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 149)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.11485810791015625.1	x^16 - 3x^15 + x^14 + 8x^13 - 11x^12 - 2x^11 + 12x^10 - x^9 - 9x^8 + 7x^6 - x^5 + 4x^4 - 15x^3 + 15x^2 - 6x + 1	\( 5^{12}\cdot 19^{6} \)	$D_4:C_4$ (as 16T26)	Trivial
16.4.4146377695556640625.1	x^16 - 2x^15 - 5x^14 + 20x^13 - 16x^12 - 27x^11 + 23x^10 + 60x^9 - 134x^8 + 73x^7 - 27x^6 + 24x^5 + 29x^4 - 24x^3 - 16x^2 + x + 1	\( 5^{12}\cdot 19^{8} \)	$D_4:C_4$ (as 16T26)	Trivial (GRH)
16.4.4611686018427387904.1	x^16 - 8x^14 + 12x^12 + 8x^10 - 90x^8 + 8x^6 + 12x^4 - 8x^2 + 1	\( 2^{62} \)	$D_4:C_4$ (as 16T26)	Trivial (GRH)
16.0.4611686018427387904.4	x^16 - 8x^14 + 40x^12 - 96x^10 + 140x^8 - 48x^6 + 16x^4 + 4	\( 2^{62} \)	$D_4:C_4$ (as 16T26)	Trivial (GRH)
16.0.10297981845947265625.1	x^16 - 4x^15 + 8x^14 - 8x^13 + 8x^12 - 10x^11 - 6x^10 + 71x^9 - 137x^8 + 103x^7 + 51x^6 - 194x^5 + 213x^4 - 124x^3 + 37x^2 + x + 1	\( 5^{12}\cdot 59^{6} \)	$D_4:C_4$ (as 16T26)	Trivial
16.0.59347523320556640625.1	x^16 - 3x^15 + 4x^14 - 8x^13 + 21x^12 - 46x^11 + 67x^10 - 89x^9 + 157x^8 - 227x^7 + 293x^6 - 342x^5 + 321x^4 - 284x^3 + 176x^2 - 56x + 16	\( 5^{12}\cdot 79^{6} \)	$D_4:C_4$ (as 16T26)	Trivial
16.0.73786976294838206464.1	x^16 - 8x^14 + 28x^12 - 40x^10 + 10x^8 + 24x^6 + 20x^4 - 8x^2 + 1	\( 2^{66} \)	$D_4:C_4$ (as 16T26)	Trivial
16.4.73786976294838206464.5	x^16 - 8x^14 + 12x^12 + 8x^10 - 34x^8 + 8x^6 + 12x^4 - 8x^2 + 1	\( 2^{66} \)	$D_4:C_4$ (as 16T26)	Trivial (GRH)
16.0.259160193017822265625.5	x^16 - 6x^15 + 15x^14 - 25x^13 + 46x^12 - 55x^11 - 21x^10 + 10x^9 + 431x^8 - 1005x^7 + 1020x^6 - 536x^5 + 201x^4 - 210x^3 + 235x^2 - 125x + 25	\( 5^{12}\cdot 101^{6} \)	$D_4:C_4$ (as 16T26)	$[2]$
16.0.3448952743104148720609.2	x^16 - x^15 + 6x^14 - 4x^13 - 2x^12 + 17x^11 + 29x^10 + 93x^9 + 178x^8 + 91x^7 - 86x^6 + 143x^5 + 432x^4 + 133x^3 - 115x^2 + 8x + 53	\( 13^{12}\cdot 23^{6} \)	$D_4:C_4$ (as 16T26)	Trivial
16.0.4798972012257385719849.2	x^16 - 2x^15 + 9x^13 - 68x^11 + 114x^10 + 271x^9 - 166x^8 - 444x^7 + 989x^6 - 389x^5 - 157x^4 + 366x^3 - 55x^2 - 39x + 47	\( 3^{6}\cdot 37^{12} \)	$D_4:C_4$ (as 16T26)	Trivial
16.0.8584430743916259765625.1	x^16 - 2x^15 - 5x^14 + 20x^13 - x^12 - 12x^11 - 42x^10 - 80x^9 + 681x^8 - 482x^7 - 1002x^6 + 1879x^5 - 386x^4 - 1089x^3 + 1089x^2 - 459x + 81	\( 5^{12}\cdot 181^{6} \)	$D_4:C_4$ (as 16T26)	$[2]$ (GRH)
16.4.35847274805742431640625.2	x^16 - 8x^14 - 25x^13 + 19x^12 + 80x^11 + 98x^10 - 145x^9 - 364x^8 - 140x^7 + 380x^6 - 755x^5 + 180x^4 + 825x^3 - 200x^2 - 200x + 25	\( 5^{12}\cdot 59^{8} \)	$D_4:C_4$ (as 16T26)	Trivial (GRH)
16.4.43190748110316471478641.1	x^16 + 6x^14 - 75x^12 - 24x^10 + 82x^8 + 1086x^6 + 924x^4 + 228x^2 + 1	\( 3^{8}\cdot 37^{12} \)	$D_4:C_4$ (as 16T26)	Trivial (GRH)
16.0.147275654405708032604569.2	x^16 - 5x^15 + 14x^14 - 23x^13 + 41x^12 - 73x^11 + 87x^10 + 62x^9 - 240x^8 - 66x^7 + 1168x^6 - 2361x^5 + 2538x^4 - 1836x^3 + 810x^2 - 729x + 729	\( 13^{12}\cdot 43^{6} \)	$D_4:C_4$ (as 16T26)	Trivial (GRH)
16.4.370387893043593994140625.1	x^16 - 6x^15 + 7x^14 + 17x^13 + 16x^12 - 229x^11 - 18x^10 + 1571x^9 - 1788x^8 - 2765x^7 + 4913x^6 + 3963x^5 - 9488x^4 - 1264x^3 + 6964x^2 + 505x - 1999	\( 5^{12}\cdot 79^{8} \)	$D_4:C_4$ (as 16T26)	Trivial (GRH)
16.0.516387172268851080441049.9	x^16 - 4x^15 + 9x^14 - 25x^13 + 61x^12 - 119x^11 + 219x^10 - 410x^9 + 751x^8 - 1230x^7 + 1971x^6 - 3213x^5 + 4941x^4 - 6075x^3 + 6561x^2 - 8748x + 6561	\( 13^{12}\cdot 53^{6} \)	$D_4:C_4$ (as 16T26)	$[4]$ (GRH)
16.0.1200326067404665657109641.2	x^16 + 30x^14 + 257x^12 + 965x^10 + 1800x^8 + 1706x^6 + 777x^4 + 134x^2 + 1	\( 13^{12}\cdot 61^{6} \)	$D_4:C_4$ (as 16T26)	$[2]$ (GRH)
16.0.1700350026389931884765625.1	x^16 - x^15 + 3x^14 + 7x^13 + 93x^12 - 18x^11 + 1061x^10 + 426x^9 + 4268x^8 + 3118x^7 + 8099x^6 + 7574x^5 + 3478x^4 + 556x^3 + 67x^2 + 8x + 1	\( 3^{8}\cdot 5^{12}\cdot 101^{6} \)	$D_4:C_4$ (as 16T26)	$[2, 12]$ (GRH)
16.16.1700350026389931884765625.1	x^16 - 5x^15 - 18x^14 + 132x^13 - 53x^12 - 762x^11 + 899x^10 + 1736x^9 - 2845x^8 - 1761x^7 + 3857x^6 + 741x^5 - 2413x^4 - 127x^3 + 602x^2 + 46x - 29	\( 3^{8}\cdot 5^{12}\cdot 101^{6} \)	$D_4:C_4$ (as 16T26)	Trivial (GRH)
16.4.1824496001102094673202161.1	x^16 - 17x^14 + 20x^12 + 201x^10 - 605x^8 - 395x^6 + 908x^4 - 477x^2 + 81	\( 13^{12}\cdot 23^{8} \)	$D_4:C_4$ (as 16T26)	Trivial (GRH)
16.0.1935020402262940309416009.1	x^16 - 2x^15 + 24x^13 + 68x^12 - 27x^11 + 120x^10 + 1216x^9 + 1120x^8 - 486x^7 + 1699x^6 + 4434x^5 + 2142x^4 - 72x^3 + 468x^2 + 189x + 81	\( 3^{6}\cdot 61^{12} \)	$D_4:C_4$ (as 16T26)	$[3]$ (GRH)
16.0.2643693128974804931640625.14	x^16 - 4x^15 - 8x^14 + 39x^13 + 44x^12 - 204x^11 - 62x^10 + 441x^9 - 82x^8 - 576x^7 + 2523x^6 + 1307x^5 - 415x^4 + 4773x^3 + 3571x^2 - 2668x + 6091	\( 5^{12}\cdot 101^{8} \)	$D_4:C_4$ (as 16T26)	$[2, 8]$ (GRH)
16.4.6280210550563314266206369.2	x^16 - 6x^15 + 27x^14 - 88x^13 + 262x^12 - 574x^11 + 972x^10 - 647x^9 - 1301x^8 + 8015x^7 - 21484x^6 + 40219x^5 - 51101x^4 + 40562x^3 - 18496x^2 + 4080x - 272	\( 17^{12}\cdot 47^{6} \)	$D_4:C_4$ (as 16T26)	Trivial (GRH)
16.4.7921483191352215537023449.1	x^16 - 12x^14 + 46x^12 + 15x^10 + 229x^8 + 378x^6 - 1652x^4 - 3117x^2 + 16	\( 17^{14}\cdot 19^{6} \)	$D_4:C_4$ (as 16T26)	$[2]$ (GRH)
16.0.8680963974111420152283136.1	x^16 + 24x^14 + 212x^12 + 920x^10 + 2138x^8 + 2680x^6 + 1724x^4 + 504x^2 + 49	\( 2^{66}\cdot 7^{6} \)	$D_4:C_4$ (as 16T26)	$[42]$ (GRH)
16.16.8680963974111420152283136.1	x^16 - 24x^14 + 212x^12 - 920x^10 + 2138x^8 - 2680x^6 + 1724x^4 - 504x^2 + 49	\( 2^{66}\cdot 7^{6} \)	$D_4:C_4$ (as 16T26)	Trivial (GRH)
16.0.8680963974111420152283136.2	x^16 - 8x^14 + 36x^12 - 104x^10 + 62x^8 + 680x^6 - 252x^4 + 392x^2 + 2401	\( 2^{66}\cdot 7^{6} \)	$D_4:C_4$ (as 16T26)	$[6]$ (GRH)
16.0.11662101038417978742443641.1	x^16 - 3x^15 + 14x^14 - 7x^13 + 42x^12 + 65x^11 + 260x^10 + 545x^9 + 1144x^8 + 1425x^7 + 3221x^6 + 5823x^5 + 8911x^4 + 7300x^3 + 5422x^2 + 2527x + 1913	\( 11^{6}\cdot 37^{12} \)	$D_4:C_4$ (as 16T26)	Trivial (GRH)
16.0.16984322409616000000000000.1	x^16 - 18x^14 - 6x^13 + 194x^12 - 144x^11 - 756x^10 + 1658x^9 + 877x^8 - 8328x^7 + 6409x^6 + 17442x^5 - 21019x^4 - 3760x^3 + 31760x^2 - 28210x + 12505	\( 2^{16}\cdot 5^{12}\cdot 101^{6} \)	$D_4:C_4$ (as 16T26)	$[2, 12]$ (GRH)
16.4.17415183620366462784744081.2	x^16 + 8x^14 + 70x^12 - 1034x^10 + 1331x^8 + 3298x^6 - 9317x^4 + 5213x^2 + 25	\( 3^{8}\cdot 61^{12} \)	$D_4:C_4$ (as 16T26)	$[3]$ (GRH)
16.4.52703064995487500398531609.9	x^16 - 2x^15 - 18x^14 + 4x^13 + 60x^12 + 102x^11 - 518x^10 + 12x^9 + 1586x^8 - 1084x^7 - 3484x^6 + 2210x^5 + 3045x^4 - 618x^3 - 280x^2 + 40x + 16	\( 17^{12}\cdot 67^{6} \)	$D_4:C_4$ (as 16T26)	Trivial (GRH)
16.0.57796118826899575367359009.1	x^16 + 33x^14 + 439x^12 + 3115x^10 + 12870x^8 + 31993x^6 + 50837x^4 + 56842x^2 + 289	\( 7^{6}\cdot 53^{12} \)	$D_4:C_4$ (as 16T26)	Trivial (GRH)
16.4.272312684996154152285848081.3	x^16 - 6x^15 + 5x^14 + 6x^13 + 114x^12 - 149x^11 - 1077x^10 + 1048x^9 + 6044x^8 - 5701x^7 - 27441x^6 + 50594x^5 + 3095x^4 - 72878x^3 + 68978x^2 - 39611x + 8567	\( 13^{12}\cdot 43^{8} \)	$D_4:C_4$ (as 16T26)	Trivial (GRH)
16.0.870295115683950043241964601.1	x^16 - 8x^15 + 27x^14 - 38x^13 + 57x^12 - 401x^11 + 651x^10 + 4547x^9 - 15357x^8 + 4513x^7 + 39317x^6 - 50833x^5 + 7276x^4 + 9972x^3 - 2741x^2 + 4675x + 2333	\( 11^{6}\cdot 53^{12} \)	$D_4:C_4$ (as 16T26)	$[3]$ (GRH)
16.4.1064377371083527836156872521.1	x^16 - 10x^14 - 102x^13 + 31x^12 + 680x^11 + 2855x^10 - 782x^9 - 8865x^8 - 18904x^7 + 12775x^6 + 25262x^5 + 2222x^4 - 1564x^3 + 1601x^2 + 340x + 16	\( 17^{14}\cdot 43^{6} \)	$D_4:C_4$ (as 16T26)	$[2]$ (GRH)
16.4.1411114225648575427835680561.3	x^16 - 2x^15 - 23x^14 + 83x^13 - 224x^12 + 705x^11 - 867x^10 - 1031x^9 + 4119x^8 - 11312x^7 + 30835x^6 - 50087x^5 + 53816x^4 - 88249x^3 + 60104x^2 - 46032x + 21217	\( 11^{8}\cdot 37^{12} \)	$D_4:C_4$ (as 16T26)	Trivial (GRH)
16.0.1450531566903202684958906641.14	x^16 - 2x^15 + 11x^14 + 15x^13 - 158x^12 + 284x^11 - 645x^10 - 1199x^9 + 3388x^8 - 7527x^7 + 27009x^6 + 10084x^5 + 65215x^4 + 77819x^3 + 99002x^2 + 96729x + 30663	\( 13^{12}\cdot 53^{8} \)	$D_4:C_4$ (as 16T26)	$[2, 16]$ (GRH)
16.4.1814980849112797822933640641.7	x^16 - 8x^15 + 32x^14 - 84x^13 + 229x^12 - 646x^11 + 909x^10 + 328x^9 - 2178x^8 + 1354x^7 - 6237x^6 + 20672x^5 - 13540x^4 - 9104x^3 + 11280x^2 - 3008x + 256	\( 17^{14}\cdot 47^{6} \)	$D_4:C_4$ (as 16T26)	$[6]$ (GRH)
16.0.2371212900396504113756570569.11	x^16 - 8x^15 + 70x^14 - 350x^13 + 1620x^12 - 5534x^11 + 16658x^10 - 39950x^9 + 82520x^8 - 138670x^7 + 196253x^6 - 223525x^5 + 206961x^4 - 147037x^3 + 78283x^2 - 27292x + 5077	\( 13^{6}\cdot 53^{12} \)	$D_4:C_4$ (as 16T26)	$[8]$ (GRH)
16.4.2832009822518079193000591441.2	x^16 - 34x^14 - 64x^13 - 207x^12 + 572x^11 + 506x^10 + 3145x^9 - 4908x^8 - 1846x^7 - 10717x^6 + 12322x^5 + 11734x^4 + 7963x^3 - 5634x^2 - 9429x + 4529	\( 7^{8}\cdot 53^{12} \)	$D_4:C_4$ (as 16T26)	Trivial (GRH)
16.0.2859655432078149808865465089.1	x^16 - 4x^15 + 2x^14 + 36x^13 - 12x^12 + 322x^11 - 414x^10 - 1608x^9 + 3910x^8 - 8532x^7 + 22452x^6 - 27010x^5 + 19077x^4 - 14268x^3 + 15896x^2 - 7160x + 4096	\( 17^{14}\cdot 19^{8} \)	$D_4:C_4$ (as 16T26)	$[104]$ (GRH)
16.4.3340206345557585382040261009.1	x^16 - 6x^15 + 21x^14 + 9x^13 - 307x^12 + 895x^11 + 167x^10 - 6988x^9 + 13605x^8 + 18828x^7 - 114234x^6 + 94011x^5 + 204683x^4 - 276266x^3 - 230872x^2 + 467792x - 150064	\( 23^{6}\cdot 41^{12} \)	$D_4:C_4$ (as 16T26)	$[3, 3]$ (GRH)
16.0.3731986953978689760254088841.1	x^16 + 5x^14 + 233x^12 - 1005x^10 + 6655x^8 - 3685x^6 + 10928x^4 + 11520x^2 + 5184	\( 17^{14}\cdot 53^{6} \)	$D_4:C_4$ (as 16T26)	$[506]$ (GRH)
16.0.4466413296812760910104974161.12	x^16 - 6x^15 - 7x^14 + 87x^13 + 9x^12 - 531x^11 + 6x^10 + 1734x^9 - 812x^8 - 4821x^7 + 7968x^6 + 15969x^5 - 9718x^4 + 11928x^3 + 50866x^2 - 51585x + 53821	\( 13^{12}\cdot 61^{8} \)	$D_4:C_4$ (as 16T26)	$[2, 40]$ (GRH)
16.4.7102266577587274170491152489.1	x^16 - 11x^14 + 37x^12 - 89x^10 - 1249x^8 + 2943x^6 - 3684x^4 - 21680x^2 + 118336	\( 17^{14}\cdot 59^{6} \)	$D_4:C_4$ (as 16T26)	$[2]$ (GRH)
16.0.12812035518280357547259227689.4	x^16 + 43x^14 + 728x^12 + 6164x^10 + 27490x^8 + 63323x^6 + 71813x^4 + 34402x^2 + 4225	\( 13^{6}\cdot 61^{12} \)	$D_4:C_4$ (as 16T26)	$[18]$ (GRH)
16.0.13872985106194361214049869121.7	x^16 - 8x^15 + 66x^14 - 322x^13 + 1506x^12 - 5214x^11 + 16738x^10 - 42616x^9 + 102318x^8 - 199490x^7 + 341320x^6 - 459372x^5 + 444127x^4 - 292762x^3 + 11928x^2 + 81780x + 38399	\( 17^{12}\cdot 47^{8} \)	$D_4:C_4$ (as 16T26)	$[2, 2, 4]$ (GRH)
16.4.15231185783695887615175635001.18	x^16 - 19x^14 + 125x^12 - 377x^10 + 2807x^8 - 28489x^6 + 118700x^4 - 167312x^2 + 256	\( 17^{14}\cdot 67^{6} \)	$D_4:C_4$ (as 16T26)	$[2]$ (GRH)
16.0.17606641095812026885331265625.13	x^16 + 3x^14 - 73x^13 + 47x^12 - 442x^11 + 1205x^10 - 3367x^9 + 15052x^8 + 10737x^7 + 106205x^6 - 11405x^5 + 145099x^4 + 329316x^3 + 1487871x^2 + 1532951x + 1171175	\( 5^{6}\cdot 101^{12} \)	$D_4:C_4$ (as 16T26)	$[5, 10]$ (GRH)