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 42 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.8.4722366482869645213696.1	x^16 - 16x^14 + 72x^12 - 32x^11 - 144x^10 + 112x^9 + 116x^8 - 128x^7 - 32x^6 + 32x^5 + 32x^4 - 16x^2 + 2	\( 2^{72} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	Trivial
16.8.4722366482869645213696.2	x^16 - 8x^14 - 12x^12 + 216x^10 - 414x^8 - 40x^6 + 108x^4 + 24x^2 + 1	\( 2^{72} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	Trivial
16.8.3393001956715501807791409.1	x^16 - 5x^15 + 10x^14 - 19x^13 + 47x^12 - 63x^11 - 211x^10 + 1216x^9 - 2476x^8 + 3572x^7 - 7167x^6 + 12696x^5 - 8215x^4 - 8270x^3 + 13675x^2 - 4043x - 509	\( 17^{14}\cdot 67^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	Trivial (GRH)
16.8.3393001956715501807791409.3	x^16 - 6x^15 + 4x^14 + 20x^13 - 17x^12 - 36x^11 + 90x^10 + 123x^9 - 338x^8 - 246x^7 + 275x^6 - 460x^5 - 1156x^4 + 329x^3 + 2432x^2 + 1703x + 239	\( 17^{14}\cdot 67^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	Trivial (GRH)
16.4.17521464151279710991512529.1	x^16 - 2x^15 + 13x^14 - 28x^13 + 56x^12 + 22x^11 - 28x^10 - 108x^9 - 1553x^8 + 2736x^7 - 7630x^6 + 12868x^5 - 10934x^4 + 13120x^3 - 2525x^2 + 454x + 4861	\( 17^{14}\cdot 101^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[2]$ (GRH)
16.12.17521464151279710991512529.3	x^16 - 6x^15 - 7x^14 + 65x^13 + 26x^12 - 107x^11 + 58x^10 - 1039x^9 - 3330x^8 + 1201x^7 + 14173x^6 + 13703x^5 - 6190x^4 - 12340x^3 - 1618x^2 + 1515x - 137	\( 17^{14}\cdot 101^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	Trivial (GRH)
16.12.59315359635608350207210369.1	x^16 - 5x^15 - 7x^14 + 66x^13 - 174x^12 - 63x^11 + 2866x^10 - 1742x^9 - 15583x^8 + 5612x^7 + 28720x^6 - 20947x^5 - 35976x^4 + 12572x^3 + 14457x^2 - 1323x - 67	\( 17^{14}\cdot 137^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	Trivial (GRH)
16.4.59315359635608350207210369.1	x^16 - 3x^15 - 14x^13 - 156x^12 + 305x^11 - 590x^10 + 2113x^9 + 130x^8 - 596x^7 - 5008x^6 - 9687x^5 - 10433x^4 + 8314x^3 + 92888x^2 - 61232x + 104464	\( 17^{14}\cdot 137^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[6]$ (GRH)
16.0.408269247409129401849217024.1	x^16 + 8x^14 - 16x^13 + 12x^12 - 304x^11 + 832x^10 - 3200x^9 + 11584x^8 - 27376x^7 + 59040x^6 - 101408x^5 + 124032x^4 - 126240x^3 + 105176x^2 - 52560x + 10607	\( 2^{62}\cdot 97^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	Trivial (GRH)
16.0.408269247409129401849217024.2	x^16 - 8x^15 + 44x^14 - 160x^13 + 494x^12 - 1192x^11 + 2448x^10 - 3672x^9 + 4829x^8 - 5192x^7 + 8112x^6 - 6280x^5 + 9350x^4 - 5296x^3 + 17428x^2 + 1960x + 2063	\( 2^{62}\cdot 97^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	Trivial (GRH)
16.0.4361204616626257617397743616.1	x^16 + 48x^14 - 48x^13 + 880x^12 - 1504x^11 + 9104x^10 - 18864x^9 + 63084x^8 - 138624x^7 + 292784x^6 - 507040x^5 + 958208x^4 - 1261120x^3 + 1259280x^2 - 608640x + 222722	\( 2^{72}\cdot 31^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[2, 2, 2, 148]$ (GRH)
16.16.4361204616626257617397743616.1	x^16 - 64x^14 - 64x^13 + 1608x^12 + 3120x^11 - 18528x^10 - 56016x^9 + 76224x^8 + 435712x^7 + 205760x^6 - 1213184x^5 - 1987144x^4 - 353952x^3 + 1514112x^2 + 1294816x + 317246	\( 2^{72}\cdot 31^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	Trivial (GRH)
16.0.4361204616626257617397743616.2	x^16 + 48x^14 - 80x^13 + 808x^12 - 2304x^11 + 8640x^10 - 21136x^9 + 57456x^8 - 120320x^7 + 257456x^6 - 419232x^5 + 588936x^4 - 573184x^3 + 526720x^2 - 330144x + 210878	\( 2^{72}\cdot 31^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[2, 2, 2, 144]$ (GRH)
16.16.4361204616626257617397743616.2	x^16 - 64x^14 - 80x^13 + 1392x^12 + 3232x^11 - 10320x^10 - 36752x^9 + 7196x^8 + 125184x^7 + 91216x^6 - 99136x^5 - 131584x^4 - 29696x^3 + 9328x^2 + 2208x - 254	\( 2^{72}\cdot 31^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	Trivial (GRH)
16.0.23043642001495833226013310976.1	x^16 - 8x^14 + 36x^12 - 72x^10 + 518x^8 - 3384x^6 + 79524x^4 - 830584x^2 + 4879681	\( 2^{72}\cdot 47^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	Trivial (GRH)
16.0.23043642001495833226013310976.2	x^16 + 16x^14 - 32x^13 + 120x^12 - 672x^11 + 1136x^10 - 4720x^9 + 12692x^8 - 24064x^7 + 60832x^6 - 102272x^5 + 159520x^4 - 227392x^3 + 238672x^2 - 225632x + 132098	\( 2^{72}\cdot 47^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	Trivial (GRH)
16.0.23043642001495833226013310976.3	x^16 - 48x^13 + 8x^12 - 96x^11 + 640x^10 - 736x^9 + 2860x^8 + 2240x^7 + 35808x^6 + 63200x^5 + 203552x^4 + 347264x^3 + 610432x^2 + 596864x + 314044	\( 2^{72}\cdot 47^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	Trivial (GRH)
16.0.23043642001495833226013310976.4	x^16 - 48x^13 + 80x^12 + 96x^11 + 496x^10 - 2544x^9 - 788x^8 + 9728x^7 + 9616x^6 - 46560x^5 - 33024x^4 + 197696x^3 - 81584x^2 - 266560x + 259522	\( 2^{72}\cdot 47^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	Trivial (GRH)
16.0.71085478368850138600216861921.1	x^16 - 3x^15 + 40x^14 - 162x^13 + 880x^12 - 3185x^11 + 11465x^10 - 31779x^9 + 72664x^8 - 124831x^7 + 156795x^6 - 131824x^5 + 57312x^4 - 5481x^3 + 7700x^2 + 330x + 139	\( 37^{4}\cdot 41^{14} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	Trivial (GRH)
16.0.71085478368850138600216861921.3	x^16 - 3x^15 + 12x^14 - 68x^13 + 71x^12 + 548x^11 - 205x^10 - 2994x^9 - 1032x^8 + 9601x^7 + 15211x^6 - 9204x^5 - 25755x^4 - 64205x^3 + 20207x^2 + 132153x + 324019	\( 37^{4}\cdot 41^{14} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	Trivial (GRH)
16.8.222363776235307126475417780224.1	x^16 + 9x^14 - 958x^12 - 2538x^10 + 249086x^8 - 421095x^6 - 11931762x^4 + 2406104x^2 + 20151121	\( 2^{16}\cdot 17^{14}\cdot 67^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[2]$ (GRH)
16.8.222363776235307126475417780224.2	x^16 - 15x^14 - 487x^12 + 2893x^10 + 87348x^8 + 193831x^6 - 2186143x^4 - 4511445x^2 + 20151121	\( 2^{16}\cdot 17^{14}\cdot 67^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[2]$ (GRH)
16.8.222363776235307126475417780224.3	x^16 - 9x^14 - 958x^12 + 2538x^10 + 249086x^8 + 421095x^6 - 11931762x^4 - 2406104x^2 + 20151121	\( 2^{16}\cdot 17^{14}\cdot 67^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[2]$ (GRH)
16.8.222363776235307126475417780224.4	x^16 + 25x^14 - 754x^12 - 13612x^10 + 173419x^8 + 1777644x^6 - 11626510x^4 + 2706867x^2 + 20151121	\( 2^{16}\cdot 17^{14}\cdot 67^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[2, 2]$ (GRH)
16.0.228732005557745506375281661426849.2	x^16 - 4x^15 + 37x^14 - 331x^13 + 1532x^12 - 7501x^11 + 38313x^10 - 145668x^9 + 498951x^8 - 1545333x^7 + 3943200x^6 - 7439391x^5 + 10291030x^4 - 9803772x^3 + 6571656x^2 - 2368160x + 430336	\( 37^{4}\cdot 73^{14} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[89]$ (GRH)
16.0.228732005557745506375281661426849.3	x^16 - 7x^15 + 38x^14 - 192x^13 + 1030x^12 - 4346x^11 + 14527x^10 - 42823x^9 + 138300x^8 - 431096x^7 + 1016744x^6 - 1671056x^5 + 1216768x^4 + 804608x^3 - 1660032x^2 + 678400x + 1859584	\( 37^{4}\cdot 73^{14} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[89]$ (GRH)
16.12.90390672967514567934462041097091729.1	x^16 - 3x^15 - 48x^14 - 122x^13 + 481x^12 + 8150x^11 + 20561x^10 - 76067x^9 - 548175x^8 - 241659x^7 + 4598000x^6 + 3143799x^5 - 16209686x^4 - 7154965x^3 + 24199071x^2 + 4282958x - 11903533	\( 61^{4}\cdot 97^{14} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	Trivial (GRH)
16.4.90390672967514567934462041097091729.1	x^16 - 2x^15 + 38x^14 + 160x^13 - 93x^12 + 5706x^11 - 2714x^10 - 5105x^9 - 56512x^8 - 1208372x^7 - 5394505x^6 - 20436854x^5 - 50423708x^4 - 128866001x^3 - 66743118x^2 + 3898849x - 84718247	\( 61^{4}\cdot 97^{14} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[2]$ (GRH)
16.8.831204768973346090928597984067970713681.1	x^16 - 4x^15 + 33x^14 - 98x^13 - 7707x^12 - 21718x^11 - 141016x^10 - 1284806x^9 - 3549491x^8 - 2155488x^7 + 10582866x^6 + 35482368x^5 + 22083648x^4 - 64346268x^3 - 63183866x^2 + 66208918x - 4615661	\( 23^{12}\cdot 41^{14} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[2, 2]$ (GRH)
16.8.831204768973346090928597984067970713681.2	x^16 - 2x^15 + 90x^14 - 286x^13 - 2072x^12 + 8650x^11 - 99203x^10 + 272878x^9 - 348651x^8 - 4611138x^7 + 59898657x^6 - 42000364x^5 - 24483833x^4 + 269660476x^3 - 6683215296x^2 + 3767796992x + 5374176512	\( 23^{12}\cdot 41^{14} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[2, 2]$ (GRH)
16.8.6140055757001090562172708710746489091361.1	x^16 - 4x^15 - 26x^14 + 598x^13 - 2813x^12 - 8568x^11 + 118599x^10 - 433002x^9 - 488858x^8 + 5813984x^7 + 8382561x^6 - 67333706x^5 - 54374353x^4 + 379926932x^3 + 124007939x^2 - 920391824x + 254211683	\( 11^{12}\cdot 89^{14} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[2]$ (GRH)
16.8.6140055757001090562172708710746489091361.2	x^16 - 3x^15 - 124x^14 + 2318x^13 - 7756x^12 - 113391x^11 + 1228607x^10 - 2698673x^9 - 29351828x^8 + 218778821x^7 - 398785415x^6 - 2066647462x^5 + 12585895662x^4 - 26338087641x^3 + 25503742812x^2 - 12111231250x + 3157789331	\( 11^{12}\cdot 89^{14} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[2]$ (GRH)
16.8.29875440679295555535575643982688502833521.1	x^16 - 7x^15 - 132x^14 + 1877x^13 - 1604x^12 - 90470x^11 + 765081x^10 - 3538362x^9 - 6534866x^8 + 215410535x^7 - 1104467286x^6 + 1608355766x^5 + 2955391761x^4 - 9056589516x^3 + 2366911254x^2 + 2013183756x - 686260787	\( 31^{12}\cdot 41^{14} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[2]$ (GRH)
16.8.29875440679295555535575643982688502833521.2	x^16 - 4x^15 + 49x^14 - 154x^13 - 17602x^12 - 55852x^11 - 772287x^10 - 6058156x^9 - 9080099x^8 + 26256544x^7 + 384213103x^6 + 778367308x^5 - 361748214x^4 - 3849727644x^3 - 16369099293x^2 + 14761359476x + 25815211523	\( 31^{12}\cdot 41^{14} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[2]$ (GRH)
16.0.249686282242731792647174886492450339042241.4	x^16 - 2x^15 + 153x^14 - 468x^13 + 30169x^12 - 86770x^11 + 3755888x^10 - 13294364x^9 + 217796337x^8 - 877574404x^7 + 6658827530x^6 - 23152161472x^5 + 126145294036x^4 - 313193327620x^3 + 1231014931084x^2 - 2040068815012x + 5489864782943	\( 37^{12}\cdot 41^{14} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[2, 2, 2, 584]$ (GRH)
16.0.249686282242731792647174886492450339042241.6	x^16 - 7x^15 + 218x^14 - 3065x^13 + 39881x^12 - 486437x^11 + 4721837x^10 - 45946626x^9 + 379919624x^8 - 2767976084x^7 + 17803648743x^6 - 93432130616x^5 + 431348541875x^4 - 1573313537696x^3 + 4687448410199x^2 - 11366868502319x + 16797845967299	\( 37^{12}\cdot 41^{14} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[2, 2, 2, 584]$ (GRH)
16.0.803416469975725073264940954221144185207724929.2	x^16 - 8x^15 + 104x^14 - 588x^13 + 17698x^12 - 98908x^11 + 1060966x^10 - 4411234x^9 + 30357096x^8 - 96026660x^7 + 488894886x^6 - 1148053948x^5 + 4600537631x^4 - 7391392826x^3 + 23803505264x^2 - 20284389474x + 51165489031	\( 37^{12}\cdot 73^{14} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[2, 2, 2, 328]$ (GRH)
16.0.803416469975725073264940954221144185207724929.7	x^16 - 4x^15 - 251x^14 + 896x^13 + 16630x^12 - 93666x^11 + 286426x^10 + 3506890x^9 - 13540961x^8 + 205373656x^7 - 797038879x^6 - 9149326000x^5 - 11184167097x^4 + 91847336586x^3 + 4606618252806x^2 + 14259307873786x + 62802119569213	\( 37^{12}\cdot 73^{14} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[2, 2, 2, 328]$ (GRH)
16.8.2002719960469295074007887826028741898882244399569.1	x^16 - 8x^15 + 172x^14 - 1064x^13 - 13749x^12 + 95962x^11 - 2719805x^10 + 12694968x^9 - 15878925x^8 - 11556770x^7 + 6319219283x^6 - 18864989696x^5 + 72782355414x^4 - 114161384246x^3 - 2815961493701x^2 + 2869903672164x + 3128974954972	\( 71^{12}\cdot 73^{14} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[2, 2, 4]$ (GRH)
16.8.2002719960469295074007887826028741898882244399569.2	x^16 - 6x^15 + 25x^14 + 562x^13 - 205185x^12 + 803174x^11 - 11510253x^10 - 123129514x^9 + 8179623956x^8 + 543896x^7 + 279834449792x^6 + 1150878405120x^5 - 55216022400064x^4 - 259884347484288x^3 - 434316312830208x^2 + 962164281331200x + 3837587340384256	\( 71^{12}\cdot 73^{14} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[2, 2, 2]$ (GRH)
16.12.17328553034618181867273005889005225191371184588849.1	x^16 - 4x^15 - 1200x^14 + 7176x^13 + 382131x^12 - 2827226x^11 - 21896116x^10 + 489716073x^9 - 5522964746x^8 - 29475464342x^7 + 764166087629x^6 - 664207203366x^5 - 29332809376400x^4 + 96649385827419x^3 + 203116946704020x^2 - 1620760775169645x + 2927618217243747	\( 61^{12}\cdot 97^{14} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[4]$ (GRH)
16.4.17328553034618181867273005889005225191371184588849.1	x^16 - 3x^15 - 479x^14 + 2816x^13 + 79228x^12 + 3884251x^11 - 27287937x^10 - 90797059x^9 - 3792716246x^8 - 13822223688x^7 - 34767420017x^6 + 23198289208957x^5 - 404015089637913x^4 + 3183147219370626x^3 - 13908684943930888x^2 + 34234229555680560x - 37606158695886896	\( 61^{12}\cdot 97^{14} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[2, 2, 12]$ (GRH)