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
20.0.149808118161024326041600.1	x^20 - 4x^18 + 10x^16 - 8x^14 + x^12 + 22x^10 + 8x^8 + 10x^6 + 44x^4 + 40x^2 + 25	\( 2^{30}\cdot 5^{2}\cdot 29^{4}\cdot 53^{4} \)	20T638	Trivial (GRH)
20.0.149808118161024326041600.2	x^20 - 6x^18 + 13x^16 + 6x^14 - 48x^12 + 24x^10 + 75x^8 - 58x^6 - 37x^4 + 10x^2 + 25	\( 2^{30}\cdot 5^{2}\cdot 29^{4}\cdot 53^{4} \)	20T638	Trivial (GRH)
20.4.1335973502986240000000000.1	x^20 + x^18 + 8x^16 + 4x^14 + 21x^12 - x^10 + 19x^8 - 15x^6 + 6x^4 - 4x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 601^{4} \)	20T638	Trivial (GRH)
20.4.1335973502986240000000000.2	x^20 - x^18 + x^16 + 2x^14 - 9x^10 + 13x^8 - 11x^6 + 4x^4 - 2x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 601^{4} \)	20T638	Trivial (GRH)
20.4.6904360924896058824196096.1	x^20 + 4x^18 + 2x^16 + x^12 - 26x^10 - 40x^8 - 18x^6 - 4x^4 + 1	\( 2^{40}\cdot 1583^{4} \)	20T638	Trivial (GRH)
20.8.6904360924896058824196096.1	x^20 - 6x^18 + 11x^16 + 8x^14 - 69x^12 + 108x^10 - 49x^8 - 34x^6 + 42x^4 - 12x^2 + 1	\( 2^{40}\cdot 1583^{4} \)	20T638	Trivial (GRH)
20.8.6904360924896058824196096.2	x^20 - 10x^18 + 41x^16 - 106x^14 + 184x^12 - 192x^10 + 91x^8 + 10x^6 - 21x^4 + 2x^2 + 1	\( 2^{40}\cdot 1583^{4} \)	20T638	Trivial (GRH)
20.12.1242593181789399040000000000.1	x^20 - 7x^18 + 16x^16 - 12x^14 - 16x^10 + 69x^8 - 88x^6 + 49x^4 - 12x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T638	Trivial (GRH)
20.4.1242593181789399040000000000.1	x^20 + 2x^18 - 6x^16 + 14x^14 + 6x^12 - 10x^10 + 12x^8 - 5x^6 - 10x^4 + 4x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T638	Trivial (GRH)
20.12.1242593181789399040000000000.2	x^20 - 2x^18 - 5x^16 - 6x^14 + 61x^12 - 117x^10 + 174x^8 - 196x^6 + 113x^4 - 25x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T638	Trivial (GRH)
20.12.1482918065659095040000000000.1	x^20 - 3x^18 - 21x^16 + 86x^14 + 41x^12 - 553x^10 + 737x^8 - 150x^6 - 157x^4 - 7x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 3469^{4} \)	20T638	Trivial (GRH)
20.8.1482918065659095040000000000.1	x^20 - 7x^18 - 14x^17 - 3x^16 + 68x^15 + 84x^14 - 50x^13 - 143x^12 - 282x^11 - 55x^10 + 772x^9 + 357x^8 - 860x^7 - 326x^6 + 482x^5 + 69x^4 - 130x^3 + 21x^2 + 14x + 1	\( 2^{20}\cdot 5^{10}\cdot 3469^{4} \)	20T638	Trivial (GRH)
20.8.1482918065659095040000000000.2	x^20 - 4x^19 - 2x^18 + 20x^17 - 23x^16 + 12x^15 + 4x^13 + 6x^12 - 32x^11 + 52x^10 - 32x^9 + 6x^8 + 4x^7 + 12x^5 - 23x^4 + 20x^3 - 2x^2 - 4x + 1	\( 2^{20}\cdot 5^{10}\cdot 3469^{4} \)	20T638	Trivial (GRH)
20.12.3828204809593746045712890625.1	x^20 - x^19 - 13x^18 + 15x^17 + 35x^16 - 40x^15 + 30x^14 - 112x^13 - 4x^12 + 6x^11 + 107x^10 + 443x^9 - 433x^8 - 352x^7 + 379x^6 - 9x^5 - 143x^4 + 68x^3 + 32x^2 - 9x - 1	\( 5^{10}\cdot 19^{6}\cdot 1699^{4} \)	20T638	Trivial (GRH)
20.4.3828204809593746045712890625.1	x^20 - 3x^19 - x^18 + 17x^17 - 7x^16 - 59x^15 + 62x^14 + 17x^13 - 125x^12 + 104x^11 + 273x^10 + 64x^9 - 1414x^8 + 2443x^7 - 2655x^6 + 2550x^5 - 2064x^4 + 1002x^3 - 194x^2 - 19x + 19	\( 5^{10}\cdot 19^{6}\cdot 1699^{4} \)	20T638	Trivial (GRH)
20.12.3828204809593746045712890625.2	x^20 - 3x^19 - 6x^18 + 32x^17 - 31x^16 - 24x^15 + 120x^14 - 252x^13 + 217x^12 - 21x^11 - 121x^10 + 512x^9 - 606x^8 + 35x^7 + 292x^6 - 457x^5 + 210x^4 + 220x^3 - 77x^2 - 23x + 1	\( 5^{10}\cdot 19^{6}\cdot 1699^{4} \)	20T638	Trivial (GRH)
20.12.3828204809593746045712890625.3	x^20 - 7x^19 + 9x^18 + 34x^17 - 79x^16 - 44x^15 + 186x^14 + 17x^13 - 240x^12 + 265x^10 - 240x^8 + 17x^7 + 186x^6 - 44x^5 - 79x^4 + 34x^3 + 9x^2 - 7x + 1	\( 5^{10}\cdot 19^{6}\cdot 1699^{4} \)	20T638	Trivial (GRH)
20.4.23726689050545520640000000000.1	x^20 + 16x^18 + 92x^16 + 176x^14 - 364x^12 - 2312x^10 - 4144x^8 - 3024x^6 - 528x^4 + 176x^2 + 16	\( 2^{24}\cdot 5^{10}\cdot 3469^{4} \)	20T638	Trivial (GRH)
20.12.303899715661508400040000000000.1	x^20 - 8x^18 - 39x^16 + 548x^14 - 1869x^12 + 2190x^10 + 623x^8 - 2658x^6 + 779x^4 + 308x^2 + 16	\( 2^{12}\cdot 5^{10}\cdot 52501^{4} \)	20T638	Trivial (GRH)
20.16.303899715661508400040000000000.1	x^20 - 7x^18 - 32x^16 + 347x^14 - 513x^12 - 2288x^10 + 8671x^8 - 10537x^6 + 4896x^4 - 715x^2 + 1	\( 2^{12}\cdot 5^{10}\cdot 52501^{4} \)	20T638	Trivial (GRH)
20.12.303899715661508400040000000000.2	x^20 - 17x^18 + 82x^16 - 3x^14 - 587x^12 + 80x^10 + 564x^8 + 2x^6 - 117x^4 - 17x^2 + 1	\( 2^{12}\cdot 5^{10}\cdot 52501^{4} \)	20T638	Trivial (GRH)
20.16.593167226263638016000000000000.1	x^20 - 7x^18 - 65x^16 + 678x^14 - 1703x^12 + 519x^10 + 3281x^8 - 4390x^6 + 1995x^4 - 375x^2 + 25	\( 2^{24}\cdot 5^{12}\cdot 3469^{4} \)	20T638	Trivial (GRH)
20.20.2429612958775861313536000000000000.1	x^20 - 29x^18 + 343x^16 - 2140x^14 + 7593x^12 - 15429x^10 + 17441x^8 - 10620x^6 + 3295x^4 - 475x^2 + 25	\( 2^{36}\cdot 5^{12}\cdot 3469^{4} \)	20T638	Trivial (GRH)
20.20.2429612958775861313536000000000000.2	x^20 - 27x^18 + 285x^16 - 1526x^14 + 4591x^12 - 8189x^10 + 8821x^8 - 5660x^6 + 2055x^4 - 375x^2 + 25	\( 2^{36}\cdot 5^{12}\cdot 3469^{4} \)	20T638	Trivial (GRH)