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 88)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.908233335668669940736.1	x^20 + 7x^18 + 22x^16 + 42x^14 + 59x^12 + 65x^10 + 55x^8 + 36x^6 + 17x^4 + 6x^2 + 1	\( 2^{10}\cdot 47^{8}\cdot 193^{2} \)	20T853	Trivial
20.0.5455129962034305811456.1	x^20 - 3x^18 + 11x^14 - 15x^12 - x^10 + 15x^8 - 5x^6 - 8x^4 + 5x^2 + 1	\( 2^{10}\cdot 11^{2}\cdot 43^{2}\cdot 47^{8} \)	20T853	Trivial
20.0.172004164305285576392704.4	x^20 + x^18 + 5x^16 + 5x^14 + 8x^12 + 9x^10 + 5x^8 + 6x^6 + 2x^4 + 1	\( 2^{20}\cdot 47^{8}\cdot 83^{2} \)	20T853	Trivial (GRH)
20.0.172004164305285576392704.5	x^20 - x^18 + 5x^16 - 5x^14 + 8x^12 - 9x^10 + 5x^8 - 6x^6 + 2x^4 + 1	\( 2^{20}\cdot 47^{8}\cdot 83^{2} \)	20T853	Trivial (GRH)
20.4.930030935724718019313664.3	x^20 - x^18 - 10x^12 + 6x^10 + 22x^8 - 35x^6 + 22x^4 - 7x^2 + 1	\( 2^{20}\cdot 47^{8}\cdot 193^{2} \)	20T853	Trivial (GRH)
20.4.930030935724718019313664.4	x^20 - 7x^18 + 22x^16 - 44x^14 + 54x^12 - 42x^10 + 16x^8 - 3x^6 + 6x^4 - 3x^2 + 1	\( 2^{20}\cdot 47^{8}\cdot 193^{2} \)	20T853	Trivial (GRH)
20.4.362168446004865338996048896.1	x^20 - 6x^19 + 15x^18 - 7x^17 - 79x^16 + 310x^15 - 656x^14 + 925x^13 - 827x^12 + 200x^11 + 832x^10 - 1890x^9 + 2521x^8 - 2528x^7 + 2029x^6 - 1314x^5 + 684x^4 - 277x^3 + 81x^2 - 14x + 1	\( 2^{10}\cdot 23^{2}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.8.6309535724727483864248745984.2	x^20 - 2x^19 + x^18 - 10x^16 + 36x^15 - 27x^14 - 38x^13 + 26x^12 - 184x^11 + 177x^10 + 396x^9 - 130x^8 - 234x^7 - 575x^6 - 202x^5 + 1165x^4 + 378x^3 - 684x^2 - 162x + 81	\( 2^{20}\cdot 3^{2}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.4.6309535724727483864248745984.3	x^20 - 9x^18 - 10x^17 + 18x^16 + 72x^15 + 86x^14 - 154x^13 - 304x^12 - 86x^11 + 220x^10 + 398x^9 - 1024x^8 - 16x^7 + 2093x^6 + 1168x^5 + 556x^4 + 1080x^3 + 85x^2 + 674x - 117	\( 2^{20}\cdot 3^{2}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.8.6309535724727483864248745984.3	x^20 - 10x^19 + 44x^18 - 108x^17 + 133x^16 + 48x^15 - 536x^14 + 1088x^13 - 1214x^12 + 832x^11 - 242x^10 - 170x^9 - 307x^8 + 544x^7 + 308x^6 - 542x^5 + 477x^4 - 68x^3 - 88x^2 + 52x - 9	\( 2^{20}\cdot 3^{2}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.4.6309535724727483864248745984.4	x^20 - 8x^19 + 28x^18 - 68x^17 + 177x^16 - 494x^15 + 1142x^14 - 2080x^13 + 3098x^12 - 3826x^11 + 3964x^10 - 3634x^9 + 3036x^8 - 2186x^7 + 1379x^6 - 810x^5 + 424x^4 - 178x^3 + 53x^2 - 10x + 1	\( 2^{20}\cdot 3^{2}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.8.6309535724727483864248745984.4	x^20 - 10x^19 + 57x^18 - 228x^17 + 691x^16 - 1652x^15 + 3142x^14 - 4712x^13 + 5294x^12 - 3684x^11 - 328x^10 + 5198x^9 - 8014x^8 + 6890x^7 - 2765x^6 - 1228x^5 + 2405x^4 - 1388x^3 + 277x^2 + 54x + 1	\( 2^{20}\cdot 3^{2}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.12.20019220282851167065375171584.1	x^20 - 13x^18 + 93x^16 - 470x^14 + 1561x^12 - 3159x^10 + 3730x^8 - 2447x^6 + 835x^4 - 141x^2 + 9	\( 2^{10}\cdot 3^{4}\cdot 19^{2}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.4.20019220282851167065375171584.1	x^20 - 9x^19 + 40x^18 - 122x^17 + 287x^16 - 512x^15 + 587x^14 - 172x^13 - 874x^12 + 1930x^11 - 1815x^10 + 505x^9 + 632x^8 - 511x^7 - 239x^6 - 287x^5 + 1562x^4 - 2083x^3 + 1408x^2 - 300x + 9	\( 2^{10}\cdot 3^{4}\cdot 19^{2}\cdot 401^{8} \)	20T853	$[2]$ (GRH)
20.4.20019220282851167065375171584.2	x^20 - 9x^19 + 43x^18 - 148x^17 + 411x^16 - 956x^15 + 1904x^14 - 3335x^13 + 5099x^12 - 6918x^11 + 8186x^10 - 8443x^9 + 7371x^8 - 5276x^7 + 2919x^6 - 1040x^5 + 152x^4 + 81x^3 + 7x^2 - 11x + 1	\( 2^{10}\cdot 3^{4}\cdot 19^{2}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.4.20019220282851167065375171584.3	x^20 - 8x^19 + 21x^18 - 5x^17 - 69x^16 + 56x^15 + 265x^14 - 617x^13 + 338x^12 + 370x^11 - 403x^10 - 391x^9 + 891x^8 - 546x^7 - 20x^6 + 206x^5 - 92x^4 - 15x^3 + 27x^2 - 9x + 1	\( 2^{10}\cdot 3^{4}\cdot 19^{2}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.12.41273232813985341024193089249.1	x^20 - x^19 - 16x^18 + 14x^17 + 61x^16 - 11x^15 + 66x^14 - 295x^13 - 949x^12 + 977x^11 + 2376x^10 - 1045x^9 - 1983x^8 + 684x^7 - 619x^6 - 1540x^5 + 1170x^4 + 1729x^3 + 170x^2 - 309x - 83	\( 3^{8}\cdot 97^{2}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.8.41273232813985341024193089249.2	x^20 - 2x^19 - 3x^18 + 6x^17 - 2x^16 + 25x^15 - 34x^14 - 88x^13 + 228x^12 - 25x^11 - 207x^10 + 188x^9 - 363x^8 - 149x^7 + 222x^6 - 563x^5 - 374x^4 + 171x^3 + 95x^2 + 2x - 1	\( 3^{8}\cdot 97^{2}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.12.56785821522547354778238713856.3	x^20 - 10x^19 + 42x^18 - 92x^17 + 74x^16 + 168x^15 - 627x^14 + 856x^13 - 121x^12 - 1606x^11 + 2564x^10 - 602x^9 - 2814x^8 + 2728x^7 + 965x^6 - 1990x^5 - 132x^4 + 612x^3 + 46x^2 - 66x - 9	\( 2^{20}\cdot 3^{4}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.8.56785821522547354778238713856.3	x^20 - 2x^19 + 7x^18 + 4x^17 - 43x^16 + 82x^15 - 99x^14 + 188x^13 - 483x^12 + 602x^11 - 332x^10 - 246x^9 + 577x^8 - 474x^7 + 615x^6 - 360x^5 + 137x^4 - 60x^3 - 94x^2 + 34x + 13	\( 2^{20}\cdot 3^{4}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.8.56785821522547354778238713856.4	x^20 - 10x^19 + 53x^18 - 176x^17 + 372x^16 - 396x^15 - 306x^14 + 2076x^13 - 4027x^12 + 3952x^11 - 419x^10 - 4816x^9 + 7703x^8 - 5980x^7 + 1639x^6 + 1382x^5 - 1719x^4 + 960x^3 - 377x^2 + 96x - 9	\( 2^{20}\cdot 3^{4}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.4.56785821522547354778238713856.5	x^20 - 4x^19 - 5x^18 + 30x^17 - 67x^16 + 14x^15 + 23x^14 - 44x^13 + 35x^12 - 14x^11 - 19x^10 - 14x^9 + 35x^8 - 44x^7 + 23x^6 + 14x^5 - 67x^4 + 30x^3 - 5x^2 - 4x + 1	\( 2^{20}\cdot 3^{4}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.8.56785821522547354778238713856.5	x^20 - 10x^19 + 32x^18 + 10x^17 - 353x^16 + 1110x^15 - 1657x^14 + 544x^13 + 3727x^12 - 11324x^11 + 19496x^10 - 23824x^9 + 23226x^8 - 20708x^7 + 17554x^6 - 12308x^5 + 5941x^4 - 1606x^3 + 107x^2 + 48x - 3	\( 2^{20}\cdot 3^{4}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.8.56785821522547354778238713856.6	x^20 - 4x^19 + x^18 - 4x^17 + 104x^16 - 256x^15 + 104x^14 + 226x^13 - 166x^12 + 244x^11 - 498x^10 - 462x^9 + 1149x^8 + 160x^7 - 791x^6 + 794x^5 - 1920x^4 + 1428x^3 + 308x^2 - 470x + 61	\( 2^{20}\cdot 3^{4}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.4.57180852133785175762361058304.1	x^20 - 4x^18 - 15x^16 + 111x^14 - 127x^12 - 558x^10 + 2159x^8 - 3377x^6 + 2823x^4 - 1275x^2 + 289	\( 2^{10}\cdot 17^{4}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.4.57180852133785175762361058304.2	x^20 - 7x^19 + 16x^18 - 16x^17 + 4x^16 + 41x^15 - 135x^14 + 186x^13 - 129x^12 + 238x^11 + 73x^10 - 176x^9 + 166x^8 + 90x^7 + 55x^6 - 12x^5 + 22x^4 + 10x^3 + 6x^2 + 7x + 3	\( 2^{10}\cdot 17^{4}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.8.71222592559838145140956205056.1	x^20 - 8x^19 + 27x^18 - 36x^17 - 28x^16 + 149x^15 - 144x^14 + 23x^13 - 78x^12 + 233x^11 - 421x^10 + 765x^9 - 46x^8 - 1523x^7 + 1027x^6 + 671x^5 - 761x^4 - 8x^3 + 197x^2 - 16x - 8	\( 2^{12}\cdot 1429^{8} \)	20T853	Trivial (GRH)
20.12.118479059719882752562004230144.2	x^20 - 15x^18 - 4x^17 + 38x^16 + 6x^15 + 115x^14 + 60x^13 - 326x^12 - 228x^11 - 610x^10 + 384x^9 + 1712x^8 + 194x^7 - 923x^6 - 908x^5 - 100x^4 + 614x^3 + 84x^2 - 112x + 27	\( 2^{20}\cdot 13^{2}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.8.118479059719882752562004230144.2	x^20 - 14x^16 + 38x^14 + 23x^12 - 93x^10 + 2x^8 + 50x^6 - x^4 - 10x^2 + 1	\( 2^{20}\cdot 13^{2}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.4.118479059719882752562004230144.3	x^20 + 8x^18 + 24x^16 + 64x^14 + 85x^12 - 35x^10 - 18x^8 + 20x^6 - 42x^4 + x^2 + 9	\( 2^{20}\cdot 13^{2}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.8.118479059719882752562004230144.3	x^20 - 11x^18 + 40x^16 - 42x^14 - 49x^12 + 110x^10 - 44x^8 - 44x^6 + 48x^4 - 13x^2 + 1	\( 2^{20}\cdot 13^{2}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.4.118479059719882752562004230144.4	x^20 + 7x^18 + 16x^16 + 7x^14 - 26x^12 - 33x^10 + 13x^8 + 28x^6 - 5x^4 - 6x^2 + 1	\( 2^{20}\cdot 13^{2}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.12.511072393702926193004148424704.5	x^20 - 6x^19 + 11x^18 + 34x^17 - 199x^16 + 142x^15 + 573x^14 - 400x^13 - 1264x^12 + 200x^11 + 2143x^10 + 156x^9 - 1991x^8 - 196x^7 + 962x^6 + 216x^5 - 205x^4 - 122x^3 + 11x^2 + 16x - 1	\( 2^{20}\cdot 3^{6}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.4.511072393702926193004148424704.5	x^20 - 10x^19 + 55x^18 - 210x^17 + 621x^16 - 1500x^15 + 3066x^14 - 5412x^13 + 8299x^12 - 11002x^11 + 12355x^10 - 11346x^9 + 7942x^8 - 3484x^7 - 38x^6 + 1496x^5 - 1244x^4 + 498x^3 - 61x^2 - 26x + 9	\( 2^{20}\cdot 3^{6}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.8.511072393702926193004148424704.9	x^20 - 6x^19 + 15x^18 - 12x^17 - 7x^16 - 78x^15 + 486x^14 - 686x^13 - 1271x^12 + 5296x^11 - 4499x^10 - 5152x^9 + 10172x^8 + 422x^7 - 8409x^6 + 808x^5 + 3711x^4 - 162x^3 - 875x^2 - 6x + 81	\( 2^{20}\cdot 3^{6}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.12.991469737933152814126207682281.1	x^20 - 8x^19 + 11x^18 + 63x^17 - 173x^16 - 135x^15 + 723x^14 - 116x^13 - 1194x^12 + 980x^11 + 177x^10 - 1904x^9 + 1581x^8 + 2000x^7 - 1402x^6 - 1005x^5 + 260x^4 + 61x^3 - 19x^2 + 19x - 1	\( 97^{2}\cdot 397^{2}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.8.1139561480957410322255299280896.1	x^20 - x^18 - 33x^16 - 151x^14 + 441x^12 + 472x^10 - 355x^8 + 18x^6 - 236x^4 - 128x^2 + 64	\( 2^{16}\cdot 1429^{8} \)	20T853	Trivial (GRH)
20.0.1621556842910944532295388898304.1	x^20 - x^19 - x^18 + 12x^17 - 3x^16 - 9x^15 + 82x^14 + 191x^13 + 437x^12 - 93x^11 - 853x^10 + 2932x^9 + 4290x^8 - 2300x^7 + 12872x^6 + 27752x^5 - 18600x^4 - 44320x^3 + 33296x^2 + 80352x + 33696	\( 2^{10}\cdot 3^{8}\cdot 19^{2}\cdot 401^{8} \)	20T853	$[2, 2]$ (GRH)
20.8.1621556842910944532295388898304.1	x^20 - x^19 - 11x^18 + 8x^17 + 104x^16 - 243x^15 - 167x^14 + 1758x^13 - 3479x^12 + 1205x^11 + 6480x^10 - 10410x^9 + 3797x^8 + 2970x^7 - 2012x^6 - 293x^5 + 353x^4 - x^3 - 33x^2 + 1	\( 2^{10}\cdot 3^{8}\cdot 19^{2}\cdot 401^{8} \)	20T853	$[2]$ (GRH)
20.0.3147056207589075007401402302464.1	x^20 + 16x^18 + 114x^16 + 516x^14 + 1657x^12 + 3986x^10 + 7492x^8 + 15190x^6 + 41096x^4 + 67804x^2 + 40401	\( 2^{20}\cdot 67^{2}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.12.4599651543326335737037335822336.2	x^20 - 10x^19 + 41x^18 - 84x^17 - 11x^16 + 700x^15 - 2454x^14 + 4724x^13 - 5048x^12 + 284x^11 + 8438x^10 - 13706x^9 + 8835x^8 + 3382x^7 - 10709x^6 + 7104x^5 - 145x^4 - 2450x^3 + 1408x^2 - 300x + 17	\( 2^{20}\cdot 3^{8}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.4.4599651543326335737037335822336.2	x^20 - 6x^19 - 4x^18 + 74x^17 - 318x^15 - 193x^14 + 612x^13 + 1819x^12 + 254x^11 - 2818x^10 - 1246x^9 - 1626x^8 - 190x^7 + 2594x^6 - 300x^5 + 982x^4 - 472x^3 + 29x^2 - 18x - 3	\( 2^{20}\cdot 3^{8}\cdot 401^{8} \)	20T853	$[2]$ (GRH)
20.8.4599651543326335737037335822336.3	x^20 - 10x^19 + 59x^18 - 246x^17 + 662x^16 - 1012x^15 - 170x^14 + 5844x^13 - 18046x^12 + 33552x^11 - 42286x^10 + 34390x^9 - 12142x^8 - 9642x^7 + 17851x^6 - 13144x^5 + 5366x^4 - 1050x^3 + x^2 + 22x + 1	\( 2^{20}\cdot 3^{8}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.4.9596803837310502957522342641664.1	x^20 + 5x^18 + x^16 - 26x^14 - 40x^12 - 8x^10 + 59x^8 + 91x^6 + 55x^4 + 14x^2 + 1	\( 2^{20}\cdot 3^{4}\cdot 13^{2}\cdot 401^{8} \)	20T853	$[2]$ (GRH)
20.8.9596803837310502957522342641664.1	x^20 - 5x^18 + x^16 + 26x^14 - 40x^12 + 8x^10 + 59x^8 - 91x^6 + 55x^4 - 14x^2 + 1	\( 2^{20}\cdot 3^{4}\cdot 13^{2}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.4.9596803837310502957522342641664.2	x^20 - 2x^18 - 2x^16 + 13x^14 - 21x^12 + 4x^10 + 23x^8 - 14x^6 - 7x^4 + 3x^2 + 1	\( 2^{20}\cdot 3^{4}\cdot 13^{2}\cdot 401^{8} \)	20T853	$[2]$ (GRH)
20.8.9596803837310502957522342641664.2	x^20 + 2x^18 - 2x^16 - 13x^14 - 21x^12 - 4x^10 + 23x^8 + 14x^6 - 7x^4 - 3x^2 + 1	\( 2^{20}\cdot 3^{4}\cdot 13^{2}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.12.13545171081939968415683335684096.1	x^20 - 3x^18 - 39x^16 + 273x^14 - 732x^12 + 996x^10 - 693x^8 + 204x^6 - 9x^2 + 1	\( 2^{20}\cdot 139^{2}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.16.16607987450941256444002281496081.1	x^20 - 8x^19 + 19x^18 + 31x^17 - 303x^16 + 698x^15 + 134x^14 - 4107x^13 + 7440x^12 + 1786x^11 - 21982x^10 + 20892x^9 + 15143x^8 - 36900x^7 + 10996x^6 + 17715x^5 - 13580x^4 + 209x^3 + 2582x^2 - 846x + 81	\( 397^{4}\cdot 401^{8} \)	20T853	Trivial (GRH)
20.8.16607987450941256444002281496081.1	x^20 - 11x^18 - 22x^17 - 41x^16 + 68x^15 + 559x^14 + 1346x^13 + 1718x^12 - 541x^11 - 5151x^10 - 9208x^9 - 4467x^8 + 5621x^7 + 12621x^6 + 9010x^5 + 1478x^4 - 4237x^3 - 4731x^2 - 1417x - 137	\( 397^{4}\cdot 401^{8} \)	20T853	Trivial (GRH)