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 168)

Label	Polynomial	Discriminant	Galois group	Class group
21.1.5737729418385982521381124421.1	x^21 - x - 1	\( 1137694897331\cdot 5043293621028391 \)	21T164	Trivial (GRH)
21.1.5947444618385982521381124421.1	x^21 + x - 1	\( 11\cdot 17\cdot 1033\cdot 1583\cdot 159503\cdot 121937899012999 \)	21T164	Trivial (GRH)
21.1.7399096241029480225646983928.1	x^21 - 2x^20 - x^19 + 7x^18 - 3x^17 - 13x^16 + 14x^15 + 13x^14 - 28x^13 - 2x^12 + 34x^11 - 15x^10 - 25x^9 + 24x^8 + 7x^7 - 21x^6 + 6x^5 + 8x^4 - 7x^3 + 2x - 1	\( 2^{3}\cdot 101\cdot 1951\cdot 7481\cdot 35629381\cdot 17609300881 \)	21T164	Trivial (GRH)
21.1.75375354289024738220986584068.1	x^21 - 2x^20 - x^19 + 7x^18 - 3x^17 - 13x^16 + 14x^15 + 13x^14 - 28x^13 - 2x^12 + 34x^11 - 15x^10 - 25x^9 + 25x^8 + 7x^7 - 22x^6 + 6x^5 + 8x^4 - 7x^3 + 2x - 1	\( 2^{2}\cdot 11\cdot 29\cdot 1447\cdot 2579\cdot 4423\cdot 3578836676945557 \)	21T164	Trivial (GRH)
21.1.219908168142218385982521381124421.1	x^21 + 2x - 1	\( 59\cdot 997\cdot 3738472504670254593994209427 \)	21T164	Trivial (GRH)
21.1.1311696805792575002084933480218624.1	x^21 - 7x^18 + 21x^15 - 35x^12 + 35x^9 - 21x^6 + 7x^3 - 2x - 1	\( 2^{18}\cdot 19\cdot 188021\cdot 1400662753064812335179 \)	21T164	Trivial (GRH)
21.1.1751501456902975002084933480218624.1	x^21 - 7x^18 + 21x^15 - 35x^12 + 35x^9 - 21x^6 + 7x^3 + 2x - 1	\( 2^{18}\cdot 29\cdot 191\cdot 6269\cdot 192415895349874457731 \)	21T164	Trivial (GRH)
21.1.5686591874280700008339733920874496.1	x^21 - 4x - 4	\( 2^{20}\cdot 2609\cdot 1020583\cdot 2036712542136910243 \)	21T164	Trivial (GRH)
21.1.5906494199835900008339733920874496.1	x^21 - 2x - 2	\( 2^{20}\cdot 3049\cdot 1847448940106914569164029 \)	21T164	Trivial (GRH)
21.1.6126396420533500008339733920874496.1	x^21 - x - 2	\( 2^{20}\cdot 17\cdot 15118577\cdot 59724677\cdot 380619938497 \)	21T164	Trivial (GRH)
21.1.6126396525391000008339733920874496.1	x^21 - x - 4	\( 2^{22}\cdot 1831\cdot 35759\cdot 321383\cdot 69414242408507 \)	21T164	Trivial (GRH)
21.1.6346298850946300008339733920874496.1	x^21 + 2x - 2	\( 2^{20}\cdot 6052302218385982521381124421 \)	21T164	Trivial (GRH)
21.1.6566201176501500008339733920874496.1	x^21 + 4x - 4	\( 2^{20}\cdot 71\cdot 954210151\cdot 92429773814019701 \)	21T164	Trivial (GRH)
21.3.38810381910436648807122136959509364.1	x^21 - 2x^20 - 2x^19 + 6x^18 + 3x^17 - 14x^16 - x^15 + 22x^14 - 7x^13 - 21x^12 + 12x^11 + 13x^10 - 12x^9 - x^8 + 4x^7 - 7x^6 + 6x^5 + 3x^4 - 8x^3 + 2x^2 + 2x - 1	\( -\,2^{2}\cdot 3^{2}\cdot 43\cdot 139\cdot 12161\cdot 3070695374003\cdot 4830100159439 \)	21T164	Trivial (GRH)
21.7.81456421401609117918191887243293452.1	x^21 - 3x^20 - 2x^19 + 16x^18 - 12x^17 - 27x^16 + 46x^15 + 13x^14 - 76x^13 + 26x^12 + 79x^11 - 73x^10 - 38x^9 + 86x^8 - 17x^7 - 47x^6 + 34x^5 + 6x^4 - 15x^3 + 4x^2 + 2x - 1	\( -\,2^{2}\cdot 37\cdot 139\cdot 51194111\cdot 77344387584200382269131 \)	21T164	Trivial (GRH)
21.5.635173019262506375451972532599400152.1	x^21 - 3x^20 - 2x^19 + 16x^18 - 12x^17 - 27x^16 + 46x^15 + 13x^14 - 76x^13 + 26x^12 + 79x^11 - 73x^10 - 38x^9 + 86x^8 - 18x^7 - 47x^6 + 34x^5 + 6x^4 - 15x^3 + 4x^2 + 3x - 1	\( 2^{3}\cdot 3^{3}\cdot 6959\cdot 382373449525433\cdot 1105105461718151 \)	21T164	Trivial (GRH)
21.3.1096847526176305781614017478618875579.1	x^21 - 3x - 1	\( -\,3^{22}\cdot 19\cdot 311\cdot 1453\cdot 95947\cdot 42429474395849 \)	21T164	Trivial (GRH)
21.1.1096847537861479818385982521381124421.1	x^21 + 3x - 1	\( 3^{21}\cdot 127\cdot 4165522027\cdot 198210546660683 \)	21T164	Trivial (GRH)
21.1.1102973928544283900008339733920874496.1	x^21 + 3x - 2	\( 2^{20}\cdot 3^{21}\cdot 904762091\cdot 111143633077 \)	21T164	Trivial (GRH)
21.7.1278927368949842240390233024324879232.1	x^21 - 3x^20 - 2x^19 + 16x^18 - 12x^17 - 27x^16 + 46x^15 + 13x^14 - 76x^13 + 26x^12 + 79x^11 - 73x^10 - 38x^9 + 86x^8 - 18x^7 - 47x^6 + 35x^5 + 6x^4 - 15x^3 + 4x^2 + 2x - 1	\( -\,2^{7}\cdot 43\cdot 5795579\cdot 27741107\cdot 364589707\cdot 3964080223 \)	21T164	Trivial (GRH)
21.3.1321708824364052697732741363499420784.1	x^21 - 2x^20 - 2x^19 + 6x^18 + 3x^17 - 14x^16 - x^15 + 22x^14 - 7x^13 - 21x^12 + 12x^11 + 13x^10 - 12x^9 - x^8 + 4x^7 - 7x^6 + 6x^5 + 3x^4 - 7x^3 + 2x^2 + x - 1	\( -\,2^{4}\cdot 2409859\cdot 34278686646294780569442583661 \)	21T164	Trivial (GRH)
21.1.1568357403125939202134971883743870976.1	x^21 - 4x - 8	\( 2^{28}\cdot 677\cdot 680193605783\cdot 12687730522631 \)	21T164	Trivial (GRH)
21.1.1568357617874304002134971883743870976.1	x^21 + 4x - 8	\( 2^{28}\cdot 23\cdot 9257\cdot 126173\cdot 217490699493582407 \)	21T164	Trivial (GRH)
21.5.4972491713626942997259510586001451652.1	x^21 - 3x^20 - 2x^19 + 16x^18 - 12x^17 - 27x^16 + 46x^15 + 13x^14 - 76x^13 + 26x^12 + 79x^11 - 73x^10 - 38x^9 + 86x^8 - 18x^7 - 47x^6 + 34x^5 + 6x^4 - 14x^3 + 4x^2 + 2x - 1	\( 2^{2}\cdot 8543\cdot 38299\cdot 309599\cdot 11606649319\cdot 1057328219989 \)	21T164	Trivial (GRH)
21.1.6273430042000486408442231284975483904.1	x^21 - x - 8	\( 2^{10}\cdot 17\cdot 193\cdot 2857\cdot 3301\cdot 197989932505647143962363 \)	21T164	Trivial (GRH)
21.17.12467389482269010020495422048363303168.1	x^21 - 3x^20 - 17x^19 + 52x^18 + 120x^17 - 368x^16 - 466x^15 + 1380x^14 + 1119x^13 - 2978x^12 - 1768x^11 + 3759x^10 + 1869x^9 - 2699x^8 - 1272x^7 + 1022x^6 + 510x^5 - 168x^4 - 104x^3 + 4x^2 + 8x + 1	\( 2^{8}\cdot 1009\cdot 81515745041\cdot 592110678165795251537 \)	21T164	Trivial (GRH)
21.1.17081298681136665652610353606982956821.1	x^21 - 9x - 9	\( 3^{22}\cdot 544318735376220280153458269 \)	21T164	Trivial (GRH)
21.1.19274993745174451252610353606982956821.1	x^21 - 3x - 3	\( 3^{21}\cdot 59\cdot 839\cdot 1225456459\cdot 30376381535273 \)	21T164	Trivial (GRH)
21.1.20371621374867788852610353606982956821.1	x^21 - 2x - 3	\( 1499\cdot 13590141010585582957044932359561679 \)	21T164	Trivial (GRH)
21.1.20371841277088486452610353606982956821.1	x^21 - x - 3	\( 18390874357\cdot 1107714667700640550497038753 \)	21T164	Trivial (GRH)
21.1.20371841277298201652610353606982956821.1	x^21 + x - 3	\( 11\cdot 350737\cdot 498579131\cdot 10590633019722418894813 \)	21T164	Trivial (GRH)
21.1.21468688809212236852610353606982956821.1	x^21 + 3x - 3	\( 3^{21}\cdot 30941\cdot 66332264830763738743427 \)	21T164	Trivial (GRH)
21.1.23662383873250022452610353606982956821.1	x^21 + 9x - 9	\( 3^{22}\cdot 37\cdot 139\cdot 193\cdot 223\cdot 3406529823078090997 \)	21T164	Trivial (GRH)
21.13.30991632631127242005516305991156547228.1	x^21 - 5x^20 - 6x^19 + 63x^18 - 19x^17 - 327x^16 + 261x^15 + 911x^14 - 932x^13 - 1507x^12 + 1644x^11 + 1590x^10 - 1570x^9 - 1166x^8 + 816x^7 + 619x^6 - 241x^5 - 199x^4 + 49x^3 + 24x^2 - 3x - 1	\( 2^{2}\cdot 31\cdot 43\cdot 15053\cdot 102413451780923\cdot 3770285596717141 \)	21T164	Trivial (GRH)
21.13.45756205480679415294398559964416419984.1	x^21 - 5x^20 - 6x^19 + 63x^18 - 19x^17 - 327x^16 + 261x^15 + 911x^14 - 932x^13 - 1507x^12 + 1644x^11 + 1590x^10 - 1570x^9 - 1166x^8 + 816x^7 + 619x^6 - 241x^5 - 200x^4 + 49x^3 + 25x^2 - 3x - 1	\( 2^{4}\cdot 103\cdot 426103\cdot 1287491\cdot 50609727688176358507171 \)	21T164	Trivial (GRH)
21.1.55860712804853791800008339733920874496.1	x^21 + 7x - 4	\( 2^{22}\cdot 7^{21}\cdot 23844472998457 \)	21T164	Trivial (GRH)
21.3.461162475446213399299991660266079125504.1	x^21 - 4x - 2	\( -\,2^{20}\cdot 173\cdot 1049\cdot 3549047\cdot 5087141\cdot 134229178198501 \)	21T164	Trivial (GRH)
21.3.461168601836896203381614017478618875579.1	x^21 - 4x - 1	\( -\,2857\cdot 3617\cdot 16240009\cdot 1502702379439\cdot 1828696957541 \)	21T164	Trivial (GRH)
21.1.461168601848581377418385982521381124421.1	x^21 + 4x - 1	\( 9011\cdot 15319\cdot 197364859\cdot 16927253439956600727491 \)	21T164	$[2]$ (GRH)
21.1.461174728239264181500008339733920874496.1	x^21 + 4x - 2	\( 2^{20}\cdot 123570257\cdot 267931349351\cdot 13283976726403 \)	21T164	Trivial (GRH)
21.1.481540443119932134452610353606982956821.1	x^21 + 4x - 3	\( 71\cdot 239\cdot 2229547\cdot 19807187\cdot 642594619262084283581 \)	21T164	Trivial (GRH)
21.3.922331077288952189699991660266079125504.1	x^21 - 8x - 4	\( -\,2^{20}\cdot 13\cdot 2707\cdot 3225203\cdot 87763589107\cdot 88304714389 \)	21T164	Trivial (GRH)
21.1.922343330082002971900008339733920874496.1	x^21 + 8x - 4	\( 2^{20}\cdot 199\cdot 761\cdot 1063\cdot 61811602837\cdot 88399883995369 \)	21T164	Trivial (GRH)
21.1.1605998035776543131786211208953723879424.1	x^21 - 2x - 4	\( 2^{38}\cdot 366433\cdot 15944488674289658740837 \)	21T164	Trivial (GRH)
21.1.1605998145727705909386211208953723879424.1	x^21 + 2x - 4	\( 2^{38}\cdot 13\cdot 739\cdot 12917\cdot 142169\cdot 331169891171711 \)	21T164	Trivial (GRH)
21.3.2398805552525318552378460195249857876691.1	x^21 - 9x - 1	\( -\,3^{7}\cdot 193\cdot 6645319\cdot 24979399\cdot 34236639882687055721 \)	21T164	Trivial (GRH)
21.1.2398805552525318554821539804750142123309.1	x^21 + 9x - 1	\( 3^{7}\cdot 39161\cdot 28008670157015724842535835757087 \)	21T164	Trivial (GRH)
21.17.2725960527801648753674435845823096440269.1	x^21 - 2x^20 - 19x^19 + 34x^18 + 151x^17 - 233x^16 - 653x^15 + 831x^14 + 1676x^13 - 1665x^12 - 2626x^11 + 1895x^10 + 2517x^9 - 1184x^8 - 1458x^7 + 363x^6 + 489x^5 - 33x^4 - 86x^3 - 6x^2 + 6x + 1	\( 3\cdot 683\cdot 1240271\cdot 39356833\cdot 49784320121\cdot 547454828827 \)	21T164	Trivial (GRH)
21.1.3807145062155006491195419919836285763584.1	x^21 + 9x - 8	\( 2^{40}\cdot 3^{7}\cdot 269\cdot 643\cdot 2339\cdot 2857\cdot 30851\cdot 44399477 \)	21T164	Trivial (GRH)
21.1.4359839315257579230676211464792429636149.1	x^21 - 3x - 7	\( 3^{21}\cdot 265403271457\cdot 1570427394240602519 \)	21T164	Trivial (GRH)