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 18 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.2.53112053233392982274207.1	x^20 - x^19 + x^18 + 2x^17 + 3x^16 - 7x^15 + 10x^14 - 6x^13 - 3x^12 - x^11 - 21x^10 - 2x^9 - 8x^8 - 32x^7 + 5x^6 - 12x^5 - 12x^4 + 3x^3 - 3x^2 - x + 1	\( -\,47^{9}\cdot 83^{4} \)	$C_2\times C_2^4:D_5$ (as 20T87)	Trivial
20.2.53112053233392982274207.2	x^20 - x^19 - x^18 - 2x^17 + 2x^16 - 2x^15 + 8x^14 - 11x^13 + 2x^12 + 2x^11 - 9x^10 + 17x^9 - x^8 - 28x^7 + 49x^6 - 46x^5 + 31x^4 - 20x^3 + 12x^2 - 5x + 1	\( -\,47^{9}\cdot 83^{4} \)	$C_2\times C_2^4:D_5$ (as 20T87)	Trivial
20.0.21716226988355149522851681.1	x^20 - 2x^19 + 6x^18 - 8x^17 + 16x^16 - 23x^15 + 35x^14 - 39x^13 + 35x^12 - 26x^11 + 19x^10 - 26x^9 + 35x^8 - 39x^7 + 35x^6 - 23x^5 + 16x^4 - 8x^3 + 6x^2 - 2x + 1	\( 3^{4}\cdot 401^{9} \)	$C_2\times C_2^4:D_5$ (as 20T87)	Trivial
20.4.21716226988355149522851681.1	x^20 - 3x^19 + 5x^18 - 12x^17 + 18x^16 - 19x^15 + 29x^14 - 34x^13 + 28x^12 - 32x^11 + 39x^10 - 32x^9 + 28x^8 - 34x^7 + 29x^6 - 19x^5 + 18x^4 - 12x^3 + 5x^2 - 3x + 1	\( 3^{4}\cdot 401^{9} \)	$C_2\times C_2^4:D_5$ (as 20T87)	Trivial (GRH)
20.12.1759014386056767111350986161.1	x^20 - 5x^19 + 7x^18 - 6x^17 + 4x^16 + 73x^15 - 249x^14 + 432x^13 - 699x^12 + 806x^11 - 263x^10 - 654x^9 + 1558x^8 - 1973x^7 + 1277x^6 - 152x^5 - 307x^4 + 187x^3 - 34x^2 - 3x + 1	\( 3^{8}\cdot 401^{9} \)	$C_2\times C_2^4:D_5$ (as 20T87)	Trivial (GRH)
20.0.1759014386056767111350986161.2	x^20 - 4x^19 + x^18 + 7x^17 + 16x^16 - 56x^15 + 64x^14 - 23x^13 - 78x^12 + 269x^11 - 382x^10 + 304x^9 - 68x^8 - 264x^7 + 647x^6 - 690x^5 + 766x^4 - 462x^3 + 339x^2 - 115x + 51	\( 3^{8}\cdot 401^{9} \)	$C_2\times C_2^4:D_5$ (as 20T87)	$[2]$
20.4.7657248876721128710150208161.1	x^20 - x^19 - x^18 - 7x^17 - 14x^16 + 35x^15 + 10x^14 + 39x^13 + 88x^12 - 106x^11 + 286x^10 + 609x^9 - 207x^8 - 643x^7 - 290x^6 - 726x^5 - 1281x^4 - 1041x^3 - 565x^2 - 176x - 31	\( 13^{4}\cdot 401^{9} \)	$C_2\times C_2^4:D_5$ (as 20T87)	Trivial
20.8.7657248876721128710150208161.1	x^20 - 5x^19 + 9x^18 + 12x^17 - 97x^16 + 193x^15 - 51x^14 - 566x^13 + 1139x^12 - 842x^11 - 620x^10 + 1936x^9 - 2134x^8 + 1333x^7 - 550x^6 + 124x^5 + 49x^4 - 47x^3 + 14x^2 + 2x - 1	\( 13^{4}\cdot 401^{9} \)	$C_2\times C_2^4:D_5$ (as 20T87)	Trivial
20.12.15831129474510904002158875449.1	x^20 - 2x^19 - 8x^18 + 26x^17 - 30x^16 - 14x^15 + 99x^14 - 110x^13 + 36x^12 + 202x^11 - 195x^10 - 202x^9 + 36x^8 + 110x^7 + 99x^6 + 14x^5 - 30x^4 - 26x^3 - 8x^2 + 2x + 1	\( 3^{10}\cdot 401^{9} \)	$C_2\times C_2^4:D_5$ (as 20T87)	Trivial (GRH)
20.4.15831129474510904002158875449.2	x^20 - x^19 - 7x^18 + 33x^16 + 61x^15 - 19x^14 - 245x^13 - 439x^12 - 206x^11 + 684x^10 + 1872x^9 + 2470x^8 + 1806x^7 + 78x^6 - 1620x^5 - 1926x^4 - 729x^3 + 378x^2 + 405x + 81	\( 3^{10}\cdot 401^{9} \)	$C_2\times C_2^4:D_5$ (as 20T87)	$[2]$
20.0.22392111040671733867877719121.1	x^20 - 4x^19 + 18x^18 - 54x^17 + 111x^16 - 231x^15 + 324x^14 - 357x^13 + 474x^12 - 348x^11 + 487x^10 - 1183x^9 + 1395x^8 - 1023x^7 + 1410x^6 - 1162x^5 - 269x^4 - 243x^3 + 468x^2 + 216x + 81	\( 17^{4}\cdot 401^{9} \)	$C_2\times C_2^4:D_5$ (as 20T87)	Trivial
20.0.22392111040671733867877719121.2	x^20 - x^19 - 2x^18 - 12x^17 + 42x^16 - 98x^14 + 59x^13 - 31x^12 + 278x^11 - 170x^10 - 636x^9 + 1005x^8 - 597x^7 - 44x^6 + 617x^5 - 233x^4 - 462x^3 + 774x^2 - 432x + 81	\( 17^{4}\cdot 401^{9} \)	$C_2\times C_2^4:D_5$ (as 20T87)	Trivial
20.4.502465502329909572653052213761.1	x^20 - 4x^19 - 7x^18 + 48x^17 - 9x^16 - 237x^15 + 348x^14 + 42x^13 - 220x^12 - 373x^11 + 692x^10 - 205x^9 - 347x^8 + 481x^7 - 101x^6 - 371x^5 + 273x^4 + 82x^3 - 176x^2 + 93x - 19	\( 37^{4}\cdot 401^{9} \)	$C_2\times C_2^4:D_5$ (as 20T87)	Trivial (GRH)
20.8.502465502329909572653052213761.1	x^20 - 8x^19 + 17x^18 + 23x^17 - 138x^16 + 165x^15 - 49x^14 + 102x^13 - 128x^12 - 432x^11 + 855x^10 - 215x^9 - 589x^8 + 327x^7 + 338x^6 - 193x^5 - 144x^4 + 58x^3 - 8x^2 + 9	\( 37^{4}\cdot 401^{9} \)	$C_2\times C_2^4:D_5$ (as 20T87)	Trivial (GRH)
20.0.5402547132170496407507117146721.1	x^20 - 5x^19 + 20x^18 - 62x^17 + 182x^16 - 447x^15 + 975x^14 - 1900x^13 + 3286x^12 - 5196x^11 + 7228x^10 - 9632x^9 + 12257x^8 - 13199x^7 + 12113x^6 - 9533x^5 + 6344x^4 - 3390x^3 + 1440x^2 - 432x + 81	\( 67^{4}\cdot 401^{9} \)	$C_2\times C_2^4:D_5$ (as 20T87)	$[5]$ (GRH)
20.0.5402547132170496407507117146721.2	x^20 - 2x^19 - 3x^18 + 20x^17 - 20x^16 - 35x^15 + 208x^14 - 230x^13 - 171x^12 + 887x^11 - 769x^10 - 1091x^9 + 4159x^8 - 6078x^7 + 4879x^6 - 1407x^5 - 1079x^4 + 1155x^3 - 90x^2 - 216x + 81	\( 67^{4}\cdot 401^{9} \)	$C_2\times C_2^4:D_5$ (as 20T87)	$[5]$ (GRH)
20.20.2706114834006068266421672175378489.1	x^20 - 3x^19 - 37x^18 + 156x^17 + 267x^16 - 1891x^15 + 140x^14 + 9731x^13 - 7675x^12 - 24030x^11 + 29458x^10 + 27931x^9 - 46585x^8 - 13731x^7 + 34996x^6 + 1527x^5 - 12441x^4 + 450x^3 + 1829x^2 - 17x - 79	\( 3^{6}\cdot 61^{4}\cdot 401^{9} \)	$C_2\times C_2^4:D_5$ (as 20T87)	Trivial (GRH)
20.20.6659802967827443834044914879928481.1	x^20 - x^19 - 43x^18 + 55x^17 + 694x^16 - 948x^15 - 5617x^14 + 7593x^13 + 25005x^12 - 31958x^11 - 62169x^10 + 73269x^9 + 82377x^8 - 88997x^7 - 50613x^6 + 50884x^5 + 10366x^4 - 9435x^3 - 1314x^2 + 513x + 81	\( 397^{4}\cdot 401^{9} \)	$C_2\times C_2^4:D_5$ (as 20T87)	Trivial (GRH)