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 57)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.28016810838376881061888.1	x^20 - 8x^19 + 30x^18 - 74x^17 + 148x^16 - 262x^15 + 380x^14 - 404x^13 + 314x^12 - 248x^11 + 276x^10 - 240x^9 + 30x^8 + 184x^7 - 204x^6 + 84x^5 + 12x^4 - 32x^3 + 20x^2 - 8x + 2	\( 2^{34}\cdot 277^{5} \)	20T797	Trivial (GRH)
20.0.67050942866528672940032.1	x^20 - 2x^19 - 4x^18 + 18x^17 - 3x^16 - 38x^15 + 51x^14 - 6x^13 - 16x^12 + 134x^11 - 99x^10 - 48x^9 + 174x^8 - 88x^7 - 49x^6 + 88x^5 - 31x^4 - 12x^3 + 16x^2 - 6x + 1	\( 2^{20}\cdot 2297^{5} \)	20T797	Trivial (GRH)
20.4.68660165495325361090592768.1	x^20 - 4x^19 + 4x^18 - 2x^17 + 15x^16 - 2x^15 - 159x^14 + 462x^13 - 733x^12 + 1002x^11 - 1448x^10 + 1852x^9 - 1774x^8 + 1204x^7 - 530x^6 + 76x^5 + 93x^4 - 90x^3 + 41x^2 - 10x + 1	\( 2^{30}\cdot 2297^{5} \)	20T797	Trivial (GRH)
20.6.3042351129053791179853791232.1	x^20 - 2x^19 + 5x^18 + 6x^17 - 52x^16 + 146x^15 - 365x^14 + 612x^13 - 927x^12 + 1086x^11 - 882x^10 + 354x^9 + 762x^8 - 1670x^7 + 2475x^6 - 2398x^5 + 1935x^4 - 1062x^3 + 314x^2 - 48x - 9	\( -\,2^{30}\cdot 4903^{5} \)	20T797	Trivial (GRH)
20.4.3110398437339049957275390625.2	x^20 - 3x^19 + 8x^18 - 20x^17 - 15x^16 + 91x^15 - 97x^14 - 16x^13 + 366x^12 - 516x^11 - 7x^10 + 1308x^9 - 2620x^8 + 1579x^7 + 1856x^6 - 6733x^5 + 10200x^4 - 9042x^3 + 5879x^2 - 2359x + 109	\( 5^{15}\cdot 269^{7} \)	20T797	Trivial (GRH)
20.0.45072472075168000000000000000.1	x^20 + x^18 - 20x^16 - 12x^14 + 124x^12 + 140x^10 + 595x^8 + 2620x^6 + 4495x^4 + 3610x^2 + 1345	\( 2^{20}\cdot 5^{15}\cdot 269^{5} \)	20T797	Trivial (GRH)
20.0.45072472075168000000000000000.2	x^20 + 4x^18 + 31x^16 + 44x^14 - 39x^12 + 175x^10 + 1130x^8 + 2750x^6 + 4220x^4 + 3690x^2 + 1345	\( 2^{20}\cdot 5^{15}\cdot 269^{5} \)	20T797	Trivial (GRH)
20.12.243095256386686436431884765625.1	x^20 - 4x^19 - 6x^18 + 71x^17 - 108x^16 - 254x^15 + 829x^14 - 129x^13 - 2111x^12 + 1963x^11 + 2115x^10 - 3543x^9 - 162x^8 + 2707x^7 - 961x^6 - 724x^5 + 572x^4 - 22x^3 - 83x^2 + 19x - 1	\( 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.8.243095256386686436431884765625.1	x^20 - 21x^18 - 41x^17 + 64x^16 + 412x^15 + 884x^14 + 1082x^13 + 722x^12 + 53x^11 - 283x^10 + 53x^9 + 722x^8 + 1082x^7 + 884x^6 + 412x^5 + 64x^4 - 41x^3 - 21x^2 + 1	\( 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.0.1697562448531136375219997900800.1	x^20 - 2x^19 + 5x^18 - 24x^17 + 70x^16 - 114x^15 + 78x^14 + 174x^13 - 853x^12 + 2502x^11 - 7516x^10 + 17494x^9 - 20080x^8 - 13454x^7 + 96689x^6 - 182618x^5 + 191409x^4 - 120740x^3 + 46159x^2 - 10388x + 1297	\( 2^{20}\cdot 5^{2}\cdot 36497^{5} \)	20T797	$[2]$ (GRH)
20.0.1697562448531136375219997900800.2	x^20 - 8x^19 + 28x^18 - 52x^17 + 54x^16 - 80x^15 + 342x^14 - 1020x^13 + 1782x^12 - 1430x^11 - 1228x^10 + 4782x^9 - 4943x^8 - 62x^7 + 5059x^6 - 3590x^5 - 1258x^4 + 1308x^3 + 3073x^2 - 5050x + 2561	\( 2^{20}\cdot 5^{2}\cdot 36497^{5} \)	20T797	$[2]$ (GRH)
20.10.4432204969617689467720296300544.1	x^20 + 6x^18 - 25x^16 - 246x^14 - 320x^12 + 692x^10 + 2195x^8 + 44x^6 - 1784x^4 + 584x^2 - 4	\( -\,2^{50}\cdot 89^{8} \)	20T797	Trivial (GRH)
20.2.4432204969617689467720296300544.1	x^20 - 6x^18 - 25x^16 + 246x^14 - 320x^12 - 692x^10 + 2195x^8 - 44x^6 - 1784x^4 - 584x^2 - 4	\( -\,2^{50}\cdot 89^{8} \)	20T797	Trivial (GRH)
20.10.4432204969617689467720296300544.2	x^20 + 8x^18 + 34x^16 - 42x^14 - 724x^12 - 902x^10 + 837x^8 + 2882x^6 - 1527x^4 + 102x^2 - 1	\( -\,2^{50}\cdot 89^{8} \)	20T797	Trivial (GRH)
20.2.4432204969617689467720296300544.2	x^20 - 8x^18 + 34x^16 + 42x^14 - 724x^12 + 902x^10 + 837x^8 - 2882x^6 - 1527x^4 - 102x^2 - 1	\( -\,2^{50}\cdot 89^{8} \)	20T797	Trivial (GRH)
20.12.6077381409667160910797119140625.1	x^20 - 10x^19 + 35x^18 - 30x^17 - 175x^16 + 788x^15 - 1355x^14 - 225x^13 + 5170x^12 - 8595x^11 + 4014x^10 + 5125x^9 - 8790x^8 + 4745x^7 + 255x^6 - 1553x^5 + 640x^4 + 25x^3 - 80x^2 + 15x + 1	\( 5^{17}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.8.6077381409667160910797119140625.1	x^20 - 4x^19 + 2x^18 - 12x^17 + 45x^16 + 42x^15 - 58x^14 - 146x^13 - 24x^12 - 85x^11 - 1120x^10 + 165x^9 + 1795x^8 + 935x^7 + 1625x^6 + 1040x^5 - 1685x^4 - 2325x^3 - 910x^2 + 5x + 5	\( 5^{17}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.6.25454644418510559398901598650368.1	x^20 - 6x^18 - 4x^17 + 26x^16 + 80x^15 - 64x^14 - 40x^13 + 556x^12 - 144x^11 - 590x^10 + 328x^9 - 1063x^8 - 552x^7 + 552x^6 - 132x^5 + 866x^4 + 280x^3 - 238x^2 + 256x + 1	\( -\,2^{40}\cdot 17^{5}\cdot 439^{5} \)	20T797	Trivial (GRH)
20.6.26101424948512167208849797808128.1	x^20 - 10x^18 - 16x^17 + 36x^16 + 176x^15 + 178x^14 - 352x^13 - 984x^12 - 336x^11 + 1158x^10 + 1024x^9 - 831x^8 - 1360x^7 + 584x^6 + 956x^5 - 412x^4 - 72x^3 + 24x^2 - 4x + 1	\( -\,2^{40}\cdot 3^{16}\cdot 223^{5} \)	20T797	Trivial (GRH)
20.6.26101424948512167208849797808128.2	x^20 - 8x^18 - 12x^17 + 50x^16 + 72x^15 - 284x^14 - 12x^13 + 1026x^12 - 1248x^11 - 2156x^10 + 9588x^9 - 16185x^8 + 15216x^7 - 5030x^6 - 8376x^5 + 16990x^4 - 16608x^3 + 9616x^2 - 3024x + 383	\( -\,2^{40}\cdot 3^{16}\cdot 223^{5} \)	20T797	Trivial (GRH)
20.0.254903851560926116768000000000000000.1	x^20 + 58x^18 + 1368x^16 + 16943x^14 + 119596x^12 + 495730x^10 + 1220435x^8 + 1754905x^6 + 1376210x^4 + 482320x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	$[2, 3332]$ (GRH)
20.12.254903851560926116768000000000000000.1	x^20 - 24x^18 - 108x^16 + 3539x^14 + 9241x^12 - 55655x^10 - 114550x^8 + 168675x^6 + 65245x^4 - 120580x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.16.254903851560926116768000000000000000.1	x^20 - 23x^18 + 113x^16 + 1407x^14 - 20829x^12 + 111275x^10 - 289555x^8 + 333065x^6 - 45205x^4 - 150725x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.4.254903851560926116768000000000000000.1	x^20 + 23x^18 + 158x^16 - 147x^14 - 6649x^12 - 29760x^10 - 40100x^8 + 42055x^6 + 149285x^4 + 120580x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	$[2]$ (GRH)
20.8.254903851560926116768000000000000000.1	x^20 - 3x^18 - 312x^16 + 292x^14 + 22601x^12 - 26205x^10 - 334365x^8 - 116715x^6 + 861665x^4 + 753625x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.0.254903851560926116768000000000000000.2	x^20 + 59x^18 + 1457x^16 + 19511x^14 + 153086x^12 + 707510x^10 + 1831320x^8 + 2368985x^6 + 1341665x^4 + 334180x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	$[2, 2964]$ (GRH)
20.12.254903851560926116768000000000000000.2	x^20 - 18x^18 - 147x^16 + 2392x^14 + 1746x^12 - 27260x^10 - 2990x^8 + 86200x^6 - 28755x^4 - 60290x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.16.254903851560926116768000000000000000.2	x^20 - 52x^18 + 1075x^16 - 11189x^14 + 60154x^12 - 142790x^10 + 15590x^8 + 396600x^6 - 323255x^4 - 120580x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.4.254903851560926116768000000000000000.2	x^20 + 26x^18 + 181x^16 - 484x^14 - 9984x^12 - 24860x^10 + 92860x^8 + 506885x^6 + 698900x^4 + 271305x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.8.254903851560926116768000000000000000.2	x^20 - 12x^18 - 155x^16 + 1211x^14 + 11159x^12 - 22280x^10 - 262900x^8 - 87530x^6 + 1475615x^4 + 1115365x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.12.254903851560926116768000000000000000.3	x^20 - 17x^18 - 37x^16 + 1438x^14 - 3744x^12 - 17895x^10 + 71565x^8 + 2500x^6 - 159065x^4 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.16.254903851560926116768000000000000000.3	x^20 - 46x^18 + 675x^16 - 3573x^14 + 2529x^12 + 27735x^10 - 57290x^8 - 20400x^6 + 140385x^4 - 120580x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.4.254903851560926116768000000000000000.3	x^20 + 33x^18 + 288x^16 - 917x^14 - 26289x^12 - 130990x^10 - 157925x^8 + 417670x^6 + 994420x^4 + 331595x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.8.254903851560926116768000000000000000.3	x^20 - 9x^18 - 208x^16 + 474x^14 + 16151x^12 + 58920x^10 - 39940x^8 - 486825x^6 - 406925x^4 + 753625x^2 + 753625	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	$[2]$ (GRH)
20.12.254903851560926116768000000000000000.4	x^20 + 13x^18 - 281x^16 - 1718x^14 + 19311x^12 - 9780x^10 - 177875x^8 + 255610x^6 + 241395x^4 - 361740x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.16.254903851560926116768000000000000000.4	x^20 - 32x^18 + 298x^16 + 863x^14 - 36029x^12 + 286120x^10 - 1109640x^8 + 2280840x^6 - 2331235x^4 + 894730x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.4.254903851560926116768000000000000000.4	x^20 + 17x^18 + 53x^16 - 663x^14 - 6449x^12 - 23085x^10 - 34385x^8 + 4845x^6 + 80745x^4 + 90435x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	$[2]$ (GRH)
20.8.254903851560926116768000000000000000.4	x^20 + 2x^18 - 235x^16 - 756x^14 + 12629x^12 + 27415x^10 - 252970x^8 - 166415x^6 + 1224730x^4 + 391885x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.12.254903851560926116768000000000000000.5	x^20 - 8x^18 - 170x^16 + 1169x^14 + 10599x^12 - 57135x^10 - 289765x^8 + 1049700x^6 + 2937550x^4 - 5275375x^2 + 753625	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.16.254903851560926116768000000000000000.5	x^20 - 25x^18 + 61x^16 + 2370x^14 - 20106x^12 + 36180x^10 + 165615x^8 - 775180x^6 + 1042625x^4 - 391885x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.4.254903851560926116768000000000000000.5	x^20 + 11x^18 - 195x^16 - 1992x^14 + 2484x^12 + 74460x^10 + 287485x^8 + 491230x^6 + 424490x^4 + 180870x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	$[2]$ (GRH)
20.8.254903851560926116768000000000000000.5	x^20 + 10x^18 - 76x^16 - 850x^14 + 824x^12 + 17270x^10 + 10740x^8 - 94555x^6 - 135150x^4 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.12.254903851560926116768000000000000000.6	x^20 + 10x^18 - 216x^16 - 1285x^14 + 18774x^12 + 26385x^10 - 616740x^8 + 1226525x^6 + 814300x^4 - 2044000x^2 + 753625	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.16.254903851560926116768000000000000000.6	x^20 - 31x^18 + 190x^16 + 2532x^14 - 37331x^12 + 179270x^10 - 383085x^8 + 309135x^6 + 57740x^4 - 150725x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.4.254903851560926116768000000000000000.6	x^20 + 26x^18 + 140x^16 - 1507x^14 - 18831x^12 - 55275x^10 + 74775x^8 + 627440x^6 + 962920x^4 + 452175x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	$[2]$ (GRH)
20.8.254903851560926116768000000000000000.6	x^20 - 4x^18 - 90x^16 + 78x^14 + 2299x^12 + 1795x^10 - 18940x^8 - 36230x^6 + 10995x^4 + 60290x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.12.254903851560926116768000000000000000.7	x^20 - 12x^18 - 187x^16 + 818x^14 + 9331x^12 - 9570x^10 - 103225x^8 + 104460x^6 + 179210x^4 - 180870x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.8.254903851560926116768000000000000000.7	x^20 + 12x^18 - 156x^16 - 2707x^14 - 6169x^12 + 54155x^10 + 177005x^8 - 448270x^6 - 1113750x^4 + 2019715x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.12.254903851560926116768000000000000000.8	x^20 - 26x^18 + 31x^16 + 3064x^14 - 21014x^12 - 6435x^10 + 397185x^8 - 878600x^6 - 377050x^4 + 1507250x^2 + 753625	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)
20.8.254903851560926116768000000000000000.8	x^20 + 4x^18 - 364x^16 + 549x^14 + 16916x^12 + 24835x^10 - 95320x^8 - 196465x^6 + 2650x^4 + 120580x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	Trivial (GRH)