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
20.0.91521641489003479390464.1	x^20 - 4x^19 + 5x^18 - 11x^16 + 19x^15 + x^14 - 48x^13 + 104x^12 - 145x^11 + 158x^10 - 167x^9 + 182x^8 - 189x^7 + 175x^6 - 133x^5 + 82x^4 - 42x^3 + 17x^2 - 5x + 1	\( 2^{8}\cdot 3^{10}\cdot 8821^{4} \)	20T760	Trivial
20.0.368755455075464475836416.1	x^20 - 4x^18 + 10x^16 - 18x^14 + 27x^12 - 34x^10 + 36x^8 - 28x^6 + 16x^4 - 6x^2 + 1	\( 2^{40}\cdot 761^{4} \)	20T760	Trivial (GRH)
20.0.1335973502986240000000000.1	x^20 + x^16 + x^12 + 7x^10 + 16x^8 + 21x^6 + 16x^4 + 7x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 601^{4} \)	20T760	Trivial (GRH)
20.0.1335973502986240000000000.2	x^20 - 2x^16 + 8x^14 - 12x^12 - 5x^10 + 34x^8 - 40x^6 + 23x^4 - 7x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 601^{4} \)	20T760	Trivial (GRH)
20.4.6904360924896058824196096.2	x^20 + 10x^18 + 41x^16 + 106x^14 + 184x^12 + 192x^10 + 91x^8 - 10x^6 - 21x^4 - 2x^2 + 1	\( 2^{40}\cdot 1583^{4} \)	20T760	Trivial (GRH)
20.4.6904360924896058824196096.3	x^20 + 6x^18 + 11x^16 - 8x^14 - 69x^12 - 108x^10 - 49x^8 + 34x^6 + 42x^4 + 12x^2 + 1	\( 2^{40}\cdot 1583^{4} \)	20T760	Trivial (GRH)
20.8.6904360924896058824196096.3	x^20 - 4x^18 + 2x^16 + x^12 + 26x^10 - 40x^8 + 18x^6 - 4x^4 + 1	\( 2^{40}\cdot 1583^{4} \)	20T760	Trivial (GRH)
20.8.11149939773041205947265625.1	x^20 - 3x^19 - x^18 + 14x^17 - 21x^16 + 20x^15 - 6x^14 - 91x^13 + 224x^12 - 130x^11 - 184x^10 + 330x^9 - 224x^8 + 85x^7 + 27x^6 - 99x^5 + 81x^4 - 13x^3 - 16x^2 + 8x - 1	\( 5^{10}\cdot 97^{2}\cdot 3319^{4} \)	20T760	Trivial (GRH)
20.4.499608613791016960000000000.1	x^20 - 9x^18 + 26x^16 - 7x^14 - 116x^12 + 172x^10 + 140x^8 - 349x^6 + 290x^4 - 306x^2 + 289	\( 2^{20}\cdot 5^{10}\cdot 17^{2}\cdot 641^{4} \)	20T760	Trivial (GRH)
20.8.1187108264302767187656250000.1	x^20 + 3x^18 - 9x^16 - 20x^14 + 27x^12 + 45x^10 - 32x^8 - 40x^6 + 11x^4 + 12x^2 + 1	\( 2^{4}\cdot 5^{10}\cdot 52501^{4} \)	20T760	Trivial (GRH)
20.0.1242593181789399040000000000.1	x^20 + 7x^18 + 16x^16 + 12x^14 + 16x^10 + 69x^8 + 88x^6 + 49x^4 + 12x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T760	Trivial (GRH)
20.8.1242593181789399040000000000.1	x^20 - 2x^18 - x^16 - 32x^14 + 60x^12 + 66x^10 - 83x^8 - 12x^6 + 31x^4 - 10x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T760	Trivial (GRH)
20.0.1242593181789399040000000000.2	x^20 + 5x^18 + x^16 - 32x^14 - 51x^12 + 26x^10 + 141x^8 + 161x^6 + 88x^4 + 20x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T760	Trivial (GRH)
20.4.1368036867057909760000000000.2	x^20 - 8x^18 + 16x^16 - 8x^14 + 96x^12 - 160x^10 - 128x^8 - 896x^6 - 2048x^2 + 1024	\( 2^{30}\cdot 5^{10}\cdot 601^{4} \)	20T760	Trivial (GRH)
20.8.3828204809593746045712890625.1	x^20 - 5x^19 + 4x^18 + 13x^17 - 37x^16 + 123x^15 - 316x^14 + 457x^13 - 574x^12 + 650x^11 - 260x^10 - 51x^9 + 44x^8 - 540x^7 - x^6 + 172x^5 + 306x^4 + 452x^3 + 322x^2 + 48x - 29	\( 5^{10}\cdot 19^{6}\cdot 1699^{4} \)	20T760	Trivial (GRH)
20.4.3828204809593746045712890625.2	x^20 - 2x^19 + x^18 - 3x^17 - 2x^15 - 2x^14 + 2x^13 - 6x^12 + 5x^11 - 7x^10 + 5x^9 - 6x^8 + 2x^7 - 2x^6 - 2x^5 - 3x^3 + x^2 - 2x + 1	\( 5^{10}\cdot 19^{6}\cdot 1699^{4} \)	20T760	Trivial (GRH)
20.12.3828204809593746045712890625.4	x^20 - 9x^19 + 31x^18 - 38x^17 - 72x^16 + 318x^15 - 333x^14 - 343x^13 + 1153x^12 - 569x^11 - 1070x^10 + 1116x^9 + 278x^8 - 489x^7 - 36x^6 + 47x^4 + 31x^3 - 15x^2 - 3x + 1	\( 5^{10}\cdot 19^{6}\cdot 1699^{4} \)	20T760	Trivial (GRH)
20.8.3895012144169049760000000000.1	x^20 - 9x^16 + 26x^12 - 4x^10 - 24x^8 + 8x^6 + x^4 - 4x^2 + 4	\( 2^{14}\cdot 5^{10}\cdot 12491^{4} \)	20T760	Trivial (GRH)
20.12.18993732228844275002500000000.1	x^20 - 6x^18 + x^16 + 40x^14 - 27x^12 - 86x^10 + 50x^8 + 63x^6 - 16x^4 - 5x^2 + 1	\( 2^{8}\cdot 5^{10}\cdot 52501^{4} \)	20T760	Trivial (GRH)
20.4.18993732228844275002500000000.1	x^20 + 17x^18 + 91x^16 + 122x^14 - 312x^12 - 772x^10 - 187x^8 + 551x^6 + 406x^4 + 81x^2 + 1	\( 2^{8}\cdot 5^{10}\cdot 52501^{4} \)	20T760	Trivial (GRH)
20.8.18993732228844275002500000000.1	x^20 + 2x^18 - 26x^16 - 57x^14 + 121x^12 + 192x^10 - 193x^8 - 172x^6 + 90x^4 + 25x^2 + 1	\( 2^{8}\cdot 5^{10}\cdot 52501^{4} \)	20T760	Trivial (GRH)
20.12.99777227294923979346572265625.1	x^20 - 4x^19 - 12x^18 + 66x^17 + 18x^16 - 414x^15 + 330x^14 + 1229x^13 - 2014x^12 - 1888x^11 + 5045x^10 + 2351x^9 - 5747x^8 - 3182x^7 + 1929x^6 + 1462x^5 - 294x^4 - 246x^3 + 66x^2 + 26x - 1	\( 5^{10}\cdot 19^{4}\cdot 97^{2}\cdot 1699^{4} \)	20T760	Trivial (GRH)
20.8.303899715661508400040000000000.1	x^20 + x^18 - 48x^16 - 149x^14 + 239x^12 + 1326x^10 + 1080x^8 - 500x^6 - 337x^4 + 107x^2 + 1	\( 2^{12}\cdot 5^{10}\cdot 52501^{4} \)	20T760	Trivial (GRH)
20.16.303899715661508400040000000000.2	x^20 - 15x^18 + 86x^16 - 225x^14 + 206x^12 + 202x^10 - 529x^8 + 286x^6 + x^4 - 18x^2 + 1	\( 2^{12}\cdot 5^{10}\cdot 52501^{4} \)	20T760	Trivial (GRH)
20.16.379627024808728330240000000000.1	x^20 - 16x^18 + 92x^16 - 176x^14 - 364x^12 + 2312x^10 - 4144x^8 + 3024x^6 - 528x^4 - 176x^2 + 16	\( 2^{28}\cdot 5^{10}\cdot 3469^{4} \)	20T760	Trivial (GRH)
20.4.905850429524471900160000000000.1	x^20 + 6x^18 - 5x^16 - 8x^14 + 76x^12 - 489x^10 + 216x^8 + 702x^6 - 2592x^4 - 1215x^2 + 729	\( 2^{20}\cdot 3^{6}\cdot 5^{10}\cdot 3319^{4} \)	20T760	Trivial (GRH)
20.4.1272415418152344616960000000000.1	x^20 + 12x^18 + 16x^16 - 272x^14 - 1024x^12 - 608x^10 + 1600x^8 + 3072x^6 + 4352x^4 + 4096x^2 + 1024	\( 2^{30}\cdot 5^{10}\cdot 3319^{4} \)	20T760	Trivial (GRH)
20.12.1272415418152344616960000000000.2	x^20 - 14x^18 + 64x^16 - 96x^14 - 512x^10 + 4416x^8 - 11264x^6 + 12544x^4 - 6144x^2 + 1024	\( 2^{30}\cdot 5^{10}\cdot 3319^{4} \)	20T760	Trivial (GRH)
20.12.1272415418152344616960000000000.3	x^20 - 4x^18 - 20x^16 - 48x^14 + 976x^12 - 3744x^10 + 11136x^8 - 25088x^6 + 28928x^4 - 12800x^2 + 1024	\( 2^{30}\cdot 5^{10}\cdot 3319^{4} \)	20T760	Trivial (GRH)
20.8.4862395450584134400640000000000.1	x^20 + 7x^18 - 3x^16 - 95x^14 - 101x^12 + 215x^10 + 174x^8 - 107x^6 - 72x^4 - 4x^2 + 1	\( 2^{16}\cdot 5^{10}\cdot 52501^{4} \)	20T760	Trivial (GRH)
20.8.6074032396939653283840000000000.1	x^20 - 3x^18 - 35x^16 + 64x^14 + 333x^12 - 259x^10 - 995x^8 - 356x^6 + 69x^4 + 29x^2 + 1	\( 2^{32}\cdot 5^{10}\cdot 3469^{4} \)	20T760	Trivial (GRH)
20.12.36019579053467556544112587890625.1	x^20 - 4x^19 - 6x^18 + 59x^17 - 49x^16 - 263x^15 + 299x^14 - 33x^13 - 965x^12 + 1284x^11 + 9296x^10 + 13582x^9 - 9493x^8 - 28237x^7 - 22667x^6 - 11937x^5 + 4488x^4 + 6048x^3 + 685x^2 - 458x - 89	\( 5^{10}\cdot 19^{6}\cdot 97^{2}\cdot 1699^{4} \)	20T760	Trivial (GRH)
20.8.36019579053467556544112587890625.1	x^20 - 4x^19 + 6x^18 + 16x^17 - 194x^16 + 478x^15 - 396x^14 - 1811x^13 + 7041x^12 - 9483x^11 + 2627x^10 + 29988x^9 - 103689x^8 + 161032x^7 - 113443x^6 - 3008x^5 + 48367x^4 - 17141x^3 + 1519x^2 + 182x - 29	\( 5^{10}\cdot 19^{6}\cdot 97^{2}\cdot 1699^{4} \)	20T760	Trivial (GRH)
20.12.70097555898814099663913906250000.1	x^20 - 4x^19 - 6x^18 + 44x^17 + 2x^16 - 248x^15 + 60x^14 + 1225x^13 - 659x^12 - 4737x^11 + 4636x^10 + 11066x^9 - 15941x^8 - 14415x^7 + 28792x^6 + 10399x^5 - 27964x^4 - 4598x^3 + 13230x^2 + 1424x - 1991	\( 2^{4}\cdot 3^{10}\cdot 5^{10}\cdot 52501^{4} \)	20T760	Trivial (GRH)
20.12.723105269206732275017356551389184.1	x^20 - 4x^18 - 5x^16 + 36x^14 - 19x^12 - 74x^10 + 86x^8 - 23x^4 + 2x^2 + 1	\( 2^{40}\cdot 3^{10}\cdot 10273^{4} \)	20T760	Trivial (GRH)
20.4.723105269206732275017356551389184.1	x^20 + 14x^18 + 76x^16 + 188x^14 + 135x^12 - 320x^10 - 725x^8 - 380x^6 + 241x^4 + 306x^2 + 81	\( 2^{40}\cdot 3^{10}\cdot 10273^{4} \)	20T760	Trivial (GRH)
20.8.723105269206732275017356551389184.1	x^20 + 8x^18 + 9x^16 - 48x^14 - 85x^12 + 90x^10 + 189x^8 - 52x^6 - 122x^4 + 6x^2 + 1	\( 2^{40}\cdot 3^{10}\cdot 10273^{4} \)	20T760	Trivial (GRH)
20.0.2429612958775861313536000000000000.1	x^20 + 27x^18 + 285x^16 + 1526x^14 + 4591x^12 + 8189x^10 + 8821x^8 + 5660x^6 + 2055x^4 + 375x^2 + 25	\( 2^{36}\cdot 5^{12}\cdot 3469^{4} \)	20T760	$[448]$ (GRH)
20.0.2429612958775861313536000000000000.2	x^20 + 29x^18 + 343x^16 + 2140x^14 + 7593x^12 + 15429x^10 + 17441x^8 + 10620x^6 + 3295x^4 + 475x^2 + 25	\( 2^{36}\cdot 5^{12}\cdot 3469^{4} \)	20T760	$[432]$ (GRH)
20.12.4014163686424571853629440000000000.1	x^20 + 12x^18 - 75x^16 - 265x^14 + 1291x^12 - 569x^10 - 2461x^8 + 2729x^6 + 98x^4 - 1121x^2 + 361	\( 2^{20}\cdot 5^{10}\cdot 19^{6}\cdot 1699^{4} \)	20T760	Trivial (GRH)
20.16.4014163686424571853629440000000000.1	x^20 - 39x^18 + 617x^16 - 5095x^14 + 23585x^12 - 61060x^10 + 81212x^8 - 39110x^6 - 10887x^4 + 7144x^2 + 361	\( 2^{20}\cdot 5^{10}\cdot 19^{6}\cdot 1699^{4} \)	20T760	Trivial (GRH)
20.20.4014163686424571853629440000000000.1	x^20 - 36x^18 + 490x^16 - 3381x^14 + 13141x^12 - 30146x^10 + 41634x^8 - 34396x^6 + 16283x^4 - 3952x^2 + 361	\( 2^{20}\cdot 5^{10}\cdot 19^{6}\cdot 1699^{4} \)	20T760	Trivial (GRH)
20.4.4014163686424571853629440000000000.1	x^20 + 26x^18 + 250x^16 + 1067x^14 + 1588x^12 - 2479x^10 - 11776x^8 - 14727x^6 - 6438x^4 + 38x^2 + 361	\( 2^{20}\cdot 5^{10}\cdot 19^{6}\cdot 1699^{4} \)	20T760	Trivial (GRH)
20.12.4014163686424571853629440000000000.2	x^20 + 10x^18 - 112x^16 - 559x^14 + 1156x^12 + 4776x^10 - 4146x^8 - 8202x^6 + 9956x^4 - 3420x^2 + 361	\( 2^{20}\cdot 5^{10}\cdot 19^{6}\cdot 1699^{4} \)	20T760	Trivial (GRH)
20.16.4014163686424571853629440000000000.2	x^20 - 13x^18 - 16x^16 + 1011x^14 - 6060x^12 + 15005x^10 - 15813x^8 + 3787x^6 + 4047x^4 - 2489x^2 + 361	\( 2^{20}\cdot 5^{10}\cdot 19^{6}\cdot 1699^{4} \)	20T760	Trivial (GRH)
20.20.1449113090799270439160227840000000000.1	x^20 - 62x^18 + 1615x^16 - 22872x^14 + 190285x^12 - 938016x^10 + 2640924x^8 - 3965376x^6 + 3033844x^4 - 1076863x^2 + 130321	\( 2^{20}\cdot 5^{10}\cdot 19^{8}\cdot 1699^{4} \)	20T760	Trivial (GRH)