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 all 46 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.36901758399676416.1	x^16 - 2x^15 + 10x^14 - 20x^13 + 45x^12 - 80x^11 + 120x^10 - 168x^9 + 199x^8 - 208x^7 + 196x^6 - 158x^5 + 107x^4 - 64x^3 + 30x^2 - 8x + 1	\( 2^{24}\cdot 3^{10}\cdot 193^{2} \)	16T1439	Trivial
16.0.473159435850612736.1	x^16 + 4x^12 - 8x^10 + 10x^8 - 16x^6 + 20x^4 - 8x^2 + 1	\( 2^{48}\cdot 41^{2} \)	16T1439	Trivial
16.0.800394260737600000000.1	x^16 - x^14 - 16x^12 + 14x^10 + 98x^8 + 235x^6 + 244x^4 + 120x^2 + 25	\( 2^{12}\cdot 5^{8}\cdot 29^{8} \)	16T1439	$[2]$
16.4.800394260737600000000.1	x^16 - 4x^14 - 13x^13 + 6x^12 + 39x^11 + 50x^10 + 9x^9 - 83x^8 - 105x^7 - 16x^6 + 59x^5 + 42x^4 + 3x^3 - 8x^2 - 4x - 1	\( 2^{12}\cdot 5^{8}\cdot 29^{8} \)	16T1439	$[2]$
16.4.2321651418902203515625.1	x^16 - 6x^15 + 23x^14 - 51x^13 + 65x^12 - 39x^11 - 52x^10 + 156x^9 - 210x^8 + 156x^7 - 52x^6 - 39x^5 + 65x^4 - 51x^3 + 23x^2 - 6x + 1	\( 5^{8}\cdot 29^{8}\cdot 109^{2} \)	16T1439	$[2]$
16.0.3775492556570109765625.1	x^16 + 9x^14 + 23x^12 + 17x^10 - 6x^8 + 12x^6 + 33x^4 + 4x^2 + 16	\( 5^{8}\cdot 29^{8}\cdot 139^{2} \)	16T1439	$[2]$
16.0.4338269771151234765625.1	x^16 - 4x^15 + 5x^14 + 10x^13 - 53x^12 + 82x^11 + 4x^10 - 250x^9 + 663x^8 - 1192x^7 + 1489x^6 - 1188x^5 + 566x^4 - 183x^3 + 101x^2 - 70x + 20	\( 5^{8}\cdot 29^{8}\cdot 149^{2} \)	16T1439	$[2]$
16.4.6261091920970078515625.1	x^16 - 4x^15 - x^14 + 21x^13 - 37x^12 + 4x^11 + 46x^10 - 21x^9 - 34x^8 + 21x^7 + 46x^6 - 4x^5 - 37x^4 - 21x^3 - x^2 + 4x + 1	\( 5^{8}\cdot 29^{8}\cdot 179^{2} \)	16T1439	$[2]$
16.0.173030739841843453515625.1	x^16 - 6x^15 + 31x^14 - 89x^13 + 211x^12 - 330x^11 + 382x^10 - 219x^9 - 49x^8 + 183x^7 - 132x^6 + 10x^5 + 41x^4 - 27x^3 + 14x^2 - 2x + 1	\( 5^{8}\cdot 29^{8}\cdot 941^{2} \)	16T1439	$[20]$
16.4.233516766217814717497344.1	x^16 - 4x^13 + 9x^12 - 20x^11 + 14x^10 - 16x^9 - 18x^8 + 4x^7 - 12x^6 + 16x^5 - 31x^4 + 8x^3 + 2x^2 - 4x + 1	\( 2^{38}\cdot 3^{10}\cdot 3793^{2} \)	16T1439	Trivial
16.0.1089261790808475313373184.1	x^16 + 16x^14 + 96x^12 + 328x^10 + 862x^8 + 1392x^6 + 912x^4 + 216x^2 + 9	\( 2^{64}\cdot 3^{10} \)	16T1439	$[2]$
16.12.1089261790808475313373184.1	x^16 - 16x^14 + 96x^12 - 328x^10 + 862x^8 - 1392x^6 + 912x^4 - 216x^2 + 9	\( 2^{64}\cdot 3^{10} \)	16T1439	Trivial (GRH)
16.4.1089261790808475313373184.1	x^16 + 8x^14 - 12x^12 - 88x^10 + 16x^8 + 120x^4 + 144x^2 + 36	\( 2^{64}\cdot 3^{10} \)	16T1439	Trivial
16.8.1089261790808475313373184.1	x^16 - 8x^14 - 12x^12 + 88x^10 + 16x^8 + 120x^4 - 144x^2 + 36	\( 2^{64}\cdot 3^{10} \)	16T1439	Trivial (GRH)
16.4.1089261790808475313373184.2	x^16 + 20x^12 + 24x^10 - 326x^8 - 624x^6 - 228x^4 + 72x^2 + 9	\( 2^{64}\cdot 3^{10} \)	16T1439	Trivial
16.8.1089261790808475313373184.2	x^16 + 20x^12 - 24x^10 - 326x^8 + 624x^6 - 228x^4 - 72x^2 + 9	\( 2^{64}\cdot 3^{10} \)	16T1439	Trivial (GRH)
16.4.1089261790808475313373184.3	x^16 - 28x^12 - 72x^10 - 176x^8 - 240x^6 + 24x^4 + 144x^2 + 36	\( 2^{64}\cdot 3^{10} \)	16T1439	Trivial
16.8.1089261790808475313373184.3	x^16 - 28x^12 + 72x^10 - 176x^8 + 240x^6 + 24x^4 - 144x^2 + 36	\( 2^{64}\cdot 3^{10} \)	16T1439	Trivial (GRH)
16.0.1921746620030977600000000.2	x^16 + 19x^14 + 134x^12 + 448x^10 + 821x^8 + 1100x^6 + 1246x^4 + 615x^2 + 25	\( 2^{12}\cdot 5^{8}\cdot 7^{4}\cdot 29^{8} \)	16T1439	$[2, 2]$
16.8.2711418606969521728515625.1	x^16 - 7x^15 + 11x^14 + 26x^13 - 105x^12 + 138x^11 + 30x^10 - 850x^9 + 1631x^8 + 925x^7 - 5070x^6 + 1977x^5 + 5100x^4 - 4161x^3 - 619x^2 + 1132x - 179	\( 5^{12}\cdot 29^{8}\cdot 149^{2} \)	16T1439	$[2]$ (GRH)
16.12.3278414891981209600000000.1	x^16 - 14x^14 + 5x^12 + 246x^10 + 928x^8 - 2186x^6 + 1321x^4 - 310x^2 + 25	\( 2^{24}\cdot 5^{8}\cdot 29^{8} \)	16T1439	$[2]$ (GRH)
16.4.3278414891981209600000000.1	x^16 - 14x^14 - 21x^12 + 38x^10 - 359x^8 - 824x^6 - 244x^4 + 48x^2 + 16	\( 2^{24}\cdot 5^{8}\cdot 29^{8} \)	16T1439	$[2, 2]$ (GRH)
16.8.3278414891981209600000000.1	x^16 + 14x^14 - 21x^12 - 38x^10 - 359x^8 + 824x^6 - 244x^4 - 48x^2 + 16	\( 2^{24}\cdot 5^{8}\cdot 29^{8} \)	16T1439	$[2]$ (GRH)
16.4.3648484877538188437890625.1	x^16 - 6x^15 + 7x^14 + 31x^13 - 95x^12 + 7x^11 + 380x^10 - 809x^9 + 323x^8 + 3373x^7 - 11738x^6 + 18868x^5 - 15217x^4 + 4402x^3 + 1848x^2 - 1899x + 499	\( 5^{8}\cdot 29^{10}\cdot 149^{2} \)	16T1439	$[2]$ (GRH)
16.8.16942867459404119507206144.1	x^16 - 4x^15 + 8x^14 - 36x^13 + 14x^12 + 444x^11 - 1014x^10 - 220x^9 + 2894x^8 - 2548x^7 - 248x^6 - 1276x^5 + 5705x^4 - 5520x^3 + 1928x^2 - 48x - 72	\( 2^{40}\cdot 17^{8}\cdot 47^{2} \)	16T1439	Trivial (GRH)
16.0.96313927189328563031640625.1	x^16 - 4x^15 + 26x^14 - 87x^13 + 268x^12 - 698x^11 + 1555x^10 - 3227x^9 + 6152x^8 - 10182x^7 + 15288x^6 - 18524x^5 + 19046x^4 - 14624x^3 + 8131x^2 - 2856x + 576	\( 5^{8}\cdot 29^{8}\cdot 149^{4} \)	16T1439	$[2, 2]$ (GRH)
16.8.96313927189328563031640625.1	x^16 - 7x^15 - 3x^14 + 117x^13 - 213x^12 - 231x^11 + 748x^10 + 326x^9 - 1966x^8 - 1840x^7 + 5945x^6 + 12072x^5 - 14843x^4 - 15050x^3 + 2634x^2 - 5115x + 1745	\( 5^{8}\cdot 29^{8}\cdot 149^{4} \)	16T1439	$[2]$ (GRH)
16.0.108144212401152158447265625.1	x^16 - 5x^14 - 15x^13 + 111x^12 - 100x^11 - 300x^10 + 870x^9 + 591x^8 - 4200x^7 + 7620x^6 - 305x^5 - 8459x^4 + 10935x^3 + 5060x^2 - 18530x + 11881	\( 5^{12}\cdot 29^{8}\cdot 941^{2} \)	16T1439	$[2, 20]$ (GRH)
16.12.121821863230510940507078656.1	x^16 - 12x^14 + 16x^12 + 236x^10 - 638x^8 - 908x^6 + 2944x^4 - 756x^2 + 49	\( 2^{50}\cdot 7^{8}\cdot 137^{2} \)	16T1439	Trivial (GRH)
16.8.146198414913373828091478016.1	x^16 - 2x^15 - 15x^14 + 50x^13 - 7x^12 - 72x^11 - 194x^10 + 440x^9 + 316x^8 + 716x^7 - 8510x^6 + 17940x^5 - 16775x^4 + 6650x^3 - 65x^2 - 518x + 49	\( 2^{32}\cdot 17^{8}\cdot 47^{4} \)	16T1439	Trivial (GRH)
16.8.520545564137112885142749184.1	x^16 - 4x^15 - 2x^14 + 16x^13 - x^12 - 4x^11 - 4x^10 - 8x^9 + 20x^8 - 8x^7 - 4x^6 - 4x^5 - x^4 + 16x^3 - 2x^2 - 4x + 1	\( 2^{28}\cdot 17^{8}\cdot 16673^{2} \)	16T1439	Trivial (GRH)
16.16.1451169020804591236241424384.1	x^16 - 32x^14 + 404x^12 - 2560x^10 + 8554x^8 - 14496x^6 + 10908x^4 - 2304x^2 + 9	\( 2^{62}\cdot 3^{10}\cdot 73^{2} \)	16T1439	Trivial (GRH)
16.0.51832117678535763588100000000.1	x^16 + 43x^14 + 526x^12 + 2072x^10 + 3733x^8 + 3420x^6 + 1586x^4 + 335x^2 + 25	\( 2^{8}\cdot 5^{8}\cdot 29^{8}\cdot 32189^{2} \)	16T1439	$[2, 2, 24]$ (GRH)
16.4.81000012766225321509609765625.1	x^16 - 5x^15 - 5x^14 + 20x^13 + 253x^12 - 818x^11 - 386x^10 + 2338x^9 - 6768x^8 + 40198x^7 - 78873x^6 + 42256x^5 - 137384x^4 + 304792x^3 - 147792x^2 - 1213216x + 1017664	\( 5^{8}\cdot 29^{10}\cdot 149^{4} \)	16T1439	$[4]$ (GRH)
16.0.169322776090667964052464992256.1	x^16 + 8x^14 + 18x^12 + 456x^10 + 673x^8 + 336x^6 + 2604x^4 + 3136x^2 + 784	\( 2^{20}\cdot 3^{8}\cdot 7^{10}\cdot 59^{2}\cdot 5003^{2} \)	16T1439	$[40]$ (GRH)
16.12.766808819747812401202828515625.1	x^16 - 26x^14 + 179x^12 - 17x^10 - 1987x^8 + 2549x^6 - 719x^4 - 12x^2 + 16	\( 5^{8}\cdot 29^{8}\cdot 1980941^{2} \)	16T1439	$[2]$ (GRH)
16.0.2902974096966413457817600000000.1	x^16 + 66x^14 + 1513x^12 + 16238x^10 + 90424x^8 + 267118x^6 + 403493x^4 + 276026x^2 + 57121	\( 2^{24}\cdot 5^{8}\cdot 29^{8}\cdot 941^{2} \)	16T1439	$[2, 2, 76]$ (GRH)
16.16.2902974096966413457817600000000.1	x^16 - 66x^14 + 1513x^12 - 16238x^10 + 90424x^8 - 267118x^6 + 403493x^4 - 276026x^2 + 57121	\( 2^{24}\cdot 5^{8}\cdot 29^{8}\cdot 941^{2} \)	16T1439	$[2]$ (GRH)
16.8.2902974096966413457817600000000.1	x^16 - 28x^14 + 374x^12 - 3548x^10 + 8623x^8 + 10364x^6 + 71806x^4 - 88464x^2 + 22801	\( 2^{24}\cdot 5^{8}\cdot 29^{8}\cdot 941^{2} \)	16T1439	$[2]$ (GRH)
16.0.2902974096966413457817600000000.2	x^16 + 16x^14 + 158x^12 + 2096x^10 - 3347x^8 + 22024x^6 + 400828x^4 + 726864x^2 + 309136	\( 2^{24}\cdot 5^{8}\cdot 29^{8}\cdot 941^{2} \)	16T1439	$[2, 2, 6]$ (GRH)
16.8.2902974096966413457817600000000.2	x^16 - 4x^15 - 24x^14 + 224x^13 - 674x^12 + 188x^11 + 6224x^10 - 23676x^9 + 37303x^8 - 2260x^7 - 130056x^6 + 186716x^5 + 149894x^4 - 591560x^3 + 554080x^2 - 214500x + 28125	\( 2^{24}\cdot 5^{8}\cdot 29^{8}\cdot 941^{2} \)	16T1439	$[2]$ (GRH)
16.8.2902974096966413457817600000000.3	x^16 - 38x^14 + 447x^12 - 4062x^10 + 30513x^8 - 144292x^6 + 411212x^4 - 598368x^2 + 309136	\( 2^{24}\cdot 5^{8}\cdot 29^{8}\cdot 941^{2} \)	16T1439	$[6]$ (GRH)
16.8.2902974096966413457817600000000.4	x^16 - 4x^15 - 16x^14 + 116x^13 - 98x^12 - 1740x^11 + 3508x^10 + 14704x^9 - 21049x^8 - 33988x^7 + 39972x^6 - 279840x^5 - 423938x^4 + 1106608x^3 + 2368316x^2 + 1253132x + 74941	\( 2^{24}\cdot 5^{8}\cdot 29^{8}\cdot 941^{2} \)	16T1439	$[2]$ (GRH)
16.4.42914840847220867781580656597794816.1	x^16 + 84x^14 + 2468x^12 + 30988x^10 + 138198x^8 - 252212x^6 - 2958100x^4 - 3327884x^2 + 5303809	\( 2^{50}\cdot 7^{8}\cdot 137^{6} \)	16T1439	$[2, 2, 2]$ (GRH)
16.4.42914840847220867781580656597794816.2	x^16 + 40x^14 + 144x^12 - 5304x^10 - 39036x^8 - 76944x^6 - 37800x^4 + 4112x^2 + 4	\( 2^{50}\cdot 7^{8}\cdot 137^{6} \)	16T1439	$[2, 2, 2, 2]$ (GRH)
16.8.144705903870176820092932857775783936.1	x^16 - 4x^15 - 82x^14 + 96x^13 + 1725x^12 + 3056x^11 + 17150x^10 + 32796x^9 - 54078x^8 + 116768x^7 - 314000x^6 - 654124x^5 + 762925x^4 - 1226092x^3 + 3299088x^2 - 2950448x + 321823	\( 2^{28}\cdot 17^{8}\cdot 16673^{4} \)	16T1439	$[2, 2]$ (GRH)