982x^8 + 856419x^7 - 6975475x^6 - 7089206x^5 + 49136920x^4 + 28122920x^3 - 178366000x^2 - 42093568x + 245954816	\( 41^{4}\cdot 73^{14} \)	$C_2^5.C_2.C_2$ (as 16T257)	Trivial (GRH)
16.0.662834267162184237456650608633249.9	x^16 - 4x^15 + 40x^14 - 148x^13 + 1571x^12 - 4118x^11 + 24526x^10 - 28397x^9 + 311548x^8 - 145806x^7 + 2070325x^6 + 6468196x^5 + 678072x^4 + 4456149x^3 + 59480154x^2 - 75302539x + 22248343	\( 17^{14}\cdot 89^{8} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[2, 2, 10]$ (GRH)
16.0.1599875043672267792208865723998201.1	x^16 + 55x^14 + 342x^12 + 24280x^10 - 221157x^8 - 108359x^6 + 14327515x^4 - 6175982x^2 + 724201	\( 41^{14}\cdot 59^{6} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[4, 4]$ (GRH)