Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.902558723428708305129.1	x^20 + x^18 - 6x^17 - x^16 - 4x^15 + 15x^14 + 7x^13 + 10x^12 - 17x^11 - 11x^10 - 17x^9 + 10x^8 + 7x^7 + 15x^6 - 4x^5 - x^4 - 6x^3 + x^2 + 1	\( 3^{10}\cdot 11119^{4} \)	20T279	Trivial
20.0.1618299543010938978304.1	x^20 + 4x^16 - 4x^12 + 4x^8 - 8x^4 + 4	\( 2^{38}\cdot 277^{4} \)	20T279	Trivial
20.0.5240475867149548650496.1	x^20 - 4x^17 - 3x^16 + 8x^14 + 8x^13 + 2x^12 - 4x^11 - 8x^10 - 4x^9 + 2x^8 + 8x^7 + 8x^6 - 3x^4 - 4x^3 + 1	\( 2^{32}\cdot 1051^{4} \)	20T279	Trivial (GRH)
20.0.7196545015488566001664.1	x^20 - 2x^19 + 2x^18 + 6x^16 - 14x^15 + 16x^14 + 2x^13 + x^12 - 12x^11 + 24x^10 + 4x^9 - 32x^8 + 52x^7 - 30x^6 + 24x^4 - 18x^3 + 8x^2 - 4x + 1	\( 2^{30}\cdot 1609^{4} \)	20T279	Trivial (GRH)
20.4.10922267596307822265625.1	x^20 - 3x^19 - x^18 + 4x^17 + 13x^16 - 26x^15 + 3x^14 + 16x^13 + 4x^12 - 21x^11 + 21x^10 - 21x^9 + 4x^8 + 16x^7 + 3x^6 - 26x^5 + 13x^4 + 4x^3 - x^2 - 3x + 1	\( 5^{10}\cdot 5783^{4} \)	20T279	Trivial (GRH)
20.0.104771030951153867124969.1	x^20 - x^19 + x^18 - 2x^17 + 2x^16 - x^15 + x^13 - 2x^12 + 3x^11 - 3x^10 + 3x^9 - 2x^8 + x^7 - x^5 + 2x^4 - 2x^3 + x^2 - x + 1	\( 3^{10}\cdot 36497^{4} \)	20T279	Trivial (GRH)
20.4.337783263126326508704161.1	x^20 - 2x^19 + x^18 + x^17 - 8x^16 + 6x^15 - 4x^14 - 10x^13 + 9x^12 - 11x^11 + 16x^10 + 19x^9 - 23x^8 - x^7 + 4x^6 - 2x^5 + 7x^4 - 3x^3 - 4x^2 + 2x + 1	\( 13^{12}\cdot 347^{4} \)	20T279	Trivial (GRH)
20.0.373326179890223832367104.2	x^20 - x^18 - x^16 + 3x^14 + x^12 - 3x^10 + x^8 + 3x^6 - x^4 - x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 1567^{4} \)	20T279	Trivial (GRH)
20.0.444622235903180809437184.1	x^20 - 2x^19 + 2x^18 + 2x^17 + 8x^16 - 14x^15 + 14x^14 + 18x^13 + 28x^12 - 30x^11 + 26x^10 + 44x^9 + 49x^8 - 18x^7 + 8x^6 + 26x^5 + 30x^4 + 4x^3 + 1	\( 2^{30}\cdot 13^{4}\cdot 347^{4} \)	20T279	Trivial (GRH)
20.0.750535733485406881022481.1	x^20 - x^19 + 2x^18 - x^17 + 3x^16 - 2x^15 - x^14 + 3x^13 - 2x^12 + 3x^11 - x^10 + 3x^9 - 2x^8 + 3x^7 - x^6 - 2x^5 + 3x^4 - x^3 + 2x^2 - x + 1	\( 3^{16}\cdot 11491^{4} \)	20T279	Trivial (GRH)
20.4.826435173591040000000000.1	x^20 + 3x^18 + 5x^16 + x^14 - 8x^12 - 6x^10 - x^8 - 6x^6 + 16x^4 - 7x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 13^{4}\cdot 41^{4} \)	20T279	Trivial (GRH)
20.4.826435173591040000000000.2	x^20 - x^18 + 6x^16 - 14x^14 + 24x^12 - 33x^10 + 24x^8 - 14x^6 + 6x^4 - x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 13^{4}\cdot 41^{4} \)	20T279	Trivial (GRH)
20.0.1097328572072844211779849.1	x^20 - x^19 + 5x^18 - 8x^17 + 20x^16 - 29x^15 + 39x^14 - 56x^13 + 58x^12 - 60x^11 + 71x^10 - 60x^9 + 58x^8 - 56x^7 + 39x^6 - 29x^5 + 20x^4 - 8x^3 + 5x^2 - x + 1	\( 3^{10}\cdot 65657^{4} \)	20T279	Trivial (GRH)
20.0.1860495326773308902342656.1	x^20 + x^18 + x^14 + x^12 + x^10 + x^8 + x^6 + x^2 + 1	\( 2^{20}\cdot 36497^{4} \)	20T279	Trivial (GRH)
20.4.3358778855072479697265625.1	x^20 - 4x^17 - 11x^15 - x^14 - 29x^13 - 3x^12 + 115x^10 - 3x^8 + 29x^7 - x^6 + 11x^5 + 4x^3 + 1	\( 5^{10}\cdot 61^{4}\cdot 397^{4} \)	20T279	Trivial (GRH)
20.4.17327212977905840634765625.1	x^20 - x^19 - x^18 + 4x^17 - 4x^16 + 7x^15 - 12x^14 + 19x^13 + 16x^12 - 73x^11 + 71x^10 + 73x^9 + 16x^8 - 19x^7 - 12x^6 - 7x^5 - 4x^4 - 4x^3 - x^2 + x + 1	\( 5^{10}\cdot 36497^{4} \)	20T279	Trivial (GRH)
20.12.201604956366467437744140625.1	x^20 - 5x^19 + 45x^17 - 85x^16 - 50x^15 + 380x^14 - 470x^13 - 185x^12 + 1120x^11 - 1151x^10 + 140x^9 + 880x^8 - 1085x^7 + 545x^6 + 75x^5 - 320x^4 + 235x^3 - 85x^2 + 15x - 1	\( 5^{16}\cdot 6029^{4} \)	20T279	Trivial (GRH)
20.12.217008357018762359619140625.1	x^20 - 5x^19 + 35x^17 - 45x^16 - 66x^15 + 175x^14 + 5x^13 - 280x^12 + 75x^11 + 297x^10 - 75x^9 - 280x^8 - 5x^7 + 175x^6 + 66x^5 - 45x^4 - 35x^3 + 5x + 1	\( 3^{4}\cdot 5^{16}\cdot 23^{4}\cdot 89^{4} \)	20T279	Trivial (GRH)
20.12.382286008207589204343914496.1	x^20 - 2x^19 - 14x^18 + 46x^17 + 17x^16 - 286x^15 + 274x^14 + 468x^13 - 1028x^12 - 272x^11 + 1318x^10 - 358x^9 - 1127x^8 + 510x^7 + 776x^6 - 88x^5 - 257x^4 - 42x^3 + 26x^2 + 10x + 1	\( 2^{30}\cdot 3^{10}\cdot 1567^{4} \)	20T279	Trivial (GRH)
20.12.455293169564857148863676416.1	x^20 - 10x^18 + 36x^16 - 48x^14 - 16x^12 + 96x^10 - 55x^8 - 36x^6 + 42x^4 - 12x^2 + 1	\( 2^{40}\cdot 13^{4}\cdot 347^{4} \)	20T279	Trivial (GRH)
20.0.1905147214615868315998879744.1	x^20 - 10x^19 + 50x^18 - 148x^17 + 286x^16 - 384x^15 + 492x^14 - 834x^13 + 1443x^12 - 1702x^11 + 1318x^10 - 764x^9 + 683x^8 - 716x^7 + 524x^6 - 200x^5 + 51x^4 - 22x^3 + 18x^2 - 6x + 1	\( 2^{30}\cdot 36497^{4} \)	20T279	$[4]$ (GRH)
20.0.2376038017203857413535432704.1	x^20 - 2x^17 + 51x^16 - 8x^15 + 2x^14 - 62x^13 + 411x^12 - 182x^11 + 54x^10 - 150x^9 + 652x^8 - 330x^7 + 102x^6 - 124x^5 + 197x^4 - 132x^3 + 50x^2 - 10x + 1	\( 2^{30}\cdot 38569^{4} \)	20T279	$[4]$ (GRH)
20.20.1950870747766649155582852857856.1	x^20 - 22x^18 + 187x^16 - 824x^14 + 2087x^12 - 3146x^10 + 2808x^8 - 1426x^6 + 377x^4 - 42x^2 + 1	\( 2^{40}\cdot 36497^{4} \)	20T279	Trivial (GRH)
20.20.2433062929616749991460283088896.1	x^20 - 22x^18 + 191x^16 - 848x^14 + 2111x^12 - 3042x^10 + 2520x^8 - 1148x^6 + 265x^4 - 28x^2 + 1	\( 2^{40}\cdot 38569^{4} \)	20T279	Trivial (GRH)