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 174)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.6926910400390625.1	x^16 - 7x^15 + 25x^14 - 55x^13 + 75x^12 - 46x^11 - 43x^10 + 140x^9 - 160x^8 + 80x^7 + 37x^6 - 109x^5 + 110x^4 - 70x^3 + 30x^2 - 8x + 1	\( 5^{15}\cdot 61^{3} \)	16T1192	Trivial
16.0.25775033599853515625.1	x^16 - x^15 - 10x^14 + 5x^13 + 45x^12 - 8x^11 - 57x^10 + 20x^9 + 20x^7 + 398x^6 + 357x^5 + 360x^4 + 375x^3 + 175x^2 + 24x + 1	\( 5^{15}\cdot 61^{5} \)	16T1192	$[2]$
16.0.25775033599853515625.2	x^16 - 2x^15 - 10x^14 + 30x^13 + 15x^12 - 156x^11 + 172x^10 + 210x^9 - 690x^8 + 580x^7 + 207x^6 - 1074x^5 + 1625x^4 - 1740x^3 + 1280x^2 - 548x + 101	\( 5^{15}\cdot 61^{5} \)	16T1192	$[2]$
16.0.25775033599853515625.3	x^16 - 2x^15 + 5x^14 - 15x^13 + 40x^12 - 51x^11 + 137x^10 - 220x^9 + 285x^8 - 395x^7 + 742x^6 - 194x^5 + 1050x^4 - 160x^3 + 525x^2 - 188x + 101	\( 5^{15}\cdot 61^{5} \)	16T1192	$[2]$
16.0.94875856000000000000.1	x^16 + 14x^14 + 84x^12 + 288x^10 + 639x^8 + 941x^6 + 821x^4 + 362x^2 + 181	\( 2^{16}\cdot 5^{12}\cdot 181^{3} \)	16T1192	Trivial
16.0.94875856000000000000.2	x^16 + 14x^14 + 69x^12 + 108x^10 - 126x^8 - 439x^6 - 69x^4 + 362x^2 + 181	\( 2^{16}\cdot 5^{12}\cdot 181^{3} \)	16T1192	Trivial
16.8.673301391207980597248.1	x^16 - 4x^15 + 2x^14 + 12x^13 - 33x^12 + 52x^11 - 32x^10 - 20x^9 + 34x^8 - 20x^7 - 18x^6 + 16x^5 + 46x^4 - 20x^3 - 16x^2 + 1	\( 2^{44}\cdot 337^{3} \)	16T1192	Trivial
16.0.1248372744720659472473.1	x^16 - 3x^15 + 3x^14 - x^13 - 13x^12 + 13x^11 + 13x^10 + 13x^9 + 65x^8 + 13x^7 + 13x^6 + 13x^5 - 13x^4 - x^3 + 3x^2 - 3x + 1	\( 13^{15}\cdot 29^{3} \)	16T1192	Trivial
16.8.3897417607086181640625.1	x^16 - 3x^15 - 5x^14 + 15x^13 - 5x^12 + 36x^11 - 13x^10 - 190x^9 + 200x^8 - 20x^7 + 17x^6 + 39x^5 - 65x^4 + 5x^3 + 5x^2 - 2x + 1	\( 3^{8}\cdot 5^{15}\cdot 269^{3} \)	16T1192	Trivial
16.0.95908900025054931640625.2	x^16 - 2x^15 - 25x^14 + 105x^13 + 120x^12 - 1241x^11 + 952x^10 + 3770x^9 - 1260x^8 - 16120x^7 + 10417x^6 + 19316x^5 + 8965x^4 - 45405x^3 - 13360x^2 + 32987x + 16441	\( 5^{15}\cdot 61^{7} \)	16T1192	$[2, 2]$ (GRH)
16.0.95908900025054931640625.3	x^16 - 6x^15 + 40x^14 - 155x^13 + 620x^12 - 1708x^11 + 5328x^10 - 10800x^9 + 27440x^8 - 40145x^7 + 84573x^6 - 77318x^5 + 145600x^4 - 53285x^3 + 118920x^2 - 2501x + 38651	\( 5^{15}\cdot 61^{7} \)	16T1192	$[2, 2]$ (GRH)
16.0.95908900025054931640625.4	x^16 - x^15 - 25x^14 + 15x^13 + 325x^12 - 128x^11 - 2757x^10 + 1080x^9 + 15780x^8 - 8660x^7 - 52137x^6 + 34507x^5 + 91200x^4 - 57600x^3 - 83455x^2 - 2951x + 114211	\( 5^{15}\cdot 61^{7} \)	16T1192	$[2, 2]$ (GRH)
16.0.149236922000000000000000.1	x^16 + 10x^14 + 50x^12 - 10x^11 + 125x^10 - 20x^9 + 195x^8 - 120x^7 + 65x^6 - 250x^5 + 95x^4 - 340x^3 - 165x^2 + 200x + 205	\( 2^{16}\cdot 5^{15}\cdot 421^{3} \)	16T1192	$[2, 2]$
16.0.198083929073978721879001.1	x^16 - 2x^15 + 10x^14 + 5x^13 - 13x^12 + 39x^11 + 234x^10 - 208x^8 + 234x^6 - 39x^5 - 13x^4 - 5x^3 + 10x^2 + 2x + 1	\( 13^{15}\cdot 157^{3} \)	16T1192	Trivial (GRH)
16.16.935900780550689386397696.1	x^16 - 8x^15 + 8x^14 + 76x^13 - 156x^12 - 248x^11 + 682x^10 + 348x^9 - 1250x^8 - 244x^7 + 1020x^6 + 140x^5 - 331x^4 - 68x^3 + 34x^2 + 12x + 1	\( 2^{44}\cdot 3761^{3} \)	16T1192	Trivial (GRH)
16.0.1049881478310074616349793.1	x^16 - 5x^15 + 30x^14 - 99x^13 + 299x^12 - 689x^11 + 1326x^10 - 1911x^9 + 2249x^8 - 1456x^7 - 26x^6 + 962x^5 - 481x^4 + 202x^3 + 95x^2 - 63x + 9	\( 13^{15}\cdot 29^{5} \)	16T1192	$[2]$ (GRH)
16.0.1049881478310074616349793.2	x^16 - 8x^15 + 30x^14 - 44x^13 - 13x^12 + 91x^11 + 130x^10 - 1079x^9 + 2808x^8 - 4485x^7 + 4810x^6 - 3211x^5 + 819x^4 + 500x^3 - 308x^2 - 119x + 87	\( 13^{15}\cdot 29^{5} \)	16T1192	$[2]$ (GRH)
16.0.1049881478310074616349793.3	x^16 - 4x^15 + x^14 + 27x^13 - 65x^12 + 91x^11 - 143x^10 - 208x^9 + 2379x^8 - 5655x^7 + 4719x^6 + 1963x^5 - 3887x^4 - 1375x^3 + 5032x^2 - 1466x + 237	\( 13^{15}\cdot 29^{5} \)	16T1192	$[2]$ (GRH)
16.16.2757842498387888526327808.1	x^16 - 32x^14 + 384x^12 - 2200x^10 + 6510x^8 - 10048x^6 + 7728x^4 - 2696x^2 + 337	\( 2^{56}\cdot 337^{3} \)	16T1192	Trivial (GRH)
16.0.2757842498387888526327808.1	x^16 + 32x^14 + 384x^12 + 2200x^10 + 6510x^8 + 10048x^6 + 7728x^4 + 2696x^2 + 337	\( 2^{56}\cdot 337^{3} \)	16T1192	$[26]$
16.8.2757842498387888526327808.1	x^16 - 4x^14 - 16x^13 - 98x^12 - 208x^11 - 320x^10 - 152x^9 + 859x^8 + 1728x^7 + 2824x^6 + 3528x^5 + 2942x^4 + 2592x^3 - 1940x^2 - 4136x - 1361	\( 2^{56}\cdot 337^{3} \)	16T1192	Trivial
16.8.2757842498387888526327808.2	x^16 - 12x^14 - 16x^13 - 58x^12 + 144x^11 + 648x^10 - 488x^9 - 141x^8 + 1088x^7 - 416x^6 - 136x^5 + 102x^4 + 224x^3 - 164x^2 + 24x - 1	\( 2^{56}\cdot 337^{3} \)	16T1192	Trivial
16.4.44125479974206216421244928.1	x^16 + 8x^14 - 24x^12 - 296x^10 - 294x^8 + 1976x^6 + 4552x^4 + 2696x^2 + 337	\( 2^{60}\cdot 337^{3} \)	16T1192	Trivial
16.12.44125479974206216421244928.1	x^16 - 16x^14 - 72x^12 + 1232x^10 - 4390x^8 + 6208x^6 - 3304x^4 + 337	\( 2^{60}\cdot 337^{3} \)	16T1192	Trivial (GRH)
16.12.44125479974206216421244928.2	x^16 + 16x^14 - 136x^12 - 688x^10 + 7642x^8 - 21760x^6 + 25304x^4 - 10784x^2 + 337	\( 2^{60}\cdot 337^{3} \)	16T1192	Trivial (GRH)
16.4.44125479974206216421244928.2	x^16 - 16x^14 - 136x^12 + 688x^10 + 7642x^8 + 21760x^6 + 25304x^4 + 10784x^2 + 337	\( 2^{60}\cdot 337^{3} \)	16T1192	Trivial
16.0.356877016993229400634765625.1	x^16 - 3x^15 - 45x^14 + 205x^13 + 485x^12 - 4234x^11 + 3952x^10 + 27060x^9 - 81165x^8 + 23670x^7 + 309122x^6 - 819991x^5 + 1147520x^4 - 1067545x^3 + 704900x^2 - 317102x + 75581	\( 5^{15}\cdot 61^{9} \)	16T1192	$[4, 4]$ (GRH)
16.0.356877016993229400634765625.2	x^16 - 3x^15 - 45x^14 + 25x^13 + 1000x^12 + 1351x^11 - 8458x^10 - 19960x^9 + 44600x^8 + 254330x^7 + 523387x^6 + 693794x^5 + 667520x^4 + 483375x^3 + 313920x^2 + 196993x + 75581	\( 5^{15}\cdot 61^{9} \)	16T1192	$[4, 4]$ (GRH)
16.0.356877016993229400634765625.3	x^16 - 3x^15 - 105x^13 + 905x^12 - 3709x^11 + 13942x^10 - 59860x^9 + 225995x^8 - 653290x^7 + 1451972x^6 - 2539361x^5 + 3485545x^4 - 3615625x^3 + 2634030x^2 - 1186107x + 246011	\( 5^{15}\cdot 61^{9} \)	16T1192	$[4, 4]$ (GRH)
16.0.356877016993229400634765625.4	x^16 - 3x^15 + 5x^14 - 10x^13 - 85x^12 - 174x^11 + 1477x^10 - 1875x^9 + 1735x^8 + 40415x^7 - 135868x^6 - 21421x^5 + 354385x^4 - 1719225x^3 + 3440025x^2 + 3484458x + 797131	\( 5^{15}\cdot 61^{9} \)	16T1192	$[4, 4]$ (GRH)
16.0.356877016993229400634765625.5	x^16 - 3x^15 - 70x^14 + 295x^13 + 2035x^12 - 10254x^11 - 26098x^10 + 175355x^9 + 61525x^8 - 1401095x^7 + 2189112x^6 + 1958559x^5 - 23390105x^4 + 34785530x^3 + 45222615x^2 - 124179562x + 309425941	\( 5^{15}\cdot 61^{9} \)	16T1192	$[2, 2, 2]$ (GRH)
16.0.882950323258772752350175913.2	x^16 - 4x^15 + 14x^14 - 90x^13 + 104x^12 - 364x^11 + 1976x^10 + 6357x^9 + 26871x^8 + 80171x^7 + 174395x^6 + 370526x^5 + 554359x^4 + 742654x^3 + 766481x^2 + 434411x + 207301	\( 13^{15}\cdot 29^{7} \)	16T1192	$[2, 2]$ (GRH)
16.0.882950323258772752350175913.3	x^16 - 2x^15 - 3x^14 - 47x^13 - 91x^12 - 117x^11 + 1950x^10 + 7956x^9 + 17628x^8 + 27001x^7 + 44668x^6 - 97565x^5 - 272701x^4 - 340644x^3 + 815305x^2 - 396615x + 415819	\( 13^{15}\cdot 29^{7} \)	16T1192	$[2, 2]$ (GRH)
16.0.882950323258772752350175913.4	x^16 - 2x^15 + 10x^14 + 44x^13 + 78x^12 + 286x^11 + 1846x^10 + 5057x^9 + 8970x^8 + 41171x^7 + 111618x^6 + 176475x^5 + 431951x^4 + 878457x^3 + 1152161x^2 + 1067861x + 481807	\( 13^{15}\cdot 29^{7} \)	16T1192	$[2, 2]$ (GRH)
16.0.1284687733176174905015164273.1	x^16 - 8x^15 + 30x^14 - 70x^13 + 121x^12 - 180x^11 + 484x^10 - 1369x^9 + 1080x^8 + 4566x^7 - 15695x^6 + 25200x^5 - 7106x^4 - 48615x^3 + 104570x^2 - 122227x + 63749	\( 29^{15}\cdot 53^{3} \)	16T1192	Trivial (GRH)
16.0.4882570767744501515595495649.1	x^16 + 26x^14 + 208x^12 - 182x^11 + 1157x^10 + 1703x^9 + 5603x^8 + 13052x^7 + 19968x^6 + 38246x^5 + 74919x^4 + 167440x^3 + 254696x^2 + 85111x + 16913	\( 13^{15}\cdot 157^{5} \)	16T1192	$[2]$ (GRH)
16.0.4882570767744501515595495649.2	x^16 - 6x^15 + 25x^14 - 34x^13 + 13x^12 + 741x^11 - 2587x^10 + 4056x^9 + 7423x^8 - 41054x^7 + 153595x^6 - 265473x^5 + 275834x^4 - 256167x^3 + 131013x^2 - 36450x + 59049	\( 13^{15}\cdot 157^{5} \)	16T1192	$[2]$ (GRH)
16.0.4882570767744501515595495649.3	x^16 - x^15 + 9x^14 + 12x^13 - 247x^11 - 442x^10 - 286x^9 - 2106x^8 + 2223x^7 + 28184x^6 + 80522x^5 + 196755x^4 + 188842x^3 - 46154x^2 - 36858x + 98757	\( 13^{15}\cdot 157^{5} \)	16T1192	$[2]$ (GRH)
16.0.49642480033862407473413572361.1	x^16 - 2x^15 + 25x^14 + 44x^13 + 218x^12 + 904x^11 + 2685x^10 + 9348x^9 + 27113x^8 + 60204x^7 + 127675x^6 + 214177x^5 + 296303x^4 + 373741x^3 + 351229x^2 + 201961x + 59321	\( 37^{15}\cdot 53^{3} \)	16T1192	$[5]$ (GRH)
16.0.742561221860627884726497942833.1	x^16 - 3x^15 + 68x^14 - 66x^13 + 715x^12 + 806x^11 + 1872x^10 + 4719x^9 + 4680x^8 + 14196x^7 - 2834x^6 - 28119x^5 - 4459x^4 + 7123x^3 + 15330x^2 - 19659x + 10037	\( 13^{15}\cdot 29^{9} \)	16T1192	$[4, 4]$ (GRH)
16.0.742561221860627884726497942833.2	x^16 - 3x^15 + 68x^14 - 300x^13 + 1885x^12 - 7826x^11 + 27495x^10 - 69069x^9 + 139386x^8 - 196755x^7 + 220597x^6 - 150618x^5 + 39416x^4 + 4289x^3 - 21135x^2 + 23943x + 10037	\( 13^{15}\cdot 29^{9} \)	16T1192	$[4, 4]$ (GRH)
16.0.742561221860627884726497942833.3	x^16 - x^15 + 9x^14 + 12x^13 + 455x^12 - 273x^11 + 3484x^10 - 1092x^9 + 82836x^8 + 301236x^7 + 1028989x^6 + 1979874x^5 + 3009409x^4 + 2711401x^3 + 1513794x^2 - 74376x + 116073	\( 13^{15}\cdot 29^{9} \)	16T1192	$[4, 4]$ (GRH)
16.0.742561221860627884726497942833.4	x^16 - 4x^15 + 27x^14 - 116x^13 + 364x^12 - 1846x^11 + 5655x^10 - 16926x^9 + 57538x^8 - 130078x^7 + 296361x^6 - 680316x^5 + 1106547x^4 - 1586595x^3 + 2213979x^2 - 2046301x + 836007	\( 13^{15}\cdot 29^{9} \)	16T1192	$[4, 4]$ (GRH)
16.0.742561221860627884726497942833.5	x^16 - 8x^15 + 30x^14 - 57x^13 + 559x^12 - 2119x^11 + 9776x^10 - 35737x^9 + 82108x^8 - 260117x^7 + 665522x^6 - 1734980x^5 + 5496296x^4 - 9197741x^3 + 22471284x^2 - 19864067x + 29925099	\( 13^{15}\cdot 29^{9} \)	16T1192	$[2, 2, 2]$ (GRH)
16.0.1327939380231806599761962890625.2	x^16 - x^15 - 90x^14 + 320x^13 + 3025x^12 - 17923x^11 - 25202x^10 + 326245x^9 - 238150x^8 - 2059220x^7 + 2136023x^6 + 6262112x^5 + 12850245x^4 - 94819515x^3 + 132820860x^2 - 56633126x + 8746001	\( 5^{15}\cdot 61^{11} \)	16T1192	$[2, 4, 4]$ (GRH)
16.0.1327939380231806599761962890625.3	x^16 - 3x^15 - 60x^14 + 120x^13 + 2105x^12 - 289x^11 - 45528x^10 - 55530x^9 + 577600x^8 + 1491835x^7 - 2801818x^6 - 13876421x^5 + 17144000x^4 + 121080785x^3 + 200316520x^2 - 11548887x + 96701741	\( 5^{15}\cdot 61^{11} \)	16T1192	$[2, 4, 4]$ (GRH)
16.0.1327939380231806599761962890625.4	x^16 - x^15 - 75x^14 + 170x^13 + 3085x^12 - 2833x^11 - 61257x^10 - 80835x^9 + 745310x^8 + 2393835x^7 - 4007092x^6 - 28769888x^5 - 24060035x^4 + 130373870x^3 + 402284320x^2 + 459900849x + 195517031	\( 5^{15}\cdot 61^{11} \)	16T1192	$[2, 4, 4]$ (GRH)
16.0.1327939380231806599761962890625.5	x^16 - x^15 - 90x^14 + 320x^13 + 3330x^12 - 17008x^11 - 44417x^10 + 404020x^9 - 42645x^8 - 4353125x^7 + 5748138x^6 + 14725862x^5 - 147940x^4 - 131725735x^3 + 190084305x^2 - 232326241x + 422035031	\( 5^{15}\cdot 61^{11} \)	16T1192	$[2, 4, 4]$ (GRH)
16.0.3608687842491875308187596442857.1	x^16 - 3x^15 + 45x^14 - 304x^13 + 1454x^12 - 5013x^11 + 14350x^10 - 33518x^9 + 65483x^8 - 201758x^7 + 330810x^6 + 184957x^5 - 1276890x^4 + 1077282x^3 + 3509953x^2 - 5019549x + 1693277	\( 29^{15}\cdot 53^{5} \)	16T1192	$[2]$ (GRH)
16.0.3608687842491875308187596442857.2	x^16 - 2x^15 - 38x^14 + 143x^13 + 840x^12 - 3500x^11 - 11651x^10 + 65836x^9 + 70664x^8 - 642987x^7 + 237830x^6 + 1961670x^5 + 71005x^4 - 5494616x^3 + 824640x^2 + 1342760x + 4856944	\( 29^{15}\cdot 53^{5} \)	16T1192	$[2]$ (GRH)