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 28 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.12.387999001772721822047119239609.1	x^20 - 10x^19 + 45x^18 - 114x^17 + 127x^16 + 240x^15 - 1411x^14 + 2973x^13 - 2597x^12 - 2829x^11 + 13038x^10 - 19450x^9 + 7037x^8 + 23309x^7 - 35470x^6 + 5789x^5 + 22918x^4 - 12852x^3 - 3848x^2 + 2784x + 288	\( 3^{2}\cdot 401^{11} \)	20T350	Trivial (GRH)
20.12.387999001772721822047119239609.2	x^20 - 2x^19 - 9x^18 + 31x^17 - 61x^16 - 80x^15 + 674x^14 - 241x^13 - 1640x^12 + 1014x^11 + 871x^10 - 694x^9 + 524x^8 - 382x^7 + 106x^6 - 95x^5 + 34x^4 + 143x^3 - 85x^2 - 27x - 1	\( 3^{2}\cdot 401^{11} \)	20T350	Trivial (GRH)
20.16.3491991015954496398424073156481.1	x^20 - 2x^19 - 29x^18 + 50x^17 + 340x^16 - 452x^15 - 2158x^14 + 1776x^13 + 8238x^12 - 2315x^11 - 18800x^10 - 4036x^9 + 22803x^8 + 15018x^7 - 9694x^6 - 13058x^5 - 2640x^4 + 2063x^3 + 1193x^2 + 210x + 9	\( 3^{4}\cdot 401^{11} \)	20T350	Trivial (GRH)
20.12.3491991015954496398424073156481.3	x^20 - 4x^19 - 6x^18 + 14x^17 + 5x^16 + 151x^15 - 107x^14 - 213x^13 - 157x^12 - 1326x^11 + 2146x^10 + 1900x^9 - 2915x^8 + 1828x^7 - 1310x^6 - 3187x^5 + 5030x^4 + 1056x^3 - 2816x^2 - 256x + 83	\( 3^{4}\cdot 401^{11} \)	20T350	Trivial (GRH)
20.12.3491991015954496398424073156481.4	x^20 - 2x^19 - 11x^18 - 2x^17 + 32x^16 + 168x^15 + 161x^14 - 442x^13 - 1178x^12 - 404x^11 + 2451x^10 + 2232x^9 - 1758x^8 - 3634x^7 - 2045x^6 + 2760x^5 + 3565x^4 + 492x^3 - 298x^2 + 10x + 1	\( 3^{4}\cdot 401^{11} \)	20T350	Trivial (GRH)
20.8.3491991015954496398424073156481.5	x^20 - 4x^19 + 10x^18 - 39x^17 + 76x^16 - 66x^15 + 7x^14 + 266x^13 - 650x^12 + 766x^11 - 387x^10 - 1140x^9 + 1269x^8 - 426x^7 + 1665x^6 + 607x^5 - 1324x^4 - 468x^3 + 219x^2 + 108x + 9	\( 3^{4}\cdot 401^{11} \)	20T350	Trivial (GRH)
20.12.12459079056924067396846384471889.1	x^20 - 4x^19 - 5x^18 + 47x^17 - 97x^16 - 74x^15 + 823x^14 - 473x^13 - 1956x^12 + 527x^11 - 823x^10 + 3101x^9 + 12158x^8 - 1021x^7 - 18920x^6 - 10853x^5 + 5962x^4 + 7241x^3 + 1949x^2 + 103x + 1	\( 17^{2}\cdot 401^{11} \)	20T350	Trivial (GRH)
20.12.12459079056924067396846384471889.2	x^20 - 6x^19 - 3x^18 + 82x^17 - 149x^16 + 10x^15 + 143x^14 - 1333x^13 + 5056x^12 - 2087x^11 - 17375x^10 + 25118x^9 + 10279x^8 - 45061x^7 + 23616x^6 + 19432x^5 - 26842x^4 + 8325x^3 + 2662x^2 - 2288x + 421	\( 17^{2}\cdot 401^{11} \)	20T350	Trivial (GRH)
20.8.31427919143590467585816658408329.2	x^20 - 8x^19 + 36x^18 - 137x^17 + 383x^16 - 637x^15 + 251x^14 + 1957x^13 - 6439x^12 + 10722x^11 - 10371x^10 + 510x^9 + 17213x^8 - 21274x^7 + 6893x^6 - 12849x^5 + 28375x^4 - 5316x^3 - 25253x^2 + 27807x - 13347	\( 3^{6}\cdot 401^{11} \)	20T350	Trivial (GRH)
20.8.31427919143590467585816658408329.3	x^20 - 8x^19 + 18x^18 + 22x^17 - 155x^16 + 182x^15 + 161x^14 - 550x^13 + 378x^12 + 188x^11 - 273x^10 - 112x^9 - 634x^8 + 2468x^7 - 2025x^6 - 3448x^5 + 6651x^4 + 1342x^3 - 5500x^2 - 254x + 1291	\( 3^{6}\cdot 401^{11} \)	20T350	Trivial (GRH)
20.4.31427919143590467585816658408329.7	x^20 - 4x^19 - 8x^18 + 4x^17 + 94x^16 + 249x^15 - 80x^14 - 1378x^13 - 3418x^12 - 3405x^11 + 3776x^10 + 20593x^9 + 42080x^8 + 64085x^7 + 74687x^6 + 72231x^5 + 56742x^4 + 34776x^3 + 15561x^2 + 4536x + 729	\( 3^{6}\cdot 401^{11} \)	20T350	$[4]$ (GRH)
20.16.44145664201696349530694455706624.1	x^20 - 35x^18 - 8x^17 + 426x^16 + 103x^15 - 2390x^14 - 491x^13 + 6529x^12 + 1454x^11 - 7832x^10 - 3568x^9 + 2368x^8 + 4737x^7 + 674x^6 - 777x^5 - 335x^4 - 352x^3 + 13x^2 + 13x - 1	\( 2^{10}\cdot 401^{11} \)	20T350	Trivial (GRH)
20.8.44145664201696349530694455706624.1	x^20 - 3x^19 + 38x^17 - 125x^16 - 23x^15 + 433x^14 + 131x^13 + 713x^12 - 4375x^11 + 1309x^10 - 2816x^9 + 12814x^8 + 2828x^7 - 8384x^6 - 9152x^5 - 2440x^4 + 10096x^3 + 976x^2 - 2688x + 288	\( 2^{10}\cdot 401^{11} \)	20T350	Trivial (GRH)
20.20.3575798800337404311986250912236544.1	x^20 - 44x^18 - 19x^17 + 800x^16 + 668x^15 - 7675x^14 - 9340x^13 + 40876x^12 + 66143x^11 - 114182x^10 - 249104x^9 + 125534x^8 + 478773x^7 + 54268x^6 - 418522x^5 - 177957x^4 + 140766x^3 + 85962x^2 - 11610x - 9829	\( 2^{10}\cdot 3^{4}\cdot 401^{11} \)	20T350	Trivial (GRH)
20.4.3600673847451055477688605112375921.3	x^20 - 4x^19 + 38x^18 - 105x^17 + 527x^16 - 1008x^15 + 3445x^14 - 4167x^13 + 9662x^12 - 184x^11 - 19841x^10 + 82259x^9 - 235873x^8 + 173129x^7 - 263315x^6 - 1062570x^5 + 785364x^4 - 2070773x^3 - 1901083x^2 + 1264948x - 524809	\( 17^{4}\cdot 401^{11} \)	20T350	$[2]$ (GRH)
20.4.3600673847451055477688605112375921.4	x^20 - 9x^19 + 40x^18 - 144x^17 + 516x^16 - 1834x^15 + 5631x^14 - 12731x^13 + 16312x^12 + 5824x^11 - 82471x^10 + 236582x^9 - 555542x^8 + 1280304x^7 - 2509850x^6 + 3871339x^5 - 4806625x^4 + 4679392x^3 - 3274691x^2 + 1427622x - 283113	\( 17^{4}\cdot 401^{11} \)	20T350	$[2]$ (GRH)
20.16.45205160142537061919431122643582976.1	x^20 - 24x^18 + 217x^16 - 769x^14 - 826x^12 + 16201x^10 - 54762x^8 + 79693x^6 - 40305x^4 - 5614x^2 + 401	\( 2^{20}\cdot 401^{11} \)	20T350	Trivial (GRH)
20.8.45205160142537061919431122643582976.1	x^20 - 11x^18 - 14x^16 + 227x^14 + 114x^12 - 1228x^10 - 1254x^8 + 1682x^6 + 3428x^4 + 2005x^2 + 401	\( 2^{20}\cdot 401^{11} \)	20T350	Trivial (GRH)
20.16.45205160142537061919431122643582976.2	x^20 - 28x^18 + 255x^16 - 460x^14 - 5141x^12 + 23419x^10 + 4859x^8 - 158056x^6 + 196446x^4 - 18847x^2 + 401	\( 2^{20}\cdot 401^{11} \)	20T350	Trivial (GRH)
20.8.45205160142537061919431122643582976.2	x^20 + 12x^18 - 190x^16 - 2372x^14 - 3058x^12 + 17124x^10 + 7099x^8 - 19428x^6 - 4456x^4 + 5614x^2 + 401	\( 2^{20}\cdot 401^{11} \)	20T350	Trivial (GRH)
20.12.45205160142537061919431122643582976.3	x^20 - 2x^18 - 142x^16 + 694x^14 + 3997x^12 - 36326x^10 + 87322x^8 - 58058x^6 - 31188x^4 + 24060x^2 + 401	\( 2^{20}\cdot 401^{11} \)	20T350	Trivial (GRH)
20.4.45205160142537061919431122643582976.3	x^20 + 37x^18 + 545x^16 + 3996x^14 + 14483x^12 + 18803x^10 - 18278x^8 - 45009x^6 + 5302x^4 + 8020x^2 + 401	\( 2^{20}\cdot 401^{11} \)	20T350	Trivial (GRH)
20.8.45205160142537061919431122643582976.3	x^20 + 28x^18 + 175x^16 - 279x^14 - 3619x^12 + 432x^10 + 16807x^8 - 923x^6 - 8429x^4 - 1203x^2 + 401	\( 2^{20}\cdot 401^{11} \)	20T350	Trivial (GRH)
20.12.45205160142537061919431122643582976.4	x^20 + 11x^18 - 14x^16 - 227x^14 + 114x^12 + 1228x^10 - 1254x^8 - 1682x^6 + 3428x^4 - 2005x^2 + 401	\( 2^{20}\cdot 401^{11} \)	20T350	Trivial (GRH)
20.8.45205160142537061919431122643582976.4	x^20 + 2x^18 - 111x^16 - 81x^14 + 2431x^12 + 2340x^10 - 14784x^8 - 24641x^6 - 114x^4 + 11228x^2 + 401	\( 2^{20}\cdot 401^{11} \)	20T350	Trivial (GRH)
20.20.3661617971545502015473920934130221056.2	x^20 - 68x^18 + 1807x^16 - 24682x^14 + 190169x^12 - 850982x^10 + 2178056x^8 - 2984028x^6 + 1910421x^4 - 498042x^2 + 32481	\( 2^{20}\cdot 3^{4}\cdot 401^{11} \)	20T350	Trivial (GRH)
20.0.96661053444309405452136701474980370297825977344.1	x^20 - 8x^19 + 613x^18 - 3750x^17 + 151980x^16 - 724333x^15 + 19969012x^14 - 74453400x^13 + 1542496749x^12 - 4377184144x^11 + 72563180273x^10 - 144348494038x^9 + 2068221953123x^8 - 2346917686507x^7 + 34524640552202x^6 - 10644189421621x^5 + 322532511927071x^4 + 87422158458786x^3 + 1573396773373304x^2 + 335190654909333x + 1431177952949883	\( 2^{10}\cdot 3^{2}\cdot 97^{2}\cdot 401^{15} \)	20T350	$[2, 2, 2, 2, 2, 2, 33228588]$ (GRH)
20.0.98980918726972831182987982310379899184973800800256.1	x^20 + 1604x^18 + 1057838x^16 + 378364753x^14 + 80925997668x^12 + 10700977711955x^10 + 870171034803357x^8 + 41765095228552836x^6 + 1076119346023005367x^4 + 11444522960549429763x^2 + 878026939499046681	\( 2^{20}\cdot 3^{2}\cdot 97^{2}\cdot 401^{15} \)	20T350	$[2, 2, 2, 2, 2, 2, 4, 258041912]$ (GRH)