Global number field search results

Further refine search

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 193)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.4096000000000000.1	x^16 - 6x^15 + 18x^14 - 36x^13 + 47x^12 - 30x^11 - 18x^10 + 72x^9 - 95x^8 + 72x^7 - 18x^6 - 30x^5 + 47x^4 - 36x^3 + 18x^2 - 6x + 1	\( 2^{24}\cdot 5^{12} \)	$C_2^2 : C_4$ (as 16T10)	Trivial
16.0.18014398509481984.1	x^16 - 8x^15 + 36x^14 - 104x^13 + 220x^12 - 368x^11 + 516x^10 - 624x^9 + 664x^8 - 624x^7 + 516x^6 - 368x^5 + 220x^4 - 104x^3 + 36x^2 - 8x + 1	\( 2^{54} \)	$C_2^2 : C_4$ (as 16T10)	Trivial
16.0.52333711181640625.1	x^16 - x^15 + 2x^13 - 4x^12 - x^11 + 7x^10 - 12x^9 + 8x^8 + 12x^7 + 7x^6 + x^5 - 4x^4 - 2x^3 + x + 1	\( 5^{12}\cdot 11^{8} \)	$C_2^2 : C_4$ (as 16T10)	Trivial
16.0.152858736488597841.1	x^16 - 3x^15 + 3x^14 - 2x^13 + 5x^12 - 8x^11 + 20x^10 - 35x^9 + 27x^7 + 50x^6 - 70x^5 - 11x^4 + 18x^3 + 3x^2 + 9x + 9	\( 3^{8}\cdot 13^{12} \)	$C_2^2 : C_4$ (as 16T10)	Trivial
16.0.1048576000000000000.6	x^16 + x^12 + 6x^8 - 4x^4 + 1	\( 2^{32}\cdot 5^{12} \)	$C_2^2 : C_4$ (as 16T10)	Trivial (GRH)
16.0.4146377695556640625.1	x^16 - x^15 - 2x^14 + 6x^13 - 2x^12 + 19x^11 - 5x^10 - 60x^9 + 96x^8 + 60x^7 - 5x^6 - 19x^5 - 2x^4 - 6x^3 - 2x^2 + x + 1	\( 5^{12}\cdot 19^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[2]$
16.0.16777216000000000000.1	x^16 - 8x^15 + 32x^14 - 84x^13 + 152x^12 - 164x^11 + 78x^10 + 48x^9 - 45x^8 + 44x^7 + 134x^6 + 156x^5 + 318x^4 + 176x^3 + 10x^2 - 8x + 1	\( 2^{36}\cdot 5^{12} \)	$C_2^2 : C_4$ (as 16T10)	$[2]$ (GRH)
16.0.16777216000000000000.5	x^16 - 8x^15 + 32x^14 - 80x^13 + 176x^12 - 400x^11 + 768x^10 - 1144x^9 + 1686x^8 - 2680x^7 + 3840x^6 - 4240x^5 + 3440x^4 - 2000x^3 + 800x^2 - 200x + 25	\( 2^{36}\cdot 5^{12} \)	$C_2^2 : C_4$ (as 16T10)	$[2]$ (GRH)
16.0.26873856000000000000.4	x^16 - 6x^15 + 18x^14 - 34x^13 + 28x^12 + 44x^11 - 190x^10 + 320x^9 - 274x^8 - 100x^7 + 940x^6 - 1654x^5 + 1533x^4 - 506x^3 + 98x^2 - 14x + 1	\( 2^{24}\cdot 3^{8}\cdot 5^{12} \)	$C_2^2 : C_4$ (as 16T10)	$[2]$
16.0.26873856000000000000.10	x^16 - 6x^15 + 18x^14 - 30x^13 + 41x^12 - 90x^11 + 252x^10 - 432x^9 + 426x^8 - 180x^7 + 90x^6 - 360x^5 + 740x^4 - 750x^3 + 450x^2 - 150x + 25	\( 2^{24}\cdot 3^{8}\cdot 5^{12} \)	$C_2^2 : C_4$ (as 16T10)	$[2]$
16.0.26873856000000000000.12	x^16 - 8x^15 + 28x^14 - 56x^13 + 82x^12 - 128x^11 + 158x^10 + 2x^9 - 120x^8 - 368x^7 + 506x^6 + 604x^5 - 433x^4 - 986x^3 - 72x^2 + 790x + 541	\( 2^{24}\cdot 3^{8}\cdot 5^{12} \)	$C_2^2 : C_4$ (as 16T10)	$[2]$ (GRH)
16.0.38182730939089616896.1	x^16 - 8x^15 + 30x^14 - 70x^13 + 114x^12 - 138x^11 + 108x^10 + 10x^9 - 19x^8 - 358x^7 + 758x^6 - 644x^5 + 264x^4 - 56x^3 - 8x^2 + 16x + 16	\( 2^{16}\cdot 17^{12} \)	$C_2^2 : C_4$ (as 16T10)	$[2]$
16.0.101415451701035401216.6	x^16 - 4x^14 + 26x^12 - 136x^10 + 320x^8 - 272x^6 + 104x^4 - 32x^2 + 16	\( 2^{44}\cdot 7^{8} \)	$C_2^2 : C_4$ (as 16T10)	Trivial (GRH)
16.0.101415451701035401216.9	x^16 + 4x^14 + 26x^12 + 136x^10 + 320x^8 + 272x^6 + 104x^4 + 32x^2 + 16	\( 2^{44}\cdot 7^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[2]$
16.0.118192468620711297024.1	x^16 - 8x^15 + 20x^14 - 8x^13 - 40x^12 + 72x^11 + 28x^10 - 256x^9 + 976x^8 - 1856x^7 + 2340x^6 - 2160x^5 + 1408x^4 - 656x^3 + 196x^2 - 24x + 1	\( 2^{54}\cdot 3^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[2]$
16.0.118192468620711297024.3	x^16 - 8x^15 + 32x^14 - 72x^13 + 64x^12 + 128x^11 - 408x^10 + 208x^9 + 1428x^8 - 2768x^7 + 1824x^6 - 208x^5 - 224x^4 + 80x^2 - 32x + 4	\( 2^{54}\cdot 3^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[2]$
16.0.118192468620711297024.15	x^16 - 8x^15 + 32x^14 - 80x^13 + 192x^12 - 496x^11 + 1024x^10 - 1696x^9 + 3044x^8 - 5392x^7 + 7808x^6 - 9568x^5 + 10144x^4 - 8416x^3 + 4608x^2 - 1344x + 196	\( 2^{54}\cdot 3^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[2]$
16.0.122130471914306640625.1	x^16 - x^15 + 6x^14 - 12x^13 + 42x^12 + 69x^11 + 147x^10 + 168x^9 + 456x^8 + 168x^7 + 147x^6 + 69x^5 + 42x^4 - 12x^3 + 6x^2 - x + 1	\( 5^{12}\cdot 29^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[2]$
16.0.208225350937744140625.1	x^16 - 2x^15 + 2x^14 - x^13 - 8x^12 - 46x^11 + 93x^10 - 78x^9 + 80x^8 + 271x^7 + 434x^6 - 866x^5 - 47x^4 - 776x^3 - 960x^2 - 512x + 4096	\( 5^{12}\cdot 31^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[3]$
16.0.343361479062744140625.2	x^16 - x^15 + 5x^14 - 3x^13 + 76x^12 - 71x^11 + 162x^10 + 113x^9 + 453x^8 - 28x^7 + 447x^6 + 496x^5 + 631x^4 + 123x^3 + 20x^2 - 4x + 1	\( 3^{8}\cdot 5^{12}\cdot 11^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[2, 2]$
16.0.343361479062744140625.3	x^16 + 5x^14 + 51x^12 + 50x^10 + 531x^8 + 170x^6 + 86x^4 + 1	\( 3^{8}\cdot 5^{12}\cdot 11^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[4]$
16.0.343361479062744140625.5	x^16 - x^15 - 3x^14 + x^13 + 14x^12 - 41x^11 - 12x^10 + 89x^9 + 163x^8 - 324x^7 + 393x^6 - 342x^5 + 225x^4 - 243x^3 + 216x^2 - 162x + 81	\( 3^{8}\cdot 5^{12}\cdot 11^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[4]$
16.0.390877006486250192896.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 46x^12 + 88x^11 - 306x^10 + 342x^9 + 156x^8 - 1136x^7 + 2026x^6 - 2216x^5 + 1679x^4 - 898x^3 + 332x^2 - 78x + 9	\( 2^{24}\cdot 13^{12} \)	$C_2^2 : C_4$ (as 16T10)	Trivial
16.0.1622647227216566419456.11	x^16 - 40x^10 + 133x^8 - 224x^6 + 316x^4 - 224x^2 + 196	\( 2^{48}\cdot 7^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[4]$
16.0.1622647227216566419456.12	x^16 + 40x^10 + 133x^8 + 224x^6 + 316x^4 + 224x^2 + 196	\( 2^{48}\cdot 7^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[4]$
16.0.1949444636015869140625.1	x^16 - 2x^15 - 4x^14 + 17x^13 + 10x^12 + 68x^11 - 327x^10 + 6x^9 + 2108x^8 - 2111x^7 + 1478x^6 - 836x^5 + 409x^4 - 254x^3 + 132x^2 - 56x + 16	\( 5^{12}\cdot 41^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[2]$ (GRH)
16.0.3429742096000000000000.3	x^16 + 24x^12 + 110x^10 + 176x^8 + 440x^6 + 989x^4 + 880x^2 + 256	\( 2^{16}\cdot 5^{12}\cdot 11^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[4]$
16.0.3429742096000000000000.5	x^16 - 3x^14 + 4x^12 + 3x^10 - 29x^8 + 15x^6 + 100x^4 - 375x^2 + 625	\( 2^{16}\cdot 5^{12}\cdot 11^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[4]$ (GRH)
16.0.3429742096000000000000.6	x^16 + 5x^14 + 80x^12 + 175x^10 + 875x^8 + 875x^6 + 2000x^4 + 625x^2 + 625	\( 2^{16}\cdot 5^{12}\cdot 11^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[2, 2]$
16.0.9774779120406941925376.1	x^16 - 4x^14 + 27x^12 + 52x^10 + 189x^8 + 902x^6 + 928x^4 - 3880x^2 + 2704	\( 2^{24}\cdot 17^{12} \)	$C_2^2 : C_4$ (as 16T10)	Trivial
16.0.35847274805742431640625.4	x^16 - 2x^15 + 4x^14 - 7x^13 - 3x^12 - 98x^11 + 129x^10 - 156x^9 + 259x^8 + 1081x^7 + 932x^6 + 735x^5 - 4274x^4 - 6735x^3 + 225x^2 + 3375x + 50625	\( 5^{12}\cdot 59^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[6]$ (GRH)
16.0.43190748110316471478641.4	x^16 - x^15 - 7x^14 - 8x^13 + 55x^12 + 18x^11 - 100x^10 + 13x^9 + 148x^8 - 55x^7 + 878x^6 + 18x^5 - 227x^4 + 14x^3 + 659x^2 - 47x + 2209	\( 3^{8}\cdot 37^{12} \)	$C_2^2 : C_4$ (as 16T10)	$[2]$ (GRH)
16.0.46803543212226806640625.3	x^16 - 2x^15 - 6x^14 + 23x^13 + 27x^12 + 92x^11 - 631x^10 - 16x^9 + 5379x^8 - 5379x^7 + 2152x^6 + 1155x^5 - 2314x^4 + 605x^3 + 775x^2 - 1125x + 625	\( 5^{12}\cdot 61^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[2]$ (GRH)
16.0.103849422541860250845184.1	x^16 + 8x^14 + 44x^12 + 72x^10 - 152x^8 - 640x^6 + 2024x^4 - 720x^2 + 324	\( 2^{54}\cdot 7^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[2, 2]$
16.16.103849422541860250845184.1	x^16 - 24x^14 + 204x^12 - 792x^10 + 1544x^8 - 1536x^6 + 744x^4 - 144x^2 + 4	\( 2^{54}\cdot 7^{8} \)	$C_2^2 : C_4$ (as 16T10)	Trivial (GRH)
16.0.138208899689636344140625.2	x^16 - 2x^15 + 3x^14 + 5x^13 + 23x^12 - 15x^11 + 55x^10 + 43x^9 + x^8 - 387x^7 + 401x^6 + 1367x^5 + 5089x^4 + 5471x^3 + 6651x^2 + 3764x + 6091	\( 5^{8}\cdot 29^{12} \)	$C_2^2 : C_4$ (as 16T10)	$[3, 6]$ (GRH)
16.0.157654670714297119140625.1	x^16 - 3x^14 - 11x^12 + 93x^10 - 59x^8 + 1860x^6 - 4400x^4 - 24000x^2 + 160000	\( 5^{12}\cdot 71^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[7]$ (GRH)
16.0.162521790654198232131121.2	x^16 - 6x^15 + 24x^14 - 84x^13 + 261x^12 - 570x^11 + 1026x^10 - 1881x^9 + 2032x^8 - 588x^7 + 1299x^6 - 1230x^5 + 2412x^4 + 1659x^3 - 1080x^2 + 1179x + 937	\( 13^{12}\cdot 17^{8} \)	$C_2^2 : C_4$ (as 16T10)	Trivial (GRH)
16.0.370387893043593994140625.4	x^16 + x^14 - 19x^12 - 39x^10 + 341x^8 - 780x^6 - 7600x^4 + 8000x^2 + 160000	\( 5^{12}\cdot 79^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[10]$ (GRH)
16.0.475262857646065983187681.5	x^16 - 2x^14 - 43x^12 + 11x^10 + 866x^8 - 949x^6 + 2484x^4 - 2112x^2 + 4096	\( 13^{8}\cdot 17^{12} \)	$C_2^2 : C_4$ (as 16T10)	$[2, 2]$ (GRH)
16.16.801298026229765869140625.1	x^16 - 39x^14 - 22x^13 + 532x^12 + 436x^11 - 3318x^10 - 2950x^9 + 10407x^8 + 8602x^7 - 17127x^6 - 11402x^5 + 14471x^4 + 6174x^3 - 5542x^2 - 838x + 631	\( 3^{8}\cdot 5^{12}\cdot 29^{8} \)	$C_2^2 : C_4$ (as 16T10)	Trivial (GRH)
16.0.961081251392109619140625.1	x^16 - 2x^15 + 12x^14 - 31x^13 + 142x^12 + 44x^11 + 793x^10 - 18x^9 + 7060x^8 - 7039x^7 + 5534x^6 - 3876x^5 + 2793x^4 - 866x^3 + 260x^2 - 72x + 16	\( 5^{12}\cdot 89^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[10]$ (GRH)
16.0.1824496001102094673202161.3	x^16 - 4x^15 + 25x^14 - 44x^13 + 147x^12 - 90x^11 + 321x^10 + 824x^9 - 498x^8 + 1926x^7 - 708x^6 - 4190x^5 + 6151x^4 + 7952x^3 - 248x^2 - 3384x + 1296	\( 13^{12}\cdot 23^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[6]$ (GRH)
16.0.2039671816037671133025841.1	x^16 - 4x^15 + 41x^14 - 126x^13 + 666x^12 - 1676x^11 + 5845x^10 - 11821x^9 + 29440x^8 - 44509x^7 + 82259x^6 - 80505x^5 + 114255x^4 - 45695x^3 + 71142x^2 + 14611x + 15451	\( 7^{8}\cdot 29^{12} \)	$C_2^2 : C_4$ (as 16T10)	Trivial (GRH)
16.0.2643693128974804931640625.7	x^16 + 11x^14 + 116x^12 + 1221x^10 + 12851x^8 + 6105x^6 + 2900x^4 + 1375x^2 + 625	\( 5^{12}\cdot 101^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[2, 2, 2, 4]$ (GRH)
16.0.4864654886938945556640625.1	x^16 - 2x^15 - 8x^14 + 29x^13 + 57x^12 + 154x^11 - 1287x^10 + 12x^9 + 13555x^8 - 13559x^7 + 9764x^6 - 5961x^5 + 3238x^4 - 1671x^3 + 765x^2 - 297x + 81	\( 5^{12}\cdot 109^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[5]$ (GRH)
16.0.8813863398580541437890625.2	x^16 + 4x^14 - 12x^12 - 1813x^10 + 15464x^8 - 29008x^6 - 3072x^4 + 16384x^2 + 65536	\( 5^{8}\cdot 41^{12} \)	$C_2^2 : C_4$ (as 16T10)	$[3, 3]$ (GRH)
16.0.9895001495080103144863201.1	x^16 + 6x^14 + 193x^12 + 579x^10 + 1794x^8 + 1611x^6 + 1592x^4 + 432x^2 + 256	\( 17^{12}\cdot 19^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[26]$ (GRH)
16.0.11654783511381160590876241.2	x^16 - 2x^15 - 11x^14 + 7x^13 + 29x^12 + 139x^11 + 527x^10 - 2880x^9 - 943x^8 + 12374x^7 - 8494x^6 - 7705x^5 + 21841x^4 - 15244x^3 + 19216x^2 - 8640x + 2304	\( 13^{12}\cdot 29^{8} \)	$C_2^2 : C_4$ (as 16T10)	$[2]$ (GRH)
16.0.17415183620366462784744081.3	x^16 - 3x^15 - 9x^14 - 42x^13 + 250x^12 - 57x^11 - 939x^10 + 8310x^9 - 4947x^8 - 15927x^7 + 57297x^6 - 95394x^5 + 112678x^4 - 83598x^3 + 47112x^2 - 20586x + 5329	\( 3^{8}\cdot 61^{12} \)	$C_2^2 : C_4$ (as 16T10)	$[2]$ (GRH)