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 32 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.4948692361728553496809.1	x^20 - 4x^19 + 9x^18 - 14x^17 + 14x^16 - 10x^15 + 20x^14 - 57x^13 + 106x^12 - 132x^11 + 121x^10 - 103x^9 + 94x^8 - 60x^7 + 10x^6 + 5x^5 + 5x^4 - 3x^3 - 2x^2 + 1	\( 17^{6}\cdot 14318531^{2} \)	20T1105	Trivial
20.0.58618491771734415376384.1	x^20 + 3x^18 + 8x^16 + 14x^14 + 20x^12 + 24x^10 + 24x^8 + 19x^6 + 12x^4 + 5x^2 + 1	\( 2^{20}\cdot 236438047^{2} \)	20T1105	Trivial (GRH)
20.0.675202762078964700676096.1	x^20 + 4x^18 + 12x^16 + 22x^14 + 32x^12 + 37x^10 + 32x^8 + 23x^6 + 11x^4 + 4x^2 + 1	\( 2^{20}\cdot 53^{2}\cdot 71^{2}\cdot 213247^{2} \)	20T1105	Trivial (GRH)
20.4.675202762078964700676096.1	x^20 - 3x^18 + 9x^16 - 12x^14 + 17x^12 - 9x^10 + 7x^8 - 5x^6 - 6x^4 - x^2 + 1	\( 2^{20}\cdot 53^{2}\cdot 71^{2}\cdot 213247^{2} \)	20T1105	Trivial (GRH)
20.0.675202762078964700676096.2	x^20 - x^14 - x^12 + x^10 + 5x^8 + 10x^6 + 10x^4 + 5x^2 + 1	\( 2^{20}\cdot 53^{2}\cdot 71^{2}\cdot 213247^{2} \)	20T1105	Trivial (GRH)
20.4.675202762078964700676096.2	x^20 + x^14 - x^12 - x^10 + 5x^8 - 10x^6 + 10x^4 - 5x^2 + 1	\( 2^{20}\cdot 53^{2}\cdot 71^{2}\cdot 213247^{2} \)	20T1105	Trivial (GRH)
20.0.11533713053509947520712704.1	x^20 + 3x^18 - x^14 + 5x^12 + 8x^6 + 8x^4 + 6x^2 + 1	\( 2^{20}\cdot 1483^{2}\cdot 2236369^{2} \)	20T1105	Trivial (GRH)
20.4.11533713053509947520712704.1	x^20 + 2x^18 + 3x^16 - 3x^14 - 17x^12 - 31x^10 - 33x^8 - 20x^6 - 7x^4 + x^2 + 1	\( 2^{20}\cdot 1483^{2}\cdot 2236369^{2} \)	20T1105	Trivial (GRH)
20.8.11533713053509947520712704.1	x^20 - x^18 + 9x^16 - 10x^14 + 23x^12 - 26x^10 - 9x^8 + 5x^6 + 14x^4 - 8x^2 + 1	\( 2^{20}\cdot 1483^{2}\cdot 2236369^{2} \)	20T1105	Trivial (GRH)
20.0.11533713053509947520712704.2	x^20 + 2x^18 - x^16 - 6x^14 - 8x^12 + 4x^10 + 23x^8 + 32x^6 + 23x^4 + 8x^2 + 1	\( 2^{20}\cdot 1483^{2}\cdot 2236369^{2} \)	20T1105	Trivial (GRH)
20.4.11533713053509947520712704.2	x^20 - x^18 - 4x^16 + 10x^14 - 13x^12 + 23x^10 - 21x^8 + 25x^6 - 15x^4 - 7x^2 + 1	\( 2^{20}\cdot 1483^{2}\cdot 2236369^{2} \)	20T1105	Trivial (GRH)
20.8.11533713053509947520712704.2	x^20 - 3x^18 + x^14 + 5x^12 - 8x^6 + 8x^4 - 6x^2 + 1	\( 2^{20}\cdot 1483^{2}\cdot 2236369^{2} \)	20T1105	Trivial (GRH)
20.4.394175448559366984516501504.1	x^20 - 3x^16 + x^14 + 2x^12 - x^10 - 3x^6 + 3x^2 + 1	\( 2^{20}\cdot 16493^{2}\cdot 1175561^{2} \)	20T1105	Trivial (GRH)
20.8.394175448559366984516501504.1	x^20 + 4x^18 + 4x^16 - 5x^14 - 15x^12 - 6x^10 + 16x^8 + 8x^6 - 7x^4 - 2x^2 + 1	\( 2^{20}\cdot 16493^{2}\cdot 1175561^{2} \)	20T1105	Trivial (GRH)
20.4.394175448559366984516501504.2	x^20 - 4x^18 + 4x^16 + 5x^14 - 15x^12 + 6x^10 + 16x^8 - 8x^6 - 7x^4 + 2x^2 + 1	\( 2^{20}\cdot 16493^{2}\cdot 1175561^{2} \)	20T1105	Trivial (GRH)
20.8.394175448559366984516501504.2	x^20 - 3x^16 - x^14 + 2x^12 + x^10 + 3x^6 - 3x^2 + 1	\( 2^{20}\cdot 16493^{2}\cdot 1175561^{2} \)	20T1105	Trivial (GRH)
20.0.5144322581541225166787313664.1	x^20 + 6x^18 + 11x^16 + 7x^14 + 4x^12 - 6x^10 - 23x^8 - 5x^6 + 15x^4 + 8x^2 + 1	\( 2^{20}\cdot 43^{2}\cdot 751^{2}\cdot 967^{2}\cdot 2243^{2} \)	20T1105	Trivial (GRH)
20.12.5144322581541225166787313664.1	x^20 - 6x^18 + 11x^16 - 7x^14 + 4x^12 + 6x^10 - 23x^8 + 5x^6 + 15x^4 - 8x^2 + 1	\( 2^{20}\cdot 43^{2}\cdot 751^{2}\cdot 967^{2}\cdot 2243^{2} \)	20T1105	Trivial (GRH)
20.12.9428099289122298266741899264.1	x^20 - 9x^18 + 32x^16 - 55x^14 + 35x^12 + 29x^10 - 57x^8 + 18x^6 + 11x^4 - 7x^2 + 1	\( 2^{20}\cdot 111847^{2}\cdot 847789^{2} \)	20T1105	Trivial (GRH)
20.4.9428099289122298266741899264.1	x^20 + 9x^18 + 32x^16 + 55x^14 + 35x^12 - 29x^10 - 57x^8 - 18x^6 + 11x^4 + 7x^2 + 1	\( 2^{20}\cdot 111847^{2}\cdot 847789^{2} \)	20T1105	Trivial (GRH)
20.12.38824875867092117130648223744.1	x^20 - 6x^18 + 10x^16 + x^14 - 12x^12 + 4x^10 - 4x^8 + 7x^6 + 4x^4 - 5x^2 + 1	\( 2^{20}\cdot 1483^{2}\cdot 129751961^{2} \)	20T1105	Trivial (GRH)
20.4.38824875867092117130648223744.1	x^20 + 6x^18 + 10x^16 - x^14 - 12x^12 - 4x^10 - 4x^8 - 7x^6 + 4x^4 + 5x^2 + 1	\( 2^{20}\cdot 1483^{2}\cdot 129751961^{2} \)	20T1105	Trivial (GRH)
20.8.38824875867092117130648223744.1	x^20 + 4x^18 + x^16 - 15x^14 - 19x^12 + 9x^10 + 25x^8 + 2x^6 - 9x^4 - x^2 + 1	\( 2^{20}\cdot 1483^{2}\cdot 129751961^{2} \)	20T1105	Trivial (GRH)
20.8.38824875867092117130648223744.2	x^20 - 4x^18 + x^16 + 15x^14 - 19x^12 - 9x^10 + 25x^8 - 2x^6 - 9x^4 + x^2 + 1	\( 2^{20}\cdot 1483^{2}\cdot 129751961^{2} \)	20T1105	Trivial (GRH)
20.12.276046894426236664438661840896.1	x^20 - 6x^18 + 7x^16 + 17x^14 - 32x^12 - 13x^10 + 36x^8 + 2x^6 - 12x^4 + 1	\( 2^{20}\cdot 460181^{2}\cdot 1114969^{2} \)	20T1105	Trivial (GRH)
20.16.276046894426236664438661840896.1	x^20 - 16x^18 + 106x^16 - 375x^14 + 759x^12 - 864x^10 + 482x^8 - 53x^6 - 52x^4 + 12x^2 + 1	\( 2^{20}\cdot 460181^{2}\cdot 1114969^{2} \)	20T1105	Trivial (GRH)
20.4.276046894426236664438661840896.1	x^20 + 14x^18 + 79x^16 + 225x^14 + 318x^12 + 135x^10 - 166x^8 - 182x^6 - 16x^4 + 24x^2 + 1	\( 2^{20}\cdot 460181^{2}\cdot 1114969^{2} \)	20T1105	Trivial (GRH)
20.8.276046894426236664438661840896.1	x^20 + 4x^18 - 2x^16 - 23x^14 - 11x^12 + 40x^10 + 30x^8 - 21x^6 - 18x^4 + 1	\( 2^{20}\cdot 460181^{2}\cdot 1114969^{2} \)	20T1105	Trivial (GRH)
20.12.276046894426236664438661840896.2	x^20 - 4x^18 - 2x^16 + 23x^14 - 11x^12 - 40x^10 + 30x^8 + 21x^6 - 18x^4 + 1	\( 2^{20}\cdot 460181^{2}\cdot 1114969^{2} \)	20T1105	Trivial (GRH)
20.16.276046894426236664438661840896.2	x^20 - 14x^18 + 79x^16 - 225x^14 + 318x^12 - 135x^10 - 166x^8 + 182x^6 - 16x^4 - 24x^2 + 1	\( 2^{20}\cdot 460181^{2}\cdot 1114969^{2} \)	20T1105	Trivial (GRH)
20.4.276046894426236664438661840896.2	x^20 + 16x^18 + 106x^16 + 375x^14 + 759x^12 + 864x^10 + 482x^8 + 53x^6 - 52x^4 - 12x^2 + 1	\( 2^{20}\cdot 460181^{2}\cdot 1114969^{2} \)	20T1105	Trivial (GRH)
20.8.276046894426236664438661840896.2	x^20 + 6x^18 + 7x^16 - 17x^14 - 32x^12 + 13x^10 + 36x^8 - 2x^6 - 12x^4 + 1	\( 2^{20}\cdot 460181^{2}\cdot 1114969^{2} \)	20T1105	Trivial (GRH)