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 16 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.122500000000000000000000.1	x^20 - 5x^18 + 15x^16 - 4x^15 - 20x^14 + 35x^12 - 10x^11 - 43x^10 + 10x^9 + 35x^8 - 20x^6 + 4x^5 + 15x^4 - 5x^2 + 1	\( 2^{20}\cdot 5^{22}\cdot 7^{2} \)	20T140	Trivial
20.0.247976342759474248351744.1	x^20 - x^19 - 9x^18 + 4x^17 + 35x^16 - x^15 - 63x^14 + 8x^13 + 73x^12 - 51x^11 - 79x^10 + 106x^9 + 106x^8 - 86x^7 - 84x^6 + 52x^5 + 84x^4 + 52x^3 + 28x^2 + 12x + 4	\( 2^{16}\cdot 13^{14}\cdot 31^{2} \)	20T140	Trivial
20.4.422500000000000000000000.1	x^20 - 5x^18 - 5x^16 - 10x^15 + 40x^14 - 10x^13 - 35x^12 + 60x^11 - 59x^10 - 100x^9 + 35x^8 - 20x^7 - 70x^6 - 15x^4 - 30x^3 - 5x^2 - 1	\( 2^{20}\cdot 5^{22}\cdot 13^{2} \)	20T140	Trivial
20.4.433765069904970043162624.1	x^20 - x^19 - 3x^18 + 4x^17 + 7x^16 - 31x^15 + 17x^14 + 50x^13 - 55x^12 - 45x^11 + 129x^10 - 32x^9 - 142x^8 + 96x^7 + 70x^6 - 94x^5 + 64x^3 - 28x^2 - 12x + 4	\( 2^{16}\cdot 13^{14}\cdot 41^{2} \)	20T140	Trivial
20.8.8106751406250000000000000000.1	x^20 - 5x^18 - 25x^16 - 82x^15 + 180x^14 + 770x^13 + 185x^12 - 2410x^11 - 4117x^10 - 2410x^9 + 185x^8 + 770x^7 + 180x^6 - 82x^5 - 25x^4 - 5x^2 + 1	\( 2^{16}\cdot 3^{2}\cdot 5^{22}\cdot 7^{8} \)	20T140	Trivial (GRH)
20.8.42077520999363600000000000000.1	x^20 - 10x^19 + 49x^18 - 156x^17 + 383x^16 - 820x^15 + 1604x^14 - 2794x^13 + 4255x^12 - 5744x^11 + 6729x^10 - 6294x^9 + 3781x^8 + 22x^7 - 4008x^6 + 6706x^5 - 5989x^4 + 2960x^3 - 775x^2 + 100x - 5	\( 2^{16}\cdot 3^{2}\cdot 5^{14}\cdot 43^{8} \)	20T140	Trivial (GRH)
20.12.152226776406250000000000000000.1	x^20 - 10x^19 + 35x^18 - 30x^17 - 115x^16 + 308x^15 - 120x^14 - 470x^13 + 645x^12 - 100x^11 - 355x^10 + 460x^9 - 465x^8 - 70x^7 + 530x^6 + 126x^5 - 345x^4 - 340x^3 + 185x^2 + 130x - 1	\( 2^{16}\cdot 5^{22}\cdot 7^{8}\cdot 13^{2} \)	20T140	Trivial (GRH)
20.4.260316795156250000000000000000.1	x^20 + 10x^18 - 10x^17 + 5x^16 - 122x^15 - 210x^14 - 530x^13 - 200x^12 + 390x^11 + 1470x^10 + 3730x^9 + 5500x^8 + 4930x^7 + 8210x^6 + 9546x^5 + 1495x^4 - 2830x^3 - 1480x^2 - 640x + 239	\( 2^{16}\cdot 5^{22}\cdot 7^{8}\cdot 17^{2} \)	20T140	Trivial (GRH)
20.12.397230818906250000000000000000.1	x^20 - 15x^18 - 10x^17 + 65x^16 + 118x^15 + 30x^14 - 650x^13 - 555x^12 + 1470x^11 + 481x^10 + 670x^9 - 1825x^8 - 4790x^7 + 7060x^6 + 720x^5 - 3685x^4 + 520x^3 + 495x^2 - 100x - 5	\( 2^{16}\cdot 3^{2}\cdot 5^{22}\cdot 7^{10} \)	20T140	Trivial (GRH)
20.16.510934781922934055328369140625.1	x^20 - 5x^19 - 15x^18 + 100x^17 + 40x^16 - 706x^15 + 355x^14 + 2075x^13 - 2440x^12 - 2235x^11 + 5922x^10 + 1335x^9 - 6420x^8 - 6465x^7 + 140x^6 + 9461x^5 + 6090x^4 - 1005x^3 - 835x^2 + 130x - 4	\( 3^{2}\cdot 5^{22}\cdot 47^{8} \)	20T140	Trivial (GRH)
20.16.673240335989817600000000000000.1	x^20 - 26x^18 + 237x^16 - 1040x^14 + 2462x^12 - 3432x^10 + 3698x^8 - 4520x^6 + 4513x^4 - 2186x^2 + 289	\( 2^{20}\cdot 3^{2}\cdot 5^{14}\cdot 43^{8} \)	20T140	Trivial (GRH)
20.4.3633314004785308837890625000000.1	x^20 + 25x^18 + 130x^16 - 275x^14 - 3435x^12 - 6789x^10 - 1130x^8 + 2035x^6 + 895x^4 + 110x^2 + 4	\( 2^{6}\cdot 5^{22}\cdot 47^{8} \)	20T140	Trivial (GRH)
20.20.8475158220156250000000000000000.1	x^20 - 25x^18 + 235x^16 - 2x^15 - 1080x^14 + 10x^13 + 2645x^12 - 10x^11 - 3557x^10 - 10x^9 + 2645x^8 + 10x^7 - 1080x^6 - 2x^5 + 235x^4 - 25x^2 + 1	\( 2^{16}\cdot 5^{22}\cdot 7^{8}\cdot 97^{2} \)	20T140	Trivial (GRH)
20.20.259748421807656250000000000000000.1	x^20 - 5x^19 - 25x^18 + 130x^17 + 275x^16 - 1357x^15 - 1805x^14 + 7270x^13 + 7715x^12 - 21175x^11 - 20991x^10 + 32690x^9 + 33580x^8 - 23600x^7 - 27650x^6 + 4802x^5 + 8960x^4 + 880x^3 - 520x^2 - 100x - 4	\( 2^{16}\cdot 3^{2}\cdot 5^{22}\cdot 7^{8}\cdot 179^{2} \)	20T140	Trivial (GRH)
20.0.415282752787656250000000000000000.1	x^20 - 5x^18 - 15x^16 - 60x^15 + 90x^14 + 200x^13 + 655x^12 + 3020x^11 + 1117x^10 - 3050x^9 + 29145x^8 + 82980x^7 + 68790x^6 + 42730x^5 + 171825x^4 + 442940x^3 + 629335x^2 + 483750x + 162871	\( 2^{16}\cdot 5^{22}\cdot 7^{10}\cdot 97^{2} \)	20T140	$[156]$ (GRH)
20.0.1368208637864347439721375491751936.1	x^20 - 5x^19 + 16x^18 + 3x^17 + 57x^16 - 202x^15 + 43x^14 - 817x^13 + 2557x^12 - 1698x^11 - 1837x^10 + 5343x^9 - 4748x^8 - 3541x^7 + 14483x^6 - 5772x^5 + 6580x^4 + 6848x^3 + 192x^2 - 2048x + 1024	\( 2^{16}\cdot 3^{2}\cdot 41^{2}\cdot 53^{14} \)	20T140	$[120]$ (GRH)