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 97)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.10812750244140625.1	x^16 - 2x^15 + x^14 + 2x^13 - 9x^12 + 19x^11 - 26x^10 + 11x^9 + 37x^8 - 99x^7 + 144x^6 - 146x^5 + 111x^4 - 63x^3 + 26x^2 - 7x + 1	\( 5^{14}\cdot 11^{6} \)	$C_2^3.C_4$ (as 16T41)	Trivial
16.0.102400000000000000.1	x^16 - 4x^15 + 4x^14 + 6x^13 - 9x^12 - 52x^11 + 226x^10 - 482x^9 + 697x^8 - 738x^7 + 596x^6 - 378x^5 + 191x^4 - 76x^3 + 24x^2 - 6x + 1	\( 2^{24}\cdot 5^{14} \)	$C_2^3.C_4$ (as 16T41)	Trivial
16.4.1308342779541015625.1	x^16 - x^14 - 8x^12 + 7x^10 + 15x^8 - 12x^6 - 18x^4 - 4x^2 + 1	\( 5^{14}\cdot 11^{8} \)	$C_2^3.C_4$ (as 16T41)	Trivial
16.4.1638400000000000000.1	x^16 - 4x^15 + 6x^14 - 6x^13 + 8x^12 - 14x^11 + 4x^10 - 8x^9 + 3x^8 + 6x^7 - 24x^6 + 12x^5 - 2x^4 + 2x^3 - 6x^2 + 2x + 1	\( 2^{28}\cdot 5^{14} \)	$C_2^3.C_4$ (as 16T41)	Trivial (GRH)
16.0.2870347385174781681.1	x^16 - 4x^15 + 11x^14 - 21x^13 + 34x^12 - 50x^11 + 66x^10 - 58x^9 + x^8 + 75x^7 - 81x^6 - 16x^5 + 124x^4 - 140x^3 + 80x^2 - 24x + 3	\( 3^{6}\cdot 13^{14} \)	$C_2^3.C_4$ (as 16T41)	Trivial
16.0.5416892584228515625.1	x^16 - 6x^15 + 24x^14 - 61x^13 + 126x^12 - 213x^11 + 356x^10 - 603x^9 + 1012x^8 - 1522x^7 + 1901x^6 - 1932x^5 + 1526x^4 - 929x^3 + 414x^2 - 124x + 31	\( 5^{14}\cdot 31^{6} \)	$C_2^3.C_4$ (as 16T41)	Trivial
16.4.25833126466573035129.1	x^16 - x^15 - 7x^14 + 34x^12 + 7x^11 - 99x^10 + 41x^9 + 57x^8 - 37x^7 - 21x^6 + 46x^5 + 34x^4 - 39x^3 - 7x^2 - x + 1	\( 3^{8}\cdot 13^{14} \)	$C_2^3.C_4$ (as 16T41)	Trivial (GRH)
16.0.26214400000000000000.5	x^16 - 10x^14 + 40x^12 - 90x^10 + 170x^8 - 300x^6 + 325x^4 - 150x^2 + 25	\( 2^{32}\cdot 5^{14} \)	$C_2^3.C_4$ (as 16T41)	Trivial (GRH)
16.0.73786976294838206464.2	x^16 - 8x^14 + 36x^12 - 88x^10 + 126x^8 - 88x^6 + 36x^4 - 8x^2 + 1	\( 2^{66} \)	$C_2^3.C_4$ (as 16T41)	Trivial
16.4.73786976294838206464.8	x^16 - 8x^14 + 28x^12 - 56x^10 + 42x^8 - 8x^6 - 12x^4 + 8x^2 + 1	\( 2^{66} \)	$C_2^3.C_4$ (as 16T41)	Trivial (GRH)
16.4.419430400000000000000.2	x^16 - 4x^14 - 8x^12 - 52x^10 - 290x^8 + 132x^6 - 968x^4 - 76x^2 + 1	\( 2^{36}\cdot 5^{14} \)	$C_2^3.C_4$ (as 16T41)	Trivial (GRH)
16.0.781862084478759765625.1	x^16 - 3x^15 + 9x^14 - 18x^13 + 23x^12 - 43x^11 + 6x^10 + 16x^9 + 78x^8 + 392x^7 + 754x^6 + 1786x^5 + 2683x^4 + 3324x^3 + 3006x^2 + 1846x + 781	\( 5^{14}\cdot 71^{6} \)	$C_2^3.C_4$ (as 16T41)	Trivial (GRH)
16.4.5205633773443603515625.1	x^16 - 11x^14 - 3x^12 + 57x^10 - 15x^8 - 52x^6 + 22x^4 - 29x^2 + 1	\( 5^{14}\cdot 31^{8} \)	$C_2^3.C_4$ (as 16T41)	Trivial (GRH)
16.0.812727608637355438705561.2	x^16 - 4x^15 - 2x^14 + 16x^13 + 198x^11 - 381x^10 - 1026x^9 + 3245x^8 + 776x^7 - 7300x^6 + 4380x^5 + 5678x^4 - 3690x^3 + 2803x^2 - 650x + 52	\( 13^{6}\cdot 17^{14} \)	$C_2^3.C_4$ (as 16T41)	$[2, 4]$ (GRH)
16.0.1929403689792242431640625.1	x^16 - 2x^15 + 24x^14 - 32x^13 + 183x^12 - 117x^11 + 396x^10 - 181x^9 - 912x^8 + 513x^7 - 3546x^6 + 2529x^5 - 187x^4 + 1706x^3 + 15096x^2 - 9291x + 48151	\( 3^{12}\cdot 5^{14}\cdot 29^{6} \)	$C_2^3.C_4$ (as 16T41)	$[2, 4, 4]$ (GRH)
16.16.1929403689792242431640625.1	x^16 - 6x^15 - 14x^14 + 156x^13 - 142x^12 - 1116x^11 + 2569x^10 + 1383x^9 - 9797x^8 + 8349x^7 + 6236x^6 - 15687x^5 + 11363x^4 - 3867x^3 + 614x^2 - 42x + 1	\( 3^{12}\cdot 5^{14}\cdot 29^{6} \)	$C_2^3.C_4$ (as 16T41)	Trivial (GRH)
16.4.3941366767857427978515625.1	x^16 + x^14 - 43x^12 - 47x^10 + 525x^8 - 68x^6 - 4078x^4 + 2299x^2 + 14641	\( 5^{14}\cdot 71^{8} \)	$C_2^3.C_4$ (as 16T41)	Trivial (GRH)
16.0.35007428516075131079076169.1	x^16 - 4x^15 + 23x^14 - 34x^13 + 88x^12 + 310x^11 - 262x^10 + 2441x^9 + 1652x^8 + 2997x^7 + 13249x^6 + 1204x^5 + 14168x^4 + 6713x^3 - 2646x^2 - 686x + 343	\( 7^{6}\cdot 29^{14} \)	$C_2^3.C_4$ (as 16T41)	Trivial (GRH)
16.0.61552138713495855712890625.1	x^16 - 7x^15 + 36x^14 - 143x^13 + 326x^12 - 401x^11 + 44x^10 + 2041x^9 - 5608x^8 + 7716x^7 - 2636x^6 - 8251x^5 + 18471x^4 - 24778x^3 + 25706x^2 - 11857x + 3191	\( 5^{14}\cdot 11^{8}\cdot 19^{6} \)	$C_2^3.C_4$ (as 16T41)	$[2, 2, 2]$ (GRH)
16.16.61552138713495855712890625.1	x^16 - 2x^15 - 41x^14 + 48x^13 + 688x^12 - 267x^11 - 5814x^10 - 1281x^9 + 25198x^8 + 15588x^7 - 55306x^6 - 50331x^5 + 54453x^4 + 68116x^3 - 10774x^2 - 33456x - 9869	\( 5^{14}\cdot 11^{8}\cdot 19^{6} \)	$C_2^3.C_4$ (as 16T41)	Trivial (GRH)
16.0.61552138713495855712890625.2	x^16 - 5x^15 + 29x^14 - 65x^13 + 152x^12 - 85x^11 + 212x^10 + 90x^9 - 10x^8 - 1685x^7 + 14128x^6 - 47550x^5 + 100442x^4 - 142525x^3 + 157306x^2 - 107825x + 30761	\( 5^{14}\cdot 11^{8}\cdot 19^{6} \)	$C_2^3.C_4$ (as 16T41)	$[2, 4, 4]$ (GRH)
16.0.137350965859713069141239809.4	x^16 + 30x^14 + 109x^12 + 95x^10 + 202x^8 + 351x^6 + 316x^4 + 1072x^2 + 256	\( 13^{8}\cdot 17^{14} \)	$C_2^3.C_4$ (as 16T41)	$[4, 4]$ (GRH)
16.0.957126807028111655268824569.1	x^16 - 3x^15 + 19x^14 - 82x^13 + 177x^12 - 603x^11 + 1509x^10 - 1404x^9 + 5870x^8 - 3549x^7 + 3038x^6 - 6908x^5 + 28884x^4 + 85257x^3 + 227610x^2 + 186138x + 145557	\( 13^{14}\cdot 79^{6} \)	$C_2^3.C_4$ (as 16T41)	Trivial (GRH)
16.0.1060259999412516731450111161.1	x^16 - 2x^15 + 22x^14 - 34x^13 + 98x^12 - 106x^11 + 366x^10 + 21x^9 + 2394x^8 + 200x^7 - 11836x^6 - 9835x^5 - 11557x^4 + 980x^3 + 99323x^2 + 68943x + 21609	\( 7^{6}\cdot 37^{14} \)	$C_2^3.C_4$ (as 16T41)	Trivial (GRH)
16.4.1715363997287681422874732281.1	x^16 + 20x^14 - 434x^12 + 2412x^10 - 3845x^8 - 3833x^6 + 436x^4 - 165x^2 + 1	\( 7^{8}\cdot 29^{14} \)	$C_2^3.C_4$ (as 16T41)	Trivial (GRH)
16.4.1814980849112797822933640641.12	x^16 - 4x^15 + 20x^14 - 61x^13 + x^12 - 52x^11 - 923x^10 + 1353x^9 + 6250x^8 - 12449x^7 - 5845x^6 + 16726x^5 - 22203x^4 + 73843x^3 + 41492x^2 + 23332x + 16967	\( 17^{14}\cdot 47^{6} \)	$C_2^3.C_4$ (as 16T41)	$[2]$ (GRH)
16.4.15231185783695887615175635001.31	x^16 - 3x^15 + 17x^14 + 54x^13 - 207x^12 + 611x^11 + 1348x^10 - 3327x^9 + 4023x^8 + 19634x^7 - 197x^6 - 37023x^5 + 74499x^4 + 229926x^3 - 185436x^2 - 316912x + 42176	\( 17^{14}\cdot 67^{6} \)	$C_2^3.C_4$ (as 16T41)	$[2, 4]$ (GRH)
16.0.44049297503430822362132869609.1	x^16 - 9x^14 - 28x^12 - 981x^10 + 10307x^8 + 3852x^6 + 357774x^4 - 944840x^2 + 1485961	\( 23^{6}\cdot 29^{14} \)	$C_2^3.C_4$ (as 16T41)	Trivial (GRH)
16.4.51952739971213319841055446889.1	x^16 - 8x^15 + 20x^14 - 33x^12 - 166x^11 + 1629x^10 - 5670x^9 + 3020x^8 + 18398x^7 - 30968x^6 + 8343x^5 + 115074x^4 - 213083x^3 - 264567x^2 + 368010x - 59643	\( 7^{8}\cdot 37^{14} \)	$C_2^3.C_4$ (as 16T41)	Trivial (GRH)
16.0.83680629612698426645202702769.4	x^16 - 7x^15 + 65x^14 - 407x^13 + 2151x^12 - 10072x^11 + 42053x^10 - 148549x^9 + 441642x^8 - 1087932x^7 + 2206158x^6 - 3596503x^5 + 4676785x^4 - 4672450x^3 + 3526208x^2 - 1788400x + 554608	\( 17^{14}\cdot 89^{6} \)	$C_2^3.C_4$ (as 16T41)	$[2, 28]$ (GRH)
16.0.4009292695690170390860412175969.3	x^16 - 18x^14 + 571x^12 - 7712x^10 + 64513x^8 - 262320x^6 + 571411x^4 - 17914x^2 + 28561	\( 17^{14}\cdot 47^{8} \)	$C_2^3.C_4$ (as 16T41)	$[2, 2, 8]$ (GRH)
16.4.5614886866882301027209678756129.7	x^16 - 8x^15 - x^14 + 147x^13 - 312x^12 + 1237x^11 - 11210x^10 + 9261x^9 - 21833x^8 + 166391x^7 + 39783x^6 + 395156x^5 + 264039x^4 + 662650x^3 + 586484x^2 + 296055x - 212671	\( 23^{6}\cdot 41^{14} \)	$C_2^3.C_4$ (as 16T41)	$[6]$ (GRH)
16.4.5973428402662444840532734135129.1	x^16 - 6x^15 + 24x^14 - 71x^13 + 102x^12 - 2071x^11 - 1977x^10 - 17693x^9 - 50858x^8 - 96551x^7 + 14598x^6 + 71270x^5 - 814270x^4 - 2949122x^3 - 4453919x^2 - 3048039x - 754857	\( 13^{14}\cdot 79^{8} \)	$C_2^3.C_4$ (as 16T41)	Trivial (GRH)
16.0.12551165043538064715930071464321.1	x^16 - 24x^14 + 484x^12 - 5833x^10 + 36700x^8 - 98607x^6 + 223934x^4 + 762575x^2 + 1841449	\( 29^{14}\cdot 59^{6} \)	$C_2^3.C_4$ (as 16T41)	$[3]$ (GRH)
16.4.23302078379314905029568288023161.1	x^16 - 8x^15 + 26x^14 - 42x^13 - 224x^12 + 1526x^11 - 4856x^10 + 10244x^9 - 10696x^8 - 1894x^7 + 28943x^6 - 53943x^5 - 55815x^4 + 187219x^3 - 236831x^2 + 136350x + 919829	\( 23^{8}\cdot 29^{14} \)	$C_2^3.C_4$ (as 16T41)	Trivial (GRH)
16.4.33662328752972862921089838254641.7	x^16 - 5x^15 - 49x^14 + 664x^13 - 3457x^12 + 9520x^11 - 8435x^10 - 36372x^9 + 139366x^8 - 134382x^7 - 310833x^6 + 1194633x^5 - 1988097x^4 + 2308085x^3 - 1852166x^2 + 705715x - 91699	\( 31^{6}\cdot 41^{14} \)	$C_2^3.C_4$ (as 16T41)	$[8]$ (GRH)
16.0.68372792983010839504523425519489.23	x^16 - 4x^15 + 25x^14 - 19x^13 + 196x^12 - 153x^11 + 4469x^10 + 2832x^9 - 1277x^8 + 122499x^7 + 173528x^6 - 1660883x^5 + 2750234x^4 - 3001184x^3 - 24662408x^2 - 10625712x + 149470784	\( 17^{14}\cdot 67^{8} \)	$C_2^3.C_4$ (as 16T41)	$[2, 4, 4, 40]$ (GRH)
16.0.97142949267676999771489894732681.1	x^16 - 33x^14 + 784x^12 - 9576x^10 + 44890x^8 + 760731x^6 - 1902935x^4 + 5169906x^2 + 189640441	\( 37^{14}\cdot 47^{6} \)	$C_2^3.C_4$ (as 16T41)	$[9]$ (GRH)
16.0.97283799690045652521048020437489.1	x^16 - 4x^15 + 55x^14 - 88x^13 + 920x^12 - 4548x^11 + 1215x^10 - 3768x^9 + 134918x^8 - 207338x^7 + 40086x^6 - 1027637x^5 + 2452312x^4 - 2392475x^3 + 10205840x^2 - 20847139x + 28188139	\( 29^{14}\cdot 83^{6} \)	$C_2^3.C_4$ (as 16T41)	Trivial (GRH)
16.0.97316019886955839743696883969849.3	x^16 - 4x^15 - 55x^14 + 292x^13 + 1089x^12 - 8804x^11 - 5925x^10 + 139988x^9 - 109229x^8 - 1258788x^7 + 2004779x^6 + 6216884x^5 - 11557040x^4 - 13141776x^3 + 22316704x^2 + 3217664x + 4983232	\( 37^{6}\cdot 41^{14} \)	$C_2^3.C_4$ (as 16T41)	$[2, 24]$ (GRH)
16.0.662834267162184237456650608633249.2	x^16 + 86x^14 + 1251x^12 + 4992x^10 + 6033x^8 + 8272x^6 + 45499x^4 + 75374x^2 + 28561	\( 17^{14}\cdot 89^{8} \)	$C_2^3.C_4$ (as 16T41)	$[4, 28]$ (GRH)
16.0.1154447610730415783388912356000569.1	x^16 - 2x^15 + 18x^14 + 158x^13 + 718x^12 + 1324x^11 + 5679x^10 + 72254x^9 + 323371x^8 + 739018x^7 + 1269996x^6 + 4996370x^5 + 15767727x^4 + 14111857x^3 - 19828694x^2 - 29709493x + 20958289	\( 37^{14}\cdot 71^{6} \)	$C_2^3.C_4$ (as 16T41)	Trivial (GRH)
16.4.1599875043672267792208865723998201.20	x^16 - 74x^14 + 3554x^12 - 5822x^11 - 71858x^10 + 287902x^9 + 75018x^8 - 1842376x^7 + 1590774x^6 + 4422342x^5 - 5089343x^4 - 1701254x^3 + 5084664x^2 - 3270488x + 775024	\( 41^{14}\cdot 59^{6} \)	$C_2^3.C_4$ (as 16T41)	$[2]$ (GRH)
16.0.2946406684936922037860575506582241.1	x^16 - 2x^15 - 5x^14 + 78x^13 - 475x^12 + 3641x^11 - 1085x^10 - 63940x^9 + 186709x^8 - 41802x^7 + 295915x^6 - 2938105x^5 + 4953545x^4 - 102100x^3 - 303276x^2 + 7064925x + 3528539	\( 37^{14}\cdot 83^{6} \)	$C_2^3.C_4$ (as 16T41)	Trivial (GRH)
16.0.2970275152580737243393920061992241.24	x^16 - 2x^15 - 13x^14 + 130x^13 - 680x^12 + 1550x^11 + 20405x^10 - 92160x^9 + 114839x^8 + 13382x^7 + 1287471x^6 - 3112866x^5 + 4334218x^4 - 2448624x^3 + 7869323x^2 - 16187548x + 112126933	\( 23^{8}\cdot 41^{14} \)	$C_2^3.C_4$ (as 16T41)	$[2, 4, 24]$ (GRH)
16.4.3465901403903727030665446298911801.17	x^16 - 4x^15 - 3x^14 + 117x^13 - 861x^12 + 8121x^11 - 15475x^10 + 59261x^9 + 129601x^8 - 1374433x^7 + 4112201x^6 - 16201717x^5 + 12050174x^4 - 22671797x^3 - 20716338x^2 + 14876208x + 167431328	\( 11^{6}\cdot 89^{14} \)	$C_2^3.C_4$ (as 16T41)	$[2]$ (GRH)
16.4.12400595700703321333205791744050409.6	x^16 - 2x^15 + 114x^14 - 492x^13 + 5241x^12 - 30478x^11 + 148761x^10 - 681392x^9 + 2453121x^8 - 7739418x^7 + 12450541x^6 - 8400012x^5 - 120605220x^4 + 169262104x^3 + 661786947x^2 + 413443500x - 11447600	\( 41^{14}\cdot 83^{6} \)	$C_2^3.C_4$ (as 16T41)	$[2]$ (GRH)
16.0.14874737901162615182149330162516201.1	x^16 - 2x^15 - x^14 - 218x^13 + 148x^12 - 274x^11 + 20046x^10 + 9204x^9 + 59155x^8 - 735816x^7 - 1221602x^6 - 2904858x^5 + 7439752x^4 + 29813275x^3 + 57198013x^2 + 53884137x + 26722273	\( 47^{6}\cdot 53^{14} \)	$C_2^3.C_4$ (as 16T41)	$[3]$ (GRH)
16.0.32349497931606921267167334562710001.19	x^16 - 2x^15 - 66x^14 + 28x^13 + 1977x^12 + 3290x^11 - 39834x^10 - 160157x^9 + 274964x^8 + 3051194x^7 + 7432505x^6 - 10471450x^5 - 86737142x^4 - 116122039x^3 + 140732982x^2 + 648497959x + 1031411207	\( 31^{8}\cdot 41^{14} \)	$C_2^3.C_4$ (as 16T41)	$[2, 2, 32]$ (GRH)
16.4.43690605516556003276152578767301401.1	x^16 + 23x^14 + 110x^12 + 4736x^10 + 33057x^8 - 138943x^6 - 447367x^4 - 187795x^2 + 279841	\( 29^{14}\cdot 59^{8} \)	$C_2^3.C_4$ (as 16T41)	$[3]$ (GRH)