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 all 49 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.8.43104723599206637824.2	x^16 - 2x^14 - 11x^12 + 14x^10 + 36x^8 - 14x^6 - 28x^4 + 2x^2 + 1	\( 2^{8}\cdot 17^{14} \)	16T817	Trivial (GRH)
16.8.689675577587306205184.1	x^16 - 7x^14 - 3x^12 + 69x^10 + 9x^8 - 144x^6 - 56x^4 + 48x^2 + 16	\( 2^{12}\cdot 17^{14} \)	16T817	Trivial
16.8.755848063425150770281.1	x^16 - 2x^15 - 4x^14 + 6x^13 + 5x^12 - 12x^11 + 6x^10 + 11x^9 - 6x^8 + 16x^7 - 31x^6 - 18x^5 + 14x^4 + 13x^3 + 8x^2 - 5x - 1	\( 17^{14}\cdot 67^{2} \)	16T817	Trivial (GRH)
16.8.1717622208732448876729.2	x^16 - 5x^15 + 4x^14 + 3x^13 + 32x^12 - 68x^11 - 13x^10 - 8x^9 + 240x^8 - 179x^7 - 98x^6 - 34x^5 + 185x^4 + 14x^3 - 64x^2 - 12x + 1	\( 17^{14}\cdot 101^{2} \)	16T817	Trivial (GRH)
16.8.3160283426693396036401.2	x^16 - 3x^15 - 7x^14 + 32x^13 - 8x^12 - 85x^11 + 24x^10 + 352x^9 - 529x^8 - 154x^7 + 1074x^6 - 969x^5 + 138x^4 + 216x^3 - 63x^2 - 19x - 1	\( 17^{14}\cdot 137^{2} \)	16T817	Trivial (GRH)
16.4.11034809241396899282944.3	x^16 + 9x^14 + 28x^12 + 29x^10 - 15x^8 - 39x^6 - 6x^4 + 9x^2 + 1	\( 2^{16}\cdot 17^{14} \)	16T817	Trivial (GRH)
16.12.11034809241396899282944.4	x^16 - 9x^14 + 28x^12 - 29x^10 - 15x^8 + 39x^6 - 6x^4 - 9x^2 + 1	\( 2^{16}\cdot 17^{14} \)	16T817	Trivial (GRH)
16.12.18889465931478580854784.1	x^16 - 8x^14 + 4x^12 + 88x^10 - 154x^8 - 56x^6 + 132x^4 - 24x^2 + 1	\( 2^{74} \)	16T817	Trivial (GRH)
16.4.18889465931478580854784.1	x^16 + 8x^14 + 4x^12 - 88x^10 - 154x^8 + 56x^6 + 132x^4 + 24x^2 + 1	\( 2^{74} \)	16T817	Trivial
16.8.18889465931478580854784.1	x^16 + 8x^14 + 4x^12 - 56x^10 + 2x^8 + 104x^6 - 68x^4 + 8x^2 + 1	\( 2^{74} \)	16T817	Trivial (GRH)
16.0.193497104236838597191936.1	x^16 - 3x^15 + 13x^14 - 46x^13 + 117x^12 - 272x^11 + 625x^10 - 1107x^9 + 1821x^8 - 2943x^7 + 4178x^6 - 5032x^5 + 7019x^4 - 8546x^3 + 8581x^2 - 6446x + 3571	\( 2^{8}\cdot 17^{14}\cdot 67^{2} \)	16T817	$[2, 10]$ (GRH)
16.12.193497104236838597191936.1	x^16 - 4x^15 - 14x^14 + 75x^13 + 18x^12 - 494x^11 + 488x^10 + 1353x^9 - 2301x^8 - 1314x^7 + 3080x^6 - 240x^5 - 1888x^4 + 624x^3 + 488x^2 - 128x - 16	\( 2^{8}\cdot 17^{14}\cdot 67^{2} \)	16T817	Trivial (GRH)
16.8.193497104236838597191936.1	x^16 - 4x^15 + 3x^14 + 24x^13 - 101x^12 + 118x^11 - 22x^10 - 75x^9 + 317x^8 + 233x^7 - 201x^6 - 1090x^5 - 817x^4 - 124x^3 + 505x^2 + 705x + 239	\( 2^{8}\cdot 17^{14}\cdot 67^{2} \)	16T817	Trivial (GRH)
16.12.193497104236838597191936.2	x^16 - 3x^15 - 9x^14 + 50x^13 - 48x^12 - 191x^11 + 530x^10 - 200x^9 - 691x^8 + 1574x^7 - 1694x^6 - 1057x^5 + 3038x^4 - 588x^3 - 973x^2 + 161x + 101	\( 2^{8}\cdot 17^{14}\cdot 67^{2} \)	16T817	Trivial (GRH)
16.0.457298012663983220674816.1	x^16 - 5x^15 + 24x^14 - 59x^13 + 128x^12 - 102x^11 + 61x^10 + 320x^9 + 134x^8 - 557x^7 + 2836x^6 - 1360x^5 + 1821x^4 + 4202x^3 + 760x^2 - 654x + 8363	\( 2^{8}\cdot 17^{14}\cdot 103^{2} \)	16T817	$[2, 16]$ (GRH)
16.8.457298012663983220674816.1	x^16 - 5x^15 + 4x^14 + 37x^13 - 138x^12 + 102x^11 + 344x^10 - 586x^9 - 151x^8 + 688x^7 - 642x^6 + 306x^5 + 2072x^4 - 785x^3 - 2308x^2 - 505x + 137	\( 2^{8}\cdot 17^{14}\cdot 103^{2} \)	16T817	Trivial (GRH)
16.12.3393001956715501807791409.2	x^16 - x^15 - 18x^14 + 5x^13 + 97x^12 + 91x^11 - 112x^10 - 556x^9 - 482x^8 + 382x^7 + 1195x^6 + 1634x^5 - 31x^4 - 1970x^3 - 920x^2 + 160x + 16	\( 17^{14}\cdot 67^{4} \)	16T817	Trivial (GRH)
16.4.3393001956715501807791409.3	x^16 - 5x^15 + 17x^14 - 39x^13 + 14x^12 + 191x^11 - 549x^10 + 1278x^9 - 1349x^8 + 786x^7 + 2560x^6 - 10256x^5 + 18416x^4 - 27136x^3 + 26112x^2 - 15360x + 4096	\( 17^{14}\cdot 67^{4} \)	16T817	$[2]$ (GRH)
16.16.18152776760150916201447424.1	x^16 - 32x^14 - 32x^13 + 344x^12 + 592x^11 - 1424x^10 - 3744x^9 + 1012x^8 + 8768x^7 + 5296x^6 - 4192x^5 - 4480x^4 - 128x^3 + 480x^2 - 64x + 2	\( 2^{74}\cdot 31^{2} \)	16T817	Trivial (GRH)
16.0.41726830242636185108217856.1	x^16 - 8x^14 + 60x^12 - 200x^10 + 610x^8 + 1528x^6 + 708x^4 + 1880x^2 + 2209	\( 2^{74}\cdot 47^{2} \)	16T817	Trivial (GRH)
16.0.41726830242636185108217856.2	x^16 - 16x^14 - 16x^13 + 96x^12 + 176x^11 - 336x^10 - 1184x^9 + 296x^8 + 5760x^7 + 9584x^6 + 5472x^5 - 824x^4 - 896x^3 + 1968x^2 + 1888x + 478	\( 2^{74}\cdot 47^{2} \)	16T817	Trivial (GRH)
16.0.41726830242636185108217856.3	x^16 + 8x^14 + 36x^12 + 136x^10 + 418x^8 + 1000x^6 + 1884x^4 + 2632x^2 + 2209	\( 2^{74}\cdot 47^{2} \)	16T817	Trivial (GRH)
16.0.41726830242636185108217856.4	x^16 - 16x^13 + 16x^12 - 80x^11 + 256x^10 - 480x^9 + 1608x^8 - 3840x^7 + 5936x^6 - 9024x^5 + 11416x^4 - 7680x^3 + 6064x^2 - 4960x + 1502	\( 2^{74}\cdot 47^{2} \)	16T817	Trivial (GRH)
16.16.44432746237320491815665664.1	x^16 - 40x^14 - 32x^13 + 612x^12 + 912x^11 - 4216x^10 - 9312x^9 + 11262x^8 + 41760x^7 + 5352x^6 - 76384x^5 - 67220x^4 + 26576x^3 + 66152x^2 + 34368x + 5983	\( 2^{72}\cdot 97^{2} \)	16T817	Trivial (GRH)
16.4.49535258684630680881135616.3	x^16 + 2x^14 - 147x^12 - 1119x^10 - 1698x^8 + 7273x^6 + 26781x^4 + 26331x^2 + 4489	\( 2^{16}\cdot 17^{14}\cdot 67^{2} \)	16T817	$[4]$ (GRH)
16.4.49535258684630680881135616.4	x^16 + 26x^14 + 181x^12 - 90x^10 - 4044x^8 - 8998x^6 + 1728x^4 + 11926x^2 + 4489	\( 2^{16}\cdot 17^{14}\cdot 67^{2} \)	16T817	$[4]$ (GRH)
16.8.49535258684630680881135616.7	x^16 - 15x^14 - 28x^12 + 717x^10 + 665x^8 - 5987x^6 - 7984x^4 + 3551x^2 + 4489	\( 2^{16}\cdot 17^{14}\cdot 67^{2} \)	16T817	Trivial (GRH)
16.8.49535258684630680881135616.8	x^16 - 9x^14 - 40x^12 + 345x^10 + 767x^8 - 3497x^6 - 5004x^4 + 9715x^2 + 4489	\( 2^{16}\cdot 17^{14}\cdot 67^{2} \)	16T817	Trivial (GRH)
16.8.15231185783695887615175635001.2	x^16 - 2x^15 - 5x^14 - 39x^13 - 121x^12 + 357x^11 + 1119x^10 + 5065x^9 + 6173x^8 - 10817x^7 - 49851x^6 - 198713x^5 - 195407x^4 - 317749x^3 + 123563x^2 + 2092986x + 129097	\( 17^{14}\cdot 67^{6} \)	16T817	$[2]$ (GRH)
16.8.24292037884309209334711647701449.2	x^16 - x^15 - 56x^14 + 144x^13 + 660x^12 - 2215x^11 - 2505x^10 + 13816x^9 - 3836x^8 - 30580x^7 + 27691x^6 + 12597x^5 - 20056x^4 + 5492x^3 + 4616x^2 + 1723x + 2797	\( 61^{2}\cdot 97^{14} \)	16T817	Trivial (GRH)
16.8.90390672967514567934462041097091729.2	x^16 - 2x^15 - 71x^14 - 110x^13 + 2035x^12 + 5510x^11 - 19628x^10 - 66886x^9 + 47565x^8 + 243276x^7 - 33562x^6 - 256662x^5 + 200402x^4 - 61110x^3 - 211266x^2 + 43844x - 47627	\( 61^{4}\cdot 97^{14} \)	16T817	Trivial (GRH)
16.8.90390672967514567934462041097091729.5	x^16 - 4x^15 - 53x^14 - 88x^13 + 1228x^12 + 7006x^11 - 1111x^10 - 117429x^9 - 223672x^8 + 843227x^7 + 112567x^6 + 2803743x^5 + 3175065x^4 - 15094129x^3 - 16279720x^2 + 21707769x + 4289443	\( 61^{4}\cdot 97^{14} \)	16T817	$[2]$ (GRH)
16.12.1571275555715210001755383712793895489.1	x^16 - 4x^15 - 103x^14 + 296x^13 + 3957x^12 - 5900x^11 - 74604x^10 - 22955x^9 + 918855x^8 + 1934875x^7 - 10886657x^6 - 19074130x^5 + 98409063x^4 + 18095388x^3 - 370583547x^2 + 361090269x - 49226183	\( 23^{10}\cdot 41^{14} \)	16T817	Trivial (GRH)
16.8.1571275555715210001755383712793895489.3	x^16 - 8x^15 + 108x^14 - 616x^13 + 1885x^12 - 3666x^11 - 70511x^10 + 372432x^9 - 1737261x^8 + 4697578x^7 - 3940881x^6 - 3038946x^5 + 14422779x^4 - 19052742x^3 - 7903064x^2 + 16252912x - 3005776	\( 23^{10}\cdot 41^{14} \)	16T817	$[2]$ (GRH)
16.8.1571275555715210001755383712793895489.7	x^16 - 6x^15 - 10x^14 + 396x^13 - 5964x^12 + 42356x^11 - 245620x^10 + 1239752x^9 - 4628026x^8 + 16756686x^7 - 39826634x^6 + 58692800x^5 + 32646687x^4 - 603931162x^3 + 1437441882x^2 - 1343332342x + 445302103	\( 23^{10}\cdot 41^{14} \)	16T817	$[2]$ (GRH)
16.4.1571275555715210001755383712793895489.9	x^16 - 2x^15 - 14x^14 + 388x^13 - 3078x^12 + 6480x^11 - 45460x^10 - 143382x^9 + 296072x^8 - 4981822x^7 + 19968220x^6 - 4230432x^5 + 296743745x^4 + 382690212x^3 + 759573920x^2 + 716455696x + 249941449	\( 23^{10}\cdot 41^{14} \)	16T817	$[2, 2]$ (GRH)
16.12.31087867512274251337747808514764310961.1	x^16 - 4x^15 - 155x^14 + 888x^13 + 5075x^12 - 43896x^11 + 36738x^10 + 632968x^9 - 3133015x^8 + 1964046x^7 + 28711844x^6 - 68240968x^5 - 34040624x^4 + 174753904x^3 + 33715784x^2 - 157790396x - 74218553	\( 31^{10}\cdot 41^{14} \)	16T817	Trivial (GRH)
16.8.31087867512274251337747808514764310961.2	x^16 - 6x^15 - 7x^14 + 288x^13 - 5235x^12 + 1684x^11 + 148983x^10 - 229221x^9 - 1154321x^8 + 2910067x^7 + 1809688x^6 - 11779338x^5 + 8819154x^4 + 11362659x^3 - 22542750x^2 + 13122331x - 2586361	\( 31^{10}\cdot 41^{14} \)	16T817	$[2]$ (GRH)
16.8.31087867512274251337747808514764310961.3	x^16 + 17x^14 - 3233x^12 + 20587x^10 + 1213530x^8 - 8974035x^6 - 80735935x^4 + 43746642x^2 + 15499969	\( 31^{10}\cdot 41^{14} \)	16T817	$[2]$ (GRH)
16.4.31087867512274251337747808514764310961.5	x^16 + 112x^14 + 3848x^12 - 1234x^10 - 2874498x^8 - 61766136x^6 - 437946455x^4 - 423979746x^2 + 268927201	\( 31^{10}\cdot 41^{14} \)	16T817	$[2, 2]$ (GRH)
16.12.50744262454554467455972799262367678441.1	x^16 - 2x^15 - 57x^14 + 597x^13 - 1849x^12 - 13831x^11 + 49484x^10 + 54030x^9 + 721609x^8 - 44849x^7 - 15451735x^6 - 6174233x^5 + 59143279x^4 + 63277728x^3 + 7184468x^2 - 4996640x - 352528	\( 11^{10}\cdot 89^{14} \)	16T817	Trivial (GRH)
16.8.50744262454554467455972799262367678441.1	x^16 - 8x^15 + 4x^14 + 112x^13 - 4365x^12 + 24370x^11 + 99979x^10 - 719664x^9 - 71786x^8 + 4866906x^7 - 9360109x^6 + 7762122x^5 + 37615615x^4 - 80920028x^3 + 100836801x^2 - 60129950x + 14685509	\( 11^{10}\cdot 89^{14} \)	16T817	$[2]$ (GRH)
16.8.50744262454554467455972799262367678441.2	x^16 - 7x^15 - 84x^14 + 577x^13 + 297x^12 - 9224x^11 + 95140x^10 - 13701x^9 - 1432142x^8 + 1672363x^7 - 3794428x^6 - 84195244x^5 + 120147984x^4 + 720593456x^3 - 1588306153x^2 + 2329602032x + 1278574016	\( 11^{10}\cdot 89^{14} \)	16T817	$[2]$ (GRH)
16.4.50744262454554467455972799262367678441.3	x^16 - 6x^15 + 104x^14 - 359x^13 + 2355x^12 - 2888x^11 + 6432x^10 + 18802x^9 + 304528x^8 + 767392x^7 - 11659280x^6 + 43841512x^5 - 36249321x^4 - 99384084x^3 + 178813720x^2 - 493047953x - 123169547	\( 11^{10}\cdot 89^{14} \)	16T817	$[2, 2]$ (GRH)
16.8.336343694112121707284133254922278323609.3	x^16 - 2x^15 + 114x^14 + 512x^13 + 1901x^12 - 8920x^11 - 171530x^10 + 412377x^9 + 1231086x^8 - 275150x^7 - 1736631x^6 - 52474780x^5 + 58963430x^4 + 195632765x^3 - 399339032x^2 + 247945353x - 49669687	\( 61^{6}\cdot 97^{14} \)	16T817	$[2]$ (GRH)
16.8.397286244885795491769071181517306466749106209.2	x^16 - 6x^15 + 124x^14 - 487x^13 - 2951x^12 - 6448x^11 - 861906x^10 + 2484917x^9 + 3448164x^8 + 85441192x^7 - 65989784x^6 - 258626096x^5 + 208451456x^4 + 55014144x^3 + 53723776x^2 - 65689600x - 15665152	\( 71^{10}\cdot 73^{14} \)	16T817	$[2, 2]$ (GRH)
16.12.397286244885795491769071181517306466749106209.3	x^16 - 4x^15 - 284x^14 - 412x^13 + 20409x^12 + 244538x^11 + 1048841x^10 - 17262064x^9 - 159907014x^8 - 153576402x^7 + 4096332547x^6 + 43159964896x^5 + 45775819228x^4 - 1072055539736x^3 - 2159676870464x^2 + 5367379047776x + 10463745523072	\( 71^{10}\cdot 73^{14} \)	16T817	$[2]$ (GRH)
16.8.397286244885795491769071181517306466749106209.7	x^16 - 4x^15 - 179x^14 + 1374x^13 - 3913x^12 - 14574x^11 + 746968x^10 - 2562342x^9 - 21733511x^8 + 77486790x^7 + 282455831x^6 - 891092496x^5 - 1833365633x^4 + 5009780308x^3 + 3843574804x^2 - 11718369616x + 7578526976	\( 71^{10}\cdot 73^{14} \)	16T817	$[2, 2]$ (GRH)
16.4.397286244885795491769071181517306466749106209.16	x^16 - 2x^15 + 284x^14 - 1567x^13 + 22547x^12 - 304668x^11 + 167473x^10 - 16109541x^9 - 22237642x^8 - 7899129x^7 - 1868635159x^6 + 7724948460x^5 - 34228322558x^4 + 67298006331x^3 - 114722294026x^2 - 187686089996x + 416833742984	\( 71^{10}\cdot 73^{14} \)	16T817	$[2, 2, 4]$ (GRH)