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 247)

Label	Polynomial	Discriminant	Galois group	Class group
21.1.238583305854552412020101.1	x^21 - 6x^18 - 6x^16 + 8x^15 - 8x^14 + 17x^13 - 3x^12 + 23x^11 - 28x^10 - 11x^9 - 45x^8 - 14x^7 - 44x^6 - 17x^5 - 21x^4 - 4x^3 - 8x^2 - 1	\( 23^{7}\cdot 41227^{3} \)	21T62	Trivial (GRH)
21.1.21420980525151261442929721.1	x^21 - x^20 - x^19 + 2x^18 + 2x^17 + x^16 - 5x^15 - x^14 + 13x^13 + 9x^12 - 7x^11 - 16x^10 - x^9 + 21x^8 + 17x^7 - 3x^6 - 11x^5 - 3x^4 + 4x^3 + 3x^2 - 1	\( 23^{7}\cdot 184607^{3} \)	21T74	Trivial (GRH)
21.1.23714597990105054274863104.1	x^21 + x^19 - 5x^18 + 8x^17 - 5x^16 + 11x^15 - 40x^14 + 33x^13 + 2x^12 + 62x^11 - 87x^10 - 12x^9 - 43x^8 + 76x^7 + 27x^6 - 15x^5 - 7x^4 - 10x^3 + 2x^2 + x + 1	\( 2^{14}\cdot 11^{8}\cdot 41^{3}\cdot 461^{3} \)	21T74	Trivial (GRH)
21.1.75911839528959490356446229.1	x^21 - x^18 - 3x^15 + 2x^12 + 4x^9 - x^6 - 2x^3 - 1	\( 3^{21}\cdot 193607^{3} \)	21T138	Trivial (GRH)
21.1.156106141952973043121291857.1	x^21 - x^20 - x^19 + 2x^18 + 5x^17 + 2x^16 - 10x^15 - 2x^14 + 23x^13 + 19x^12 - 11x^11 - 28x^10 + 8x^9 + 47x^8 + 23x^7 - 13x^6 - 24x^5 - 7x^4 + 11x^3 + 6x^2 - 1	\( 23^{7}\cdot 71^{9} \)	$S_3\times D_7$ (as 21T8)	Trivial (GRH)
21.1.1261412107834594448324876441.1	x^21 + 3x^19 - x^18 + x^17 + 8x^16 - 7x^15 + 24x^14 - 15x^13 + 7x^12 + 25x^11 - 42x^10 + 46x^9 - 39x^8 - 12x^7 + 15x^6 - 14x^5 + x^4 + 10x^3 - x^2 + 2x + 1	\( 31^{7}\cdot 71^{9} \)	$S_3\times D_7$ (as 21T8)	Trivial (GRH)
21.1.1901751171347368714361726129.1	x^21 - x^14 + 1	\( 7^{21}\cdot 23^{7} \)	21T29	Trivial (GRH)
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)
21.1.9900725472657912423302447104.1	x^21 - 3x^20 - 2x^19 + 25x^18 - 40x^17 - 24x^16 + 156x^15 - 215x^14 + 131x^13 - 57x^12 + 294x^11 - 907x^10 + 1374x^9 - 1171x^8 + 439x^7 + 387x^6 - 847x^5 + 669x^4 - 179x^3 - 142x^2 + 156x - 38	\( 2^{14}\cdot 11^{10}\cdot 13^{12} \)	$D_{21}:C_3$ (as 21T10)	Trivial (GRH)
21.1.15367056821818447650208822777.1	x^21 + x^7 - 1	\( 7^{21}\cdot 31^{7} \)	21T29	Trivial (GRH)
21.1.34154868120917133312000000000.1	x^21 - 10x^18 + 36x^15 - 76x^12 - 224x^9 - 144x^6 - 32x^3 - 16	\( 2^{20}\cdot 3^{34}\cdot 5^{9} \)	$S_3\times F_7$ (as 21T15)	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)
21.1.265283078340996577927735640721.1	x^21 - 8x^20 + 36x^19 - 114x^18 + 285x^17 - 562x^16 + 781x^15 - 627x^14 + 169x^13 - 27x^12 + 434x^11 - 868x^10 + 760x^9 - 92x^8 - 397x^7 + 225x^6 + 212x^5 - 441x^4 + 355x^3 - 154x^2 + 34x - 3	\( 3^{16}\cdot 151^{10} \)	21T51	Trivial (GRH)
21.1.265283078340996577927735640721.2	x^21 - 4x^20 + 15x^19 - 38x^18 + 87x^17 - 166x^16 + 291x^15 - 534x^14 + 954x^13 - 1218x^12 + 1775x^11 - 1990x^10 + 2612x^9 - 2193x^8 + 2151x^7 - 1538x^6 + 990x^5 - 641x^4 + 574x^3 + 439x^2 + 407x + 169	\( 3^{16}\cdot 151^{10} \)	21T75	Trivial (GRH)
21.1.265283078340996577927735640721.3	x^21 - 6x^20 + 12x^19 - 4x^18 - 7x^17 - 47x^16 + 158x^15 - 112x^14 - 277x^13 + 800x^12 - 683x^11 - 929x^10 + 3169x^9 - 2711x^8 - 1350x^7 + 4467x^6 - 2049x^5 - 2691x^4 + 4230x^3 - 2223x^2 + 378x + 81	\( 3^{16}\cdot 151^{10} \)	21T75	Trivial (GRH)
21.1.1078228439505013455412874919936.1	x^21 - 3x^19 - 2x^18 - 9x^17 - 12x^16 + 23x^15 + 54x^14 + 36x^13 + 8x^12 - 243x^11 - 810x^10 - 351x^9 + 2196x^8 + 6807x^7 + 14494x^6 + 22572x^5 + 23256x^4 + 15184x^3 + 6048x^2 + 1344x + 128	\( 2^{14}\cdot 3^{21}\cdot 184607^{3} \)	21T152	Trivial (GRH)
21.1.1078228439505013455412874919936.2	x^21 + 3x^19 - 2x^18 - 27x^17 + 12x^16 - 27x^15 - 36x^14 + 381x^13 - 192x^12 - 27x^11 + 198x^10 - 1026x^9 - 954x^8 + 2655x^7 + 98x^6 - 1116x^5 + 480x^4 + 368x^3 - 288x^2 - 192x + 128	\( 2^{14}\cdot 3^{21}\cdot 184607^{3} \)	21T152	Trivial (GRH)
21.1.7083212072929370650536855994368.1	x^21 - 18x^18 + 90x^15 - 108x^12 + 432x^9 + 1296x^6 - 216x^3 + 864	\( 2^{26}\cdot 3^{27}\cdot 7^{12} \)	$S_3\times F_7$ (as 21T15)	Trivial (GRH)
21.1.7857627321843320792892969664512.1	x^21 - 3x^19 - 2x^18 - 9x^17 - 12x^16 + 23x^15 + 54x^14 - 45x^13 - 208x^12 - 459x^11 - 906x^10 + 362x^9 + 5112x^8 + 11667x^7 + 18814x^6 + 24732x^5 + 23832x^4 + 15248x^3 + 6048x^2 + 1344x + 128	\( 2^{14}\cdot 3^{21}\cdot 71^{9} \)	21T131	Trivial (GRH)
21.1.7857627321843320792892969664512.2	x^21 + 6x^19 - 2x^18 + 36x^17 + 18x^16 + 135x^15 + 18x^14 + 300x^13 + 448x^12 + 1620x^11 + 2160x^10 + 2722x^9 + 2538x^8 + 3087x^7 + 3382x^6 + 1944x^5 - 168x^4 - 608x^3 - 576x^2 - 192x - 128	\( 2^{14}\cdot 3^{21}\cdot 71^{9} \)	21T131	Trivial (GRH)
21.1.21487929345620722812146586898401.1	x^21 - 9x^20 + 37x^19 - 84x^18 + 105x^17 - 62x^16 + 92x^15 - 450x^14 + 800x^13 + 216x^12 - 1254x^11 - 2043x^10 + 6711x^9 - 3102x^8 - 7x^7 - 2603x^6 + 6489x^5 - 6487x^4 + 3977x^3 - 1257x^2 + 160x + 1	\( 3^{20}\cdot 151^{10} \)	21T51	$[3]$ (GRH)
21.1.39987268032456435383175526376221.1	x^21 + 21x^19 + 189x^17 + 952x^15 + 2940x^13 + 5733x^11 + 7007x^9 + 5144x^7 + 2051x^5 + 329x^3 - 7x - 1	\( 7^{19}\cdot 23^{7}\cdot 101^{3} \)	21T87	Trivial (GRH)
21.1.219908168142218385982521381124421.1	x^21 + 2x - 1	\( 59\cdot 997\cdot 3738472504670254593994209427 \)	21T164	Trivial (GRH)
21.1.283127009136682212088030700907133.1	x^21 + 21x^19 + 189x^17 + 952x^15 - 8x^14 + 2940x^13 - 112x^12 + 5733x^11 - 616x^10 + 7007x^9 - 1680x^8 + 5166x^7 - 2352x^6 + 2205x^5 - 1568x^4 + 637x^3 - 392x^2 + 147x - 19	\( 7^{21}\cdot 23^{7}\cdot 53^{3} \)	21T87	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)
21.1.2322524889444393135652695649026048.1	x^21 - 7x^20 + 11x^19 - x^18 + 29x^17 - 31x^16 - 207x^15 + 283x^14 + 178x^13 - 774x^12 + 1676x^11 - 1948x^10 - 1140x^9 + 7012x^8 - 10652x^7 + 6060x^6 + 7976x^5 - 23032x^4 + 27464x^3 - 19144x^2 + 7592x - 1352	\( 2^{33}\cdot 3^{19}\cdot 7^{17} \)	$S_3\times F_7$ (as 21T15)	$[3]$ (GRH)
21.1.2421032603211455207440720697704448.1	x^21 - 6x^20 + 16x^19 - 26x^18 + 29x^17 - 36x^16 + 50x^15 - 50x^14 + 35x^13 - 14x^12 + 100x^11 - 22x^10 - 25x^9 - 112x^8 - 78x^7 - 286x^6 - 632x^5 - 1000x^4 - 1000x^3 - 688x^2 - 288x - 64	\( 2^{14}\cdot 11^{10}\cdot 283^{3}\cdot 6311^{3} \)	21T62	Trivial (GRH)
21.1.2807535013090453863383795166015625.1	x^21 - 7x^20 + 35x^19 - 112x^18 + 266x^17 - 490x^16 + 693x^15 - 1355x^14 + 3360x^13 - 7224x^12 + 12166x^11 - 16709x^10 + 21700x^9 - 32417x^8 + 39987x^7 - 39067x^6 + 26600x^5 - 12320x^4 + 4389x^3 - 1575x^2 + 945x - 405	\( 5^{14}\cdot 7^{28} \)	$D_{21}$ (as 21T5)	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)
21.1.6126396525391100008339733920874496.1	x^21 - 2	\( 2^{20}\cdot 3^{21}\cdot 7^{21} \)	$S_3\times F_7$ (as 21T15)	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)
21.1.116234663759754077598636637937221632.1	x^21 + 12x^19 - 8x^18 + 108x^17 - 144x^16 + 642x^15 - 1188x^14 + 3222x^13 - 6656x^12 + 13527x^11 - 26370x^10 + 44193x^9 - 70452x^8 + 102702x^7 - 135604x^6 + 159192x^5 - 145872x^4 + 91808x^3 - 36288x^2 + 8064x - 768	\( 2^{14}\cdot 3^{17}\cdot 11^{9}\cdot 13^{12} \)	21T142	Trivial (GRH)
21.1.140982304436617562370493756640408961.1	x^21 - 9x^19 - x^18 + 90x^17 + 33x^16 - 517x^15 + 792x^14 + 2043x^13 - 5479x^12 + 1746x^11 + 30675x^10 - 29471x^9 - 28809x^8 + 255240x^7 - 240039x^6 + 419256x^5 + 41958x^4 + 4131x^3 + 176418x^2 - 546750x + 270459	\( 3^{28}\cdot 151^{10} \)	$D_{21}$ (as 21T5)	Trivial (GRH)
21.1.297767057903624960000000000000000000.1	x^21 + 21x^19 - 2x^18 + 209x^17 - 26x^16 + 1081x^15 - 450x^14 + 2345x^13 - 2990x^12 - 107x^11 - 5360x^10 - 1817x^9 + 13424x^8 + 28897x^7 + 59776x^6 + 72068x^5 + 63024x^4 + 32992x^3 + 7616x^2 + 576x + 64	\( 2^{26}\cdot 5^{19}\cdot 7^{17} \)	$S_3\times F_7$ (as 21T15)	$[3]$ (GRH)
21.1.301059380309170415238823998755176448.1	x^21 - 68x^14 + 1294x^7 + 32	\( 2^{33}\cdot 7^{21}\cdot 13^{7} \)	$S_3\times F_7$ (as 21T15)	Trivial (GRH)
21.1.309663421430338978631523663046883017.1	x^21 - 28x^17 - 14x^16 + 189x^15 - 418x^14 - 2009x^13 + 1960x^12 + 7406x^11 - 5600x^10 - 13370x^9 + 23842x^8 + 70415x^7 + 78400x^6 + 40278x^5 - 14868x^4 - 24325x^3 - 490x^2 + 3136x - 1128	\( 7^{21}\cdot 31^{7}\cdot 67^{4} \)	21T102	Trivial (GRH)
21.1.886508722213234018394285560019042304.1	x^21 - 42x^18 + 672x^15 - 392x^12 - 4480x^9 - 7840x^6 - 4928x^3 - 1024	\( 2^{14}\cdot 3^{24}\cdot 7^{24} \)	$D_{21}:C_3$ (as 21T10)	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)
21.1.1568357403125939202134971883743870976.1	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)
21.1.5210503898883871484358277809046552576.1	x^21 - 21x^19 + 189x^17 - 952x^15 - 10x^14 + 2940x^13 + 140x^12 - 5733x^11 - 770x^10 + 7007x^9 + 2100x^8 - 5111x^7 - 2940x^6 + 1820x^5 + 1960x^4 + 133x^3 - 490x^2 - 238x - 38	\( 2^{20}\cdot 7^{24}\cdot 11^{10} \)	21T72	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)