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 87)

Label	Polynomial	Discriminant	Galois group	Class group
20.2.42686966776427487214592.1	x^20 - 4x^19 + 2x^18 + 19x^17 - 38x^16 - 3x^15 + 94x^14 - 109x^13 - 26x^12 + 181x^11 - 166x^10 - 10x^9 + 172x^8 - 191x^7 + 67x^6 + 92x^5 - 154x^4 + 107x^3 - 41x^2 + 9x - 1	\( -\,2^{10}\cdot 47^{9}\cdot 193^{2} \)	20T848	Trivial (GRH)
20.2.42686966776427487214592.2	x^20 + 4x^18 + 8x^16 + 15x^14 + 10x^12 - 45x^10 - 131x^8 - 184x^6 - 191x^4 - 141x^2 - 47	\( -\,2^{10}\cdot 47^{9}\cdot 193^{2} \)	20T848	Trivial (GRH)
20.0.22392111040671733867877719121.3	x^20 - 5x^19 + 25x^18 - 69x^17 + 193x^16 - 390x^15 + 811x^14 - 1314x^13 + 2052x^12 - 2758x^11 + 3321x^10 - 3826x^9 + 3208x^8 - 3203x^7 + 2107x^6 - 562x^5 + 776x^4 + 415x^3 - 670x^2 - 188x + 177	\( 17^{4}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.0.22392111040671733867877719121.4	x^20 - 6x^19 + 17x^18 - 14x^17 - 44x^16 + 169x^15 - 222x^14 + 18x^13 + 444x^12 - 1059x^11 + 2372x^10 - 5798x^9 + 12099x^8 - 19680x^7 + 25390x^6 - 26968x^5 + 24047x^4 - 17963x^3 + 10880x^2 - 4847x + 1191	\( 17^{4}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.4.145229546847951000937415607296.1	x^20 - 6x^19 + 13x^18 - 3x^17 - 62x^16 + 142x^15 - 53x^14 - 271x^13 + 449x^12 - 275x^11 - 505x^10 + 652x^9 - 599x^8 - 240x^7 + 465x^6 - 403x^5 + 202x^4 - 101x^3 + 80x^2 - 39x + 9	\( 2^{10}\cdot 23^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.8.145229546847951000937415607296.1	x^20 - 29x^16 - 143x^14 - 43x^12 + 616x^10 + 2491x^8 - 765x^6 + 175x^4 - 1203x^2 + 401	\( 2^{10}\cdot 23^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.4.145229546847951000937415607296.2	x^20 - 8x^19 + 32x^18 - 48x^17 - 111x^16 + 900x^15 - 3168x^14 + 7942x^13 - 15636x^12 + 24861x^11 - 32009x^10 + 32985x^9 - 26571x^8 + 16109x^7 - 6970x^6 + 2044x^5 - 422x^4 + 61x^3 + 17x^2 - 7x - 1	\( 2^{10}\cdot 23^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.4.145229546847951000937415607296.3	x^20 - 7x^19 + 19x^18 - 10x^17 - 96x^16 + 376x^15 - 722x^14 + 574x^13 + 589x^12 - 870x^11 - 4806x^10 + 16019x^9 - 19034x^8 + 6028x^7 + 5878x^6 - 2868x^5 - 3517x^4 + 2515x^3 + 453x^2 - 672x + 83	\( 2^{10}\cdot 23^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.12.281124869512857892173749682176.3	x^20 - 6x^19 + 10x^18 + 14x^17 - 89x^16 + 120x^15 - 44x^14 - 26x^13 + 1089x^12 - 1914x^11 - 2322x^10 + 4360x^9 + 2420x^8 - 4278x^7 - 1396x^6 + 2330x^5 + 242x^4 - 600x^3 + 35x^2 + 54x - 9	\( 2^{20}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.8.281124869512857892173749682176.7	x^20 - x^18 + 6x^16 - 44x^15 - 137x^14 + 86x^13 + 341x^12 - 186x^11 - 402x^10 + 2528x^9 + 4445x^8 - 2840x^7 - 11639x^6 - 7962x^5 + 3197x^4 + 6836x^3 + 1923x^2 - 1314x - 621	\( 2^{20}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.8.281124869512857892173749682176.8	x^20 - 6x^18 - 10x^17 + 10x^16 + 18x^15 - 93x^14 - 60x^13 + 507x^12 + 884x^11 - 65x^10 - 636x^9 + 2060x^8 + 4324x^7 - 161x^6 - 7446x^5 - 8961x^4 - 5122x^3 - 1566x^2 - 238x - 13	\( 2^{20}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.4.281124869512857892173749682176.11	x^20 - 10x^19 + 62x^18 - 256x^17 + 783x^16 - 1774x^15 + 2925x^14 - 3038x^13 + 372x^12 + 5766x^11 - 13472x^10 + 18618x^9 - 17947x^8 + 12464x^7 - 6281x^6 + 2078x^5 + 48x^4 - 684x^3 + 487x^2 - 164x + 23	\( 2^{20}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.4.281124869512857892173749682176.12	x^20 - 10x^19 + 38x^18 - 30x^17 - 286x^16 + 1226x^15 - 2032x^14 - 116x^13 + 7752x^12 - 18248x^11 + 24844x^10 - 25066x^9 + 22105x^8 - 17028x^7 + 9753x^6 - 4160x^5 + 2002x^4 - 720x^3 - 125x^2 + 40x + 59	\( 2^{20}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.4.281124869512857892173749682176.13	x^20 - 2x^19 - 10x^18 + 16x^17 + 80x^16 - 92x^15 - 495x^14 + 348x^13 + 2239x^12 - 334x^11 - 6224x^10 - 2614x^9 + 7713x^8 + 6774x^7 - 1414x^6 - 1642x^5 + 2469x^4 + 3124x^3 + 1831x^2 + 780x + 169	\( 2^{20}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.4.891967481491479777023938200576.1	x^20 - 2x^19 - 16x^18 - 9x^17 + 80x^16 + 232x^15 + 339x^14 + 43x^13 - 1013x^12 - 1559x^11 - 793x^10 - 1821x^9 - 5142x^8 - 6019x^7 - 4617x^6 - 4834x^5 - 5302x^4 - 3510x^3 - 1515x^2 - 729x - 243	\( 2^{10}\cdot 3^{2}\cdot 19^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.8.891967481491479777023938200576.1	x^20 - 11x^18 - 21x^17 + 25x^16 + 183x^15 + 246x^14 - 454x^13 - 1325x^12 - 686x^11 + 1189x^10 + 3473x^9 + 3224x^8 + 871x^7 - 2544x^6 - 7186x^5 - 5562x^4 - 2789x^3 + 948x^2 + 3542x + 13	\( 2^{10}\cdot 3^{2}\cdot 19^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.4.891967481491479777023938200576.2	x^20 - x^19 + 5x^18 + 10x^17 - 12x^16 + 20x^15 - 6x^14 - 247x^13 - 350x^12 - 332x^11 - 1000x^10 - 1198x^9 + 144x^8 + 698x^7 + 77x^6 + 1488x^5 + 3665x^4 + 3547x^3 + 2175x^2 + 1200x + 317	\( 2^{10}\cdot 3^{2}\cdot 19^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.8.891967481491479777023938200576.2	x^20 - 11x^18 + 13x^16 - 102x^15 + 132x^14 + 1188x^13 + 901x^12 - 3526x^11 - 8701x^10 - 3014x^9 + 13882x^8 + 20328x^7 + 8757x^6 - 10256x^5 - 14196x^4 - 9186x^3 - 2384x^2 + 450x + 27	\( 2^{10}\cdot 3^{2}\cdot 19^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.4.891967481491479777023938200576.3	x^20 + 8x^18 - 31x^16 - 261x^14 - 519x^12 - 846x^10 - 2277x^8 - 1693x^6 + 4847x^4 + 8421x^2 + 3609	\( 2^{10}\cdot 3^{2}\cdot 19^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.8.891967481491479777023938200576.3	x^20 - 9x^19 + 27x^18 - 11x^17 - 106x^16 + 216x^15 - 82x^14 - 325x^13 + 1277x^12 - 3015x^11 + 2899x^10 + 2789x^9 - 10612x^8 + 10728x^7 + 2310x^6 - 18444x^5 + 13629x^4 + 10374x^3 - 16604x^2 + 2534x + 2477	\( 2^{10}\cdot 3^{2}\cdot 19^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.4.891967481491479777023938200576.4	x^20 - x^19 + 6x^18 - 11x^17 + 31x^16 - 67x^15 + 104x^14 - 200x^13 + 324x^12 - 411x^11 + 526x^10 - 558x^9 + 349x^8 + 115x^7 - 574x^6 + 569x^5 + 143x^4 - 536x^3 - 2x^2 + 162x + 27	\( 2^{10}\cdot 3^{2}\cdot 19^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.8.891967481491479777023938200576.4	x^20 - x^19 + 11x^18 - 8x^17 + 6x^16 - 97x^15 - 314x^14 - 465x^13 - 737x^12 + 8x^11 + 2549x^10 + 2544x^9 - 1438x^8 - 2553x^7 - 777x^6 + 1000x^5 + 1229x^4 - 86x^3 - 369x^2 - 81x - 1	\( 2^{10}\cdot 3^{2}\cdot 19^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.8.2530123825615721029563747139584.1	x^20 - 10x^19 + 40x^18 - 50x^17 - 211x^16 + 1146x^15 - 2314x^14 + 670x^13 + 8535x^12 - 23960x^11 + 29823x^10 - 4738x^9 - 50774x^8 + 102076x^7 - 118150x^6 + 100846x^5 - 65472x^4 + 32442x^3 - 13068x^2 + 3798x - 513	\( 2^{20}\cdot 3^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.8.2530123825615721029563747139584.2	x^20 - 15x^18 - 12x^17 + 61x^16 - 40x^15 - 399x^14 - 188x^13 + 833x^12 + 1960x^11 + 1324x^10 - 760x^9 - 1997x^8 - 5140x^7 - 6641x^6 - 1382x^5 + 5955x^4 + 7368x^3 + 4526x^2 + 1306x - 37	\( 2^{20}\cdot 3^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.8.2530123825615721029563747139584.3	x^20 - 10x^19 + 52x^18 - 168x^17 + 326x^16 - 184x^15 - 1055x^14 + 3946x^13 - 6976x^12 + 5652x^11 + 3783x^10 - 17046x^9 + 21355x^8 - 8716x^7 - 10922x^6 + 18492x^5 - 10219x^4 + 308x^3 + 2233x^2 - 992x + 131	\( 2^{20}\cdot 3^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.8.2530123825615721029563747139584.4	x^20 - 6x^19 + 13x^18 - 18x^17 - 14x^16 + 310x^15 - 683x^14 - 668x^13 + 2967x^12 + 844x^11 - 6613x^10 - 2476x^9 + 10408x^8 + 5680x^7 - 10420x^6 - 7160x^5 + 5128x^4 + 4768x^3 - 464x^2 - 1248x - 288	\( 2^{20}\cdot 3^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.0.8027707333423317993215443805184.1	x^20 + 6x^18 - 29x^17 + 36x^16 - 164x^15 + 488x^14 - 671x^13 + 2298x^12 - 4409x^11 + 6705x^10 - 15288x^9 + 21661x^8 - 31432x^7 + 44490x^6 - 48387x^5 + 56899x^4 - 30293x^3 + 58575x^2 - 24832x + 9409	\( 2^{10}\cdot 3^{4}\cdot 19^{2}\cdot 401^{9} \)	20T848	$[2]$ (GRH)
20.12.8027707333423317993215443805184.1	x^20 - 9x^19 + 32x^18 - 60x^17 + 7x^16 + 410x^15 - 1397x^14 + 2542x^13 - 2802x^12 - 214x^11 + 6955x^10 - 8875x^9 - 576x^8 + 7645x^7 - 3343x^6 + 467x^5 + 1332x^4 - 2175x^3 - 708x^2 + 54x + 13	\( 2^{10}\cdot 3^{4}\cdot 19^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.4.8027707333423317993215443805184.1	x^20 - 7x^19 + 26x^18 - 64x^17 + 91x^16 - 276x^15 + 512x^14 - 594x^13 + 1836x^12 - 900x^11 + 4558x^10 - 1667x^9 + 6322x^8 - 1587x^7 + 3285x^6 + 1083x^5 - 994x^4 + 1368x^3 - 276x^2 + 153x + 9	\( 2^{10}\cdot 3^{4}\cdot 19^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.8.8027707333423317993215443805184.1	x^20 - 8x^19 + 5x^18 + 92x^17 - 147x^16 - 463x^15 + 660x^14 + 2982x^13 - 4694x^12 - 10077x^11 + 22534x^10 + 9759x^9 - 46713x^8 + 7793x^7 + 45782x^6 - 16445x^5 - 26312x^4 + 10456x^3 + 8344x^2 - 2304x - 1248	\( 2^{10}\cdot 3^{4}\cdot 19^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.4.8027707333423317993215443805184.2	x^20 - x^19 + 22x^18 - 37x^17 + 228x^16 - 515x^15 + 1515x^14 - 3560x^13 + 7331x^12 - 14271x^11 + 24976x^10 - 36724x^9 + 53172x^8 - 73282x^7 + 97375x^6 - 147405x^5 + 187645x^4 - 148797x^3 + 65323x^2 - 13950x + 1011	\( 2^{10}\cdot 3^{4}\cdot 19^{2}\cdot 401^{9} \)	20T848	$[2]$ (GRH)
20.8.8027707333423317993215443805184.2	x^20 - 9x^19 + 16x^18 + 47x^17 - 96x^16 - 210x^15 + 266x^14 + 655x^13 - 333x^12 - 1349x^11 + 298x^10 + 1310x^9 - 25x^8 - 425x^7 - 656x^6 + 742x^5 - 109x^4 - 145x^3 + 68x^2 - 8x - 1	\( 2^{10}\cdot 3^{4}\cdot 19^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.4.8027707333423317993215443805184.3	x^20 - 8x^19 + 29x^18 - 59x^17 + 49x^16 + 37x^15 + 18x^14 - 398x^13 + 149x^12 + 2354x^11 - 4757x^10 + 1965x^9 - 6784x^8 + 21013x^7 - 7300x^6 - 2340x^5 - 18748x^4 + 6951x^3 + 4402x^2 + 2274x + 139	\( 2^{10}\cdot 3^{4}\cdot 19^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.8.8027707333423317993215443805184.3	x^20 - x^19 - 7x^18 + 7x^17 + 24x^16 - 107x^15 - 25x^14 + 1094x^13 - 765x^12 - 5370x^11 + 7496x^10 + 9317x^9 - 21351x^8 - 2171x^7 + 24644x^6 - 8066x^5 - 11221x^4 + 6913x^3 + 757x^2 - 1665x + 379	\( 2^{10}\cdot 3^{4}\cdot 19^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.0.10015348012400946058975158354944.1	x^20 - 4x^19 + x^18 + 16x^17 - 73x^16 + 166x^15 + 150x^14 - 1076x^13 + 1303x^12 - 140x^11 - 3577x^10 + 12122x^9 - 9802x^8 - 20532x^7 + 35271x^6 + 4824x^5 - 25354x^4 - 14554x^3 + 29838x^2 - 6580x + 421	\( 2^{10}\cdot 191^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.0.10015348012400946058975158354944.2	x^20 - 15x^18 + 174x^16 - 953x^14 + 2317x^12 - 2803x^10 + 4559x^8 - 6189x^6 + 4802x^4 - 2005x^2 + 401	\( 2^{10}\cdot 191^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.8.16550566358408121750701428788849.1	x^20 - 4x^19 - 3x^18 + 30x^17 + 28x^16 - 232x^15 - 207x^14 + 1759x^13 - 425x^12 - 5916x^11 + 631x^10 + 24024x^9 - 13038x^8 - 57641x^7 + 58317x^6 + 55485x^5 - 72282x^4 - 36287x^3 + 40489x^2 + 27947x - 22579	\( 3^{8}\cdot 97^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.12.16550566358408121750701428788849.2	x^20 - 7x^19 + 2x^18 + 85x^17 - 122x^16 - 420x^15 + 748x^14 + 1161x^13 - 2186x^12 - 2015x^11 + 4758x^10 + 2059x^9 - 7987x^8 + 416x^7 + 6586x^6 - 4254x^5 - 1336x^4 + 4411x^3 + 50x^2 - 1280x - 277	\( 3^{8}\cdot 97^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.16.81245087289215930838213658148864.1	x^20 - 2x^19 - 21x^18 + 196x^16 + 400x^15 - 1136x^14 - 2838x^13 + 4048x^12 + 7382x^11 - 8548x^10 - 8450x^9 + 9532x^8 + 4208x^7 - 4967x^6 - 954x^5 + 1120x^4 + 138x^3 - 97x^2 - 12x + 1	\( 2^{20}\cdot 17^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.4.81245087289215930838213658148864.1	x^20 - 7x^18 + 7x^16 + 15x^14 + 27x^12 - 62x^10 + 151x^8 - 407x^6 - 383x^4 + 802x^2 + 3609	\( 2^{20}\cdot 17^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.8.81245087289215930838213658148864.1	x^20 - 6x^19 + 7x^18 + 32x^17 - 208x^16 + 518x^15 - 723x^14 + 168x^13 + 2071x^12 - 5444x^11 + 5354x^10 + 2974x^9 - 17049x^8 + 18604x^7 + 9350x^6 - 29066x^5 + 4554x^4 + 13684x^3 - 2141x^2 - 2378x - 221	\( 2^{20}\cdot 17^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.16.81245087289215930838213658148864.2	x^20 - 29x^18 - 32x^17 + 180x^16 + 342x^15 + 180x^14 - 1186x^13 - 3698x^12 + 3930x^11 + 6064x^10 - 18628x^9 + 9462x^8 + 40286x^7 - 31581x^6 - 32516x^5 + 19232x^4 + 13580x^3 - 2825x^2 - 2454x - 317	\( 2^{20}\cdot 17^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.4.81245087289215930838213658148864.2	x^20 - 15x^18 + 79x^16 - 314x^14 + 929x^12 - 2171x^10 + 4104x^8 - 6201x^6 + 7274x^4 - 6416x^2 + 3609	\( 2^{20}\cdot 17^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.8.81245087289215930838213658148864.2	x^20 - 4x^19 + 2x^18 + 20x^17 - 56x^16 + 50x^15 + 21x^14 - 64x^13 + 159x^12 - 924x^11 + 1213x^10 + 552x^9 - 3675x^8 + 888x^7 + 2564x^6 - 3060x^5 - 4400x^4 - 346x^3 + 475x^2 + 12x - 9	\( 2^{20}\cdot 17^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.0.81245087289215930838213658148864.3	x^20 - 28x^17 + 27x^16 - 94x^15 + 317x^14 + 48x^13 + 467x^12 - 2738x^11 + 507x^10 + 4890x^9 - 1129x^8 - 8098x^7 + 5124x^6 - 10404x^5 + 34209x^4 - 22032x^3 - 3645x^2 - 5832x + 19683	\( 2^{20}\cdot 17^{2}\cdot 401^{9} \)	20T848	$[2]$ (GRH)
20.8.81245087289215930838213658148864.3	x^20 - 8x^19 + 26x^18 + 2x^17 - 337x^16 + 1222x^15 - 1777x^14 - 704x^13 + 8454x^12 - 15616x^11 + 8003x^10 + 16282x^9 - 35246x^8 + 27754x^7 - 2726x^6 - 13474x^5 + 11088x^4 - 2700x^3 - 326x^2 + 62x + 1	\( 2^{20}\cdot 17^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.0.81245087289215930838213658148864.4	x^20 - 6x^19 + 23x^18 - 72x^17 + 248x^16 - 754x^15 + 1979x^14 - 4998x^13 + 13005x^12 - 29418x^11 + 56261x^10 - 98698x^9 + 162105x^8 - 216362x^7 + 216043x^6 - 152100x^5 + 84358x^4 - 42598x^3 + 19749x^2 - 8064x + 2997	\( 2^{20}\cdot 17^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.8.81245087289215930838213658148864.4	x^20 - 4x^19 - 19x^18 + 112x^17 - 26x^16 - 502x^15 - 279x^14 + 3474x^13 - 1949x^12 - 6288x^11 + 4971x^10 + 4936x^9 - 3819x^8 - 1668x^7 + 563x^6 + 48x^5 + 60x^4 + 242x^3 - 145x^2 + 10x + 3	\( 2^{20}\cdot 17^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.8.81245087289215930838213658148864.5	x^20 - 4x^19 - 7x^18 + 34x^17 + 70x^16 - 190x^15 - 655x^14 + 574x^13 + 3666x^12 + 792x^11 - 13227x^10 - 5906x^9 + 27504x^8 + 4624x^7 - 15466x^6 + 6186x^5 - 21731x^4 - 13714x^3 - 2079x^2 - 1100x - 71	\( 2^{20}\cdot 17^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)
20.4.148715055972301824959913581871104.1	x^20 + 2x^18 - 46x^16 - 44x^14 + 155x^12 + 1077x^10 + 2021x^8 + 2306x^6 + 2494x^4 + 1604x^2 + 401	\( 2^{20}\cdot 23^{2}\cdot 401^{9} \)	20T848	Trivial (GRH)