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 263)

Label	Polynomial	Discriminant	Galois group	Class group
16.4.4146377695556640625.2	x^16 - 2x^15 + x^14 + 3x^13 - 21x^12 + 37x^11 - 18x^10 + 9x^9 - 22x^8 - 8x^7 + 63x^6 - 101x^5 + 109x^4 - 76x^3 + 34x^2 - 9x + 1	\( 5^{12}\cdot 19^{8} \)	$C_2^4.D_4$ (as 16T330)	Trivial
16.0.4146377695556640625.3	x^16 - 3x^15 + 4x^14 - 5x^12 + 8x^11 - 5x^9 + x^8 + 5x^7 - 8x^5 - 5x^4 + 4x^2 + 3x + 1	\( 5^{12}\cdot 19^{8} \)	$C_2^4.D_4$ (as 16T330)	$[2]$
16.4.27577431709228515625.1	x^16 - 4x^15 + x^14 + 9x^13 + x^12 - 43x^11 + 28x^10 + 67x^9 - 33x^8 - 66x^7 + 12x^6 + 66x^5 + 6x^4 - 17x^3 - x^2 + 3x + 1	\( 5^{12}\cdot 7^{4}\cdot 19^{6} \)	$C_2^4.D_4$ (as 16T330)	Trivial
16.4.73786976294838206464.1	x^16 - 4x^12 - 32x^11 - 24x^10 + 16x^9 + 36x^8 + 48x^7 + 16x^6 - 48x^5 - 32x^4 + 16x^3 + 16x^2 - 2	\( 2^{66} \)	$C_2^4.D_4$ (as 16T330)	Trivial (GRH)
16.4.73786976294838206464.2	x^16 - 8x^14 + 16x^12 - 32x^11 - 24x^10 + 80x^9 - 2x^8 - 80x^7 + 40x^6 + 32x^5 - 32x^4 + 8x^2 - 1	\( 2^{66} \)	$C_2^4.D_4$ (as 16T330)	Trivial (GRH)
16.0.73786976294838206464.8	x^16 - 8x^14 + 28x^12 - 16x^11 - 40x^10 + 64x^9 - 80x^7 + 96x^6 - 32x^5 + 16x^3 + 2	\( 2^{66} \)	$C_2^4.D_4$ (as 16T330)	Trivial (GRH)
16.0.73786976294838206464.11	x^16 + 8x^12 - 16x^11 + 16x^10 - 16x^9 + 18x^8 - 48x^7 + 96x^6 - 112x^5 + 144x^4 - 80x^3 + 80x^2 - 16x + 7	\( 2^{66} \)	$C_2^4.D_4$ (as 16T330)	Trivial (GRH)
16.8.259160193017822265625.1	x^16 - 2x^15 - 9x^14 + 7x^13 + 6x^12 + 9x^11 + 24x^10 - 44x^9 + 17x^8 - 44x^7 + 24x^6 + 9x^5 + 6x^4 + 7x^3 - 9x^2 - 2x + 1	\( 5^{12}\cdot 101^{6} \)	$C_2^4.D_4$ (as 16T330)	Trivial (GRH)
16.8.259160193017822265625.2	x^16 - 8x^15 + 26x^14 - 42x^13 + 6x^12 + 146x^11 - 351x^10 + 369x^9 - 28x^8 - 496x^7 + 734x^6 - 504x^5 + 146x^4 + 23x^3 - 24x^2 + 2x + 1	\( 5^{12}\cdot 101^{6} \)	$C_2^4.D_4$ (as 16T330)	Trivial (GRH)
16.0.1496842348095947265625.3	x^16 - 3x^15 + 6x^14 - 23x^13 + 53x^12 - 71x^11 + 126x^10 - 252x^9 + 297x^8 - 249x^7 + 277x^6 - 302x^5 + 291x^4 - 290x^3 + 215x^2 - 100x + 25	\( 5^{12}\cdot 19^{10} \)	$C_2^4.D_4$ (as 16T330)	$[2, 2]$
16.4.1496842348095947265625.4	x^16 - 3x^15 + 3x^14 - 2x^13 - 38x^12 + 118x^11 - 206x^10 + 326x^9 - 148x^8 - 293x^7 + 651x^6 - 1181x^5 + 1462x^4 - 1634x^3 + 1382x^2 - 724x + 131	\( 5^{12}\cdot 19^{10} \)	$C_2^4.D_4$ (as 16T330)	$[2]$ (GRH)
16.4.35847274805742431640625.1	x^16 - 7x^15 + 30x^14 - 109x^13 + 279x^12 - 519x^11 + 755x^10 - 605x^9 - 69x^8 + 565x^7 - 475x^6 - 232x^5 + 276x^4 + 41x^3 - 42x^2 + x + 1	\( 5^{12}\cdot 59^{8} \)	$C_2^4.D_4$ (as 16T330)	Trivial (GRH)
16.0.35847274805742431640625.2	x^16 + 13x^14 - 11x^13 + 66x^12 - 116x^11 + 265x^10 - 246x^9 + 658x^8 - 185x^7 + 487x^6 - 195x^5 + 952x^4 + 608x^3 + 485x^2 + 58x + 11	\( 5^{12}\cdot 59^{8} \)	$C_2^4.D_4$ (as 16T330)	$[2]$ (GRH)
16.0.43190748110316471478641.1	x^16 - x^15 + 6x^14 - 23x^13 + 26x^12 - 90x^11 + 269x^10 - 281x^9 + 453x^8 - 967x^7 + 673x^6 + 99x^5 + 9x^4 - 45x^3 - 126x^2 + 27x + 81	\( 3^{8}\cdot 37^{12} \)	$C_2^4.D_4$ (as 16T330)	$[2]$ (GRH)
16.4.43190748110316471478641.2	x^16 - 5x^15 + 6x^14 + 9x^13 - 31x^12 - 43x^11 + 147x^10 + 42x^9 - 276x^8 - 454x^7 + 524x^6 + 387x^5 - 438x^4 - 296x^3 + 88x^2 + 87x + 9	\( 3^{8}\cdot 37^{12} \)	$C_2^4.D_4$ (as 16T330)	Trivial (GRH)
16.4.370387893043593994140625.2	x^16 - 2x^15 - 6x^13 + 6x^12 + 52x^11 - 69x^10 - 75x^9 + 174x^8 + 30x^7 - 71x^6 - 349x^5 - 149x^4 + 78x^3 + 180x^2 + 104x + 16	\( 5^{12}\cdot 79^{8} \)	$C_2^4.D_4$ (as 16T330)	Trivial (GRH)
16.0.370387893043593994140625.2	x^16 - 8x^15 + 26x^14 - 42x^13 + 115x^12 - 508x^11 + 1308x^10 - 1931x^9 + 3538x^8 - 8154x^7 + 15113x^6 - 19304x^5 + 17574x^4 - 11431x^3 + 4722x^2 - 1019x + 101	\( 5^{12}\cdot 79^{8} \)	$C_2^4.D_4$ (as 16T330)	$[2]$ (GRH)
16.4.388716732992848243307769.2	x^16 - 2x^14 - 2x^13 + 47x^12 - 108x^11 - 58x^10 + 587x^9 - 797x^8 + 290x^7 + 1321x^6 - 2790x^5 + 1914x^4 + 205x^3 - 1259x^2 + 873x - 213	\( 3^{10}\cdot 37^{12} \)	$C_2^4.D_4$ (as 16T330)	$[2]$ (GRH)
16.0.388716732992848243307769.4	x^16 - 2x^14 - 22x^13 + 10x^12 - 4x^11 + 85x^10 + 56x^9 + 133x^8 + 384x^7 - 422x^6 + 54x^5 - 939x^4 - 387x^3 + 162x^2 - 1053x + 2673	\( 3^{10}\cdot 37^{12} \)	$C_2^4.D_4$ (as 16T330)	$[2, 2]$ (GRH)
16.8.516387172268851080441049.1	x^16 - 4x^15 + 2x^14 + 30x^13 - 136x^12 + 148x^11 + 92x^10 + 83x^9 - 240x^8 - 1210x^7 + 1960x^6 + 1213x^5 - 2573x^4 - 1092x^3 + 871x^2 + 377x - 13	\( 13^{12}\cdot 53^{6} \)	$C_2^4.D_4$ (as 16T330)	Trivial (GRH)
16.8.516387172268851080441049.2	x^16 - 4x^15 - x^14 + 17x^13 - 18x^12 - 5x^11 + 61x^10 + 4x^9 - 106x^8 - 89x^7 - 358x^6 + 71x^5 + 1516x^4 - 71x^3 - 1135x^2 + 117x + 81	\( 13^{12}\cdot 53^{6} \)	$C_2^4.D_4$ (as 16T330)	Trivial (GRH)
16.8.1200326067404665657109641.1	x^16 - 4x^15 - 11x^14 + 43x^13 - 2x^12 - 20x^11 + 53x^10 - 91x^9 + 63x^8 - 91x^7 + 53x^6 - 20x^5 - 2x^4 + 43x^3 - 11x^2 - 4x + 1	\( 13^{12}\cdot 61^{6} \)	$C_2^4.D_4$ (as 16T330)	Trivial (GRH)
16.8.1200326067404665657109641.2	x^16 - 10x^14 - 17x^12 + 304x^10 - 27x^8 - 2569x^6 + 997x^4 + 5593x^2 + 1	\( 13^{12}\cdot 61^{6} \)	$C_2^4.D_4$ (as 16T330)	Trivial (GRH)
16.0.1700350026389931884765625.2	x^16 - x^15 + 9x^14 + 17x^13 + 20x^12 + 64x^11 + 570x^10 - 955x^9 + 2351x^8 - 2350x^7 + 1905x^6 - 1326x^5 + 680x^4 + 132x^3 + 74x^2 + 9x + 1	\( 3^{8}\cdot 5^{12}\cdot 101^{6} \)	$C_2^4.D_4$ (as 16T330)	$[2, 6]$ (GRH)
16.0.1700350026389931884765625.3	x^16 - 8x^15 + 24x^14 - 28x^13 + 19x^12 - 114x^11 + 308x^10 - 209x^9 + 39x^8 - 728x^7 + 1394x^6 - 639x^5 + 728x^4 - 1764x^3 + 1534x^2 - 557x + 1801	\( 3^{8}\cdot 5^{12}\cdot 101^{6} \)	$C_2^4.D_4$ (as 16T330)	$[2, 6]$ (GRH)
16.4.1824496001102094673202161.2	x^16 - 9x^14 + 6x^12 + 420x^10 - 1585x^8 - 351x^6 + 1599x^4 + 1014x^2 + 169	\( 13^{12}\cdot 23^{8} \)	$C_2^4.D_4$ (as 16T330)	Trivial (GRH)
16.0.1824496001102094673202161.4	x^16 - 4x^15 + 4x^14 - 30x^13 + 34x^12 + 68x^11 + 347x^10 + 472x^9 - 214x^8 - 2752x^7 - 5851x^6 - 6360x^5 + 2900x^4 + 19292x^3 + 30602x^2 + 20098x + 5057	\( 13^{12}\cdot 23^{8} \)	$C_2^4.D_4$ (as 16T330)	$[2]$ (GRH)
16.8.2643693128974804931640625.1	x^16 - 7x^15 + 11x^14 + 12x^13 - 31x^12 + 37x^11 - 78x^10 - 4x^9 - 234x^8 + 350x^7 + 1252x^6 - 444x^5 - 2731x^4 + 40x^3 + 2520x^2 + 76x - 649	\( 5^{12}\cdot 101^{8} \)	$C_2^4.D_4$ (as 16T330)	$[2]$ (GRH)
16.8.2643693128974804931640625.2	x^16 - 9x^14 - 13x^13 - 113x^12 - 91x^11 - 328x^10 + 90x^9 - 173x^8 + 533x^7 + 53x^6 - 198x^5 + 911x^4 + 321x^3 - 147x^2 + 3x + 1	\( 5^{12}\cdot 101^{8} \)	$C_2^4.D_4$ (as 16T330)	$[2]$ (GRH)
16.8.2643693128974804931640625.4	x^16 - 12x^14 - 26x^13 - 8x^12 + 509x^11 + 601x^10 - 3148x^9 - 3740x^8 + 5842x^7 + 11063x^6 - 4218x^5 - 17333x^4 + 4989x^3 + 9863x^2 - 4383x + 11	\( 5^{12}\cdot 101^{8} \)	$C_2^4.D_4$ (as 16T330)	Trivial (GRH)
16.8.2643693128974804931640625.7	x^16 - 3x^15 - 17x^14 + 59x^13 + 52x^12 - 28x^11 - 1477x^10 + 2407x^9 + 3895x^8 - 10463x^7 - 2149x^6 + 16879x^5 + 7702x^4 - 49086x^3 + 50023x^2 - 20795x + 3011	\( 5^{12}\cdot 101^{8} \)	$C_2^4.D_4$ (as 16T330)	Trivial (GRH)
16.0.6280210550563314266206369.1	x^16 + 7x^14 - 4x^12 - 87x^10 + 55x^8 + 365x^6 - 608x^4 + 283x^2 + 1	\( 17^{12}\cdot 47^{6} \)	$C_2^4.D_4$ (as 16T330)	$[2]$ (GRH)
16.0.6280210550563314266206369.2	x^16 - 7x^15 + 11x^14 + 46x^13 - 157x^12 + 12x^11 + 494x^10 - 430x^9 - 394x^8 + 547x^7 - 163x^6 - 260x^5 + 1441x^4 - 1320x^3 + 546x^2 - 124x + 13	\( 17^{12}\cdot 47^{6} \)	$C_2^4.D_4$ (as 16T330)	$[2]$ (GRH)
16.16.16984322409616000000000000.1	x^16 - 23x^14 + 199x^12 - 827x^10 + 1756x^8 - 1920x^6 + 1065x^4 - 275x^2 + 25	\( 2^{16}\cdot 5^{12}\cdot 101^{6} \)	$C_2^4.D_4$ (as 16T330)	Trivial (GRH)
16.8.16984322409616000000000000.1	x^16 - 11x^14 - 29x^12 + 214x^10 + 546x^8 - 5x^6 - 315x^4 + 25x^2 + 25	\( 2^{16}\cdot 5^{12}\cdot 101^{6} \)	$C_2^4.D_4$ (as 16T330)	Trivial (GRH)
16.8.16984322409616000000000000.2	x^16 - 64x^12 - 25x^10 + 681x^8 - 25x^6 - 64x^4 + 1	\( 2^{16}\cdot 5^{12}\cdot 101^{6} \)	$C_2^4.D_4$ (as 16T330)	Trivial (GRH)
16.16.16984322409616000000000000.2	x^16 - 22x^14 + 189x^12 - 808x^10 + 1811x^8 - 2065x^6 + 1115x^4 - 275x^2 + 25	\( 2^{16}\cdot 5^{12}\cdot 101^{6} \)	$C_2^4.D_4$ (as 16T330)	Trivial (GRH)
16.0.16984322409616000000000000.3	x^16 + 22x^14 + 189x^12 + 808x^10 + 1811x^8 + 2065x^6 + 1115x^4 + 275x^2 + 25	\( 2^{16}\cdot 5^{12}\cdot 101^{6} \)	$C_2^4.D_4$ (as 16T330)	$[4, 8]$ (GRH)
16.0.16984322409616000000000000.4	x^16 + 23x^14 + 199x^12 + 827x^10 + 1756x^8 + 1920x^6 + 1065x^4 + 275x^2 + 25	\( 2^{16}\cdot 5^{12}\cdot 101^{6} \)	$C_2^4.D_4$ (as 16T330)	$[4, 12]$ (GRH)
16.4.17415183620366462784744081.1	x^16 - 4x^15 + 15x^14 - 35x^13 + 57x^12 - 244x^10 + 1080x^9 - 3132x^8 + 6869x^7 - 13789x^6 + 20160x^5 - 26109x^4 + 27603x^3 - 15471x^2 + 8505x - 675	\( 3^{8}\cdot 61^{12} \)	$C_2^4.D_4$ (as 16T330)	$[3]$ (GRH)
16.0.17415183620366462784744081.2	x^16 - 3x^15 + 12x^14 + 2x^13 + 13x^12 + 25x^11 + 517x^10 - 1271x^9 + 4370x^8 - 4519x^7 + 6904x^6 + 8355x^5 + 2316x^4 + 1449x^3 + 4530x^2 - 675x + 3375	\( 3^{8}\cdot 61^{12} \)	$C_2^4.D_4$ (as 16T330)	$[6]$ (GRH)
16.0.46446361314096914306640625.1	x^16 - 6x^15 + 23x^14 - 56x^13 + 96x^12 - 168x^11 + 820x^10 - 3230x^9 + 6426x^8 + 100x^7 - 30670x^6 + 71234x^5 - 54911x^4 - 58866x^3 + 186315x^2 - 184558x + 79211	\( 5^{12}\cdot 11^{8}\cdot 31^{6} \)	$C_2^4.D_4$ (as 16T330)	$[2, 2, 4]$ (GRH)
16.0.52703064995487500398531609.3	x^16 - x^15 + 18x^14 + 16x^13 + 175x^12 + 81x^11 + 401x^10 - 464x^9 + 15x^8 - 1766x^7 + 1740x^6 + 1208x^5 + 2864x^4 - 6368x^3 + 1664x^2 + 6656x + 4096	\( 17^{12}\cdot 67^{6} \)	$C_2^4.D_4$ (as 16T330)	$[2]$ (GRH)
16.0.52703064995487500398531609.4	x^16 - 6x^15 + 21x^14 - 53x^13 + 198x^12 - 520x^11 + 1385x^10 - 2062x^9 + 6223x^8 - 7834x^7 + 18335x^6 - 10682x^5 + 48920x^4 - 7166x^3 + 74286x^2 - 14083x + 49981	\( 17^{12}\cdot 67^{6} \)	$C_2^4.D_4$ (as 16T330)	$[2]$ (GRH)
16.4.124784363598789404541015625.4	x^16 - x^15 - 15x^14 + 78x^13 - 174x^12 + 26x^11 + 94x^10 - 15x^9 - 636x^8 + 220x^7 - 134x^6 - 113x^5 + 206x^4 + 609x^3 + 360x^2 + 108x + 81	\( 5^{12}\cdot 59^{10} \)	$C_2^4.D_4$ (as 16T330)	$[2]$ (GRH)
16.0.124784363598789404541015625.5	x^16 - 6x^15 + 27x^14 - 74x^13 + 179x^12 - 446x^11 + 1128x^10 - 2631x^9 + 3693x^8 - 5889x^7 + 20768x^6 - 79152x^5 + 204035x^4 - 351523x^3 + 557706x^2 - 743902x + 652231	\( 5^{12}\cdot 59^{10} \)	$C_2^4.D_4$ (as 16T330)	$[2, 2]$ (GRH)
16.0.146504330269581929271525376.1	x^16 - 4x^15 + 18x^14 - 4x^13 + 57x^12 - 72x^11 + 1668x^10 - 1800x^9 + 8433x^8 - 13324x^7 + 23058x^6 - 22620x^5 + 14797x^4 - 6032x^3 + 1508x^2 - 112x + 4	\( 2^{46}\cdot 113^{6} \)	$C_2^4.D_4$ (as 16T330)	$[2, 18]$ (GRH)
16.0.146504330269581929271525376.2	x^16 - 4x^15 + 6x^14 - 28x^13 + 39x^12 - 136x^11 + 540x^10 - 368x^9 + 4469x^8 + 1548x^7 + 21334x^6 + 21780x^5 + 59589x^4 + 74432x^3 + 105624x^2 + 78392x + 89246	\( 2^{46}\cdot 113^{6} \)	$C_2^4.D_4$ (as 16T330)	$[2, 18]$ (GRH)
16.4.156736652583298165062696729.1	x^16 + 14x^14 - 40x^13 + 99x^12 - 359x^11 + 231x^10 - 405x^9 - 2805x^8 + 1069x^7 + 1233x^6 - 6799x^5 + 58619x^4 + 46998x^3 + 23524x^2 + 59820x - 9225	\( 3^{10}\cdot 61^{12} \)	$C_2^4.D_4$ (as 16T330)	$[6]$ (GRH)
16.0.156736652583298165062696729.5	x^16 - 6x^15 + 15x^14 - 39x^13 + 69x^12 - 114x^11 + 388x^10 - 462x^9 + 879x^8 - 1011x^7 + 2385x^6 + 3843x^5 + 15196x^4 + 47622x^3 + 83325x^2 + 73575x + 50625	\( 3^{10}\cdot 61^{12} \)	$C_2^4.D_4$ (as 16T330)	$[2, 6]$ (GRH)