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 matches 1-50 of 60)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.715801729191629440000.1	x^20 + 2x^18 + 2x^16 + 4x^14 + 11x^12 + 14x^10 + 11x^8 + 6x^6 + 5x^4 + 4x^2 + 1	\( 2^{10}\cdot 5^{4}\cdot 5783^{4} \)	20T964	Trivial
20.0.1267791677353905767424.1	x^20 + 5x^18 + 14x^16 + 27x^14 + 41x^12 + 53x^10 + 55x^8 + 43x^6 + 22x^4 + 7x^2 + 1	\( 2^{10}\cdot 3^{4}\cdot 11119^{4} \)	20T964	Trivial
20.0.2380891600778249012224.1	x^20 + 5x^18 + 12x^16 + 19x^14 + 28x^12 + 50x^10 + 70x^8 + 62x^6 + 32x^4 + 9x^2 + 1	\( 2^{10}\cdot 17^{4}\cdot 2297^{4} \)	20T964	Trivial
20.0.8436100343241961897984.1	x^20 - 2x^19 + 2x^18 + 4x^17 - 21x^16 + 44x^15 - 57x^14 + 36x^13 + 46x^12 - 220x^11 + 505x^10 - 860x^9 + 1168x^8 - 1278x^7 + 1123x^6 - 784x^5 + 427x^4 - 176x^3 + 52x^2 - 10x + 1	\( 2^{20}\cdot 17^{2}\cdot 2297^{4} \)	20T964	Trivial (GRH)
20.4.29319238827689141862400.1	x^20 - 2x^19 - 2x^18 + 8x^17 + 7x^16 - 32x^15 - x^14 + 60x^13 + 3x^12 - 108x^11 + 14x^10 + 112x^9 - 4x^8 - 96x^7 - 21x^6 + 52x^5 + 26x^4 - 18x^3 - 22x^2 - 8x - 1	\( 2^{20}\cdot 5^{2}\cdot 5783^{4} \)	20T964	Trivial (GRH)
20.4.47669167735583779323904.1	x^20 - 6x^19 + 17x^18 - 30x^17 + 26x^16 + 12x^15 - 58x^14 + 62x^13 - 20x^12 - 26x^11 + 43x^10 - 26x^9 - 20x^8 + 62x^7 - 58x^6 + 12x^5 + 26x^4 - 30x^3 + 17x^2 - 6x + 1	\( 2^{20}\cdot 7^{2}\cdot 5519^{4} \)	20T964	Trivial (GRH)
20.4.688077672624913964532736.1	x^20 - 6x^19 + 19x^18 - 51x^17 + 109x^16 - 167x^15 + 218x^14 - 255x^13 + 201x^12 - 84x^11 - 43x^10 + 137x^9 - 68x^8 + 32x^7 - 81x^6 + 17x^5 - x^4 + 15x^3 + x^2 + 6x + 1	\( 2^{10}\cdot 17^{6}\cdot 2297^{4} \)	20T964	Trivial (GRH)
20.4.732980970692228546560000.1	x^20 - 2x^18 + 2x^16 - 4x^14 + 11x^12 - 14x^10 + 11x^8 - 6x^6 + 5x^4 - 4x^2 + 1	\( 2^{20}\cdot 5^{4}\cdot 5783^{4} \)	20T964	Trivial (GRH)
20.4.732980970692228546560000.2	x^20 - 2x^18 + 2x^16 - 2x^14 + x^12 + 7x^10 - 13x^8 + 2x^6 + 8x^4 - 6x^2 + 1	\( 2^{20}\cdot 5^{4}\cdot 5783^{4} \)	20T964	Trivial (GRH)
20.0.1860495326773308902342656.3	x^20 + x^18 + 6x^16 + 18x^14 + 26x^12 + 32x^10 + 20x^8 + x^6 - 2x^4 - x^2 + 1	\( 2^{20}\cdot 36497^{4} \)	20T964	Trivial (GRH)
20.0.1860495326773308902342656.4	x^20 + 4x^18 + 12x^16 + 35x^14 + 63x^12 + 64x^10 + 42x^8 + 26x^6 + 16x^4 + 5x^2 + 1	\( 2^{20}\cdot 36497^{4} \)	20T964	Trivial (GRH)
20.4.1860495326773308902342656.4	x^20 - 4x^18 + 12x^16 - 35x^14 + 63x^12 - 64x^10 + 42x^8 - 26x^6 + 16x^4 - 5x^2 + 1	\( 2^{20}\cdot 36497^{4} \)	20T964	Trivial (GRH)
20.4.1860495326773308902342656.5	x^20 - 2x^18 + 4x^16 - 13x^14 + 29x^12 - 2x^10 + 18x^8 - 18x^6 + 10x^4 - 5x^2 + 1	\( 2^{20}\cdot 36497^{4} \)	20T964	Trivial (GRH)
20.4.2060764600365471574508544.1	x^20 + 8x^18 + 28x^16 + 64x^14 + 111x^12 + 138x^10 + 112x^8 + 40x^6 - 20x^4 - 16x^2 + 1	\( 2^{10}\cdot 3^{4}\cdot 17^{4}\cdot 4153^{4} \)	20T964	Trivial (GRH)
20.8.2060764600365471574508544.1	x^20 - 5x^18 + 4x^16 + 14x^14 - 33x^12 - 3x^10 + 65x^8 - 14x^6 - 43x^4 + 4x^2 + 1	\( 2^{10}\cdot 3^{4}\cdot 17^{4}\cdot 4153^{4} \)	20T964	Trivial (GRH)
20.4.2060764600365471574508544.2	x^20 - 15x^16 - 12x^14 + 33x^12 + 64x^10 + 88x^8 + 94x^6 + 51x^4 + 12x^2 + 1	\( 2^{10}\cdot 3^{4}\cdot 17^{4}\cdot 4153^{4} \)	20T964	Trivial (GRH)
20.4.2438032999196926988517376.2	x^20 - 5x^18 + 9x^16 - 12x^14 + 27x^12 - 49x^10 + 54x^8 - 41x^6 + 22x^4 - 8x^2 + 1	\( 2^{20}\cdot 17^{4}\cdot 2297^{4} \)	20T964	Trivial (GRH)
20.8.4085400993762722886713344.1	x^20 - 5x^18 - 2x^17 + 21x^16 - 42x^14 - 30x^13 + 10x^12 + 40x^11 + 30x^10 + 66x^9 + 33x^8 - 58x^7 - 27x^6 + 2x^5 + 9x^4 + 16x^3 + 2x^2 - 4x - 1	\( 2^{20}\cdot 13^{4}\cdot 97^{2}\cdot 347^{4} \)	20T964	Trivial (GRH)
20.4.18546881403289244170576896.1	x^20 - 5x^19 + 8x^18 - 17x^16 + 6x^15 + 40x^14 - 16x^13 - 68x^12 + 55x^11 + 76x^10 - 62x^9 - 97x^8 + 16x^7 + 42x^6 - 2x^5 + 3x^4 + 31x^3 + 26x^2 + 9x + 1	\( 2^{10}\cdot 3^{6}\cdot 17^{4}\cdot 4153^{4} \)	20T964	Trivial (GRH)
20.8.18546881403289244170576896.1	x^20 - 5x^19 + 8x^18 - 10x^17 + 16x^16 - 4x^15 - x^14 + x^13 - 28x^12 + 24x^11 - 32x^10 + 15x^9 + 27x^8 - 10x^7 - 17x^6 - 38x^5 + 33x^4 + 19x^3 - 16x^2 - x + 1	\( 2^{10}\cdot 3^{6}\cdot 17^{4}\cdot 4153^{4} \)	20T964	Trivial (GRH)
20.8.30022900559553681267097600.1	x^20 - 4x^19 + 6x^18 - 8x^17 + 7x^16 - 20x^15 + 64x^14 - 60x^13 - 52x^12 + 426x^11 - 888x^10 + 1038x^9 - 635x^8 - 364x^7 + 1192x^6 - 1406x^5 + 1055x^4 - 498x^3 + 142x^2 - 22x + 1	\( 2^{30}\cdot 5^{2}\cdot 5783^{4} \)	20T964	Trivial (GRH)
20.0.626072689707529169661853696.1	x^20 + 7x^18 + 15x^16 + x^14 - 34x^12 - 31x^10 + 18x^8 + 46x^6 + 33x^4 + 10x^2 + 1	\( 2^{20}\cdot 7^{4}\cdot 137^{4}\cdot 163^{4} \)	20T964	$[2]$ (GRH)
20.12.626072689707529169661853696.2	x^20 - 7x^18 + 15x^16 - x^14 - 34x^12 + 31x^10 + 18x^8 - 46x^6 + 33x^4 - 10x^2 + 1	\( 2^{20}\cdot 7^{4}\cdot 137^{4}\cdot 163^{4} \)	20T964	Trivial (GRH)
20.8.743440706348303704240685056.1	x^20 - 5x^18 - 24x^16 + 51x^14 + 215x^12 - 32x^10 - 632x^8 - 614x^6 - 119x^4 + 41x^2 + 1	\( 2^{24}\cdot 83^{4}\cdot 983^{4} \)	20T964	Trivial (GRH)
20.8.743440706348303704240685056.2	x^20 - 5x^19 - x^18 + 23x^17 - 9x^16 - 12x^15 - 36x^13 + 8x^12 + 30x^11 - 14x^10 + 30x^9 + 8x^8 - 36x^7 - 12x^5 - 9x^4 + 23x^3 - x^2 - 5x + 1	\( 2^{24}\cdot 83^{4}\cdot 983^{4} \)	20T964	Trivial (GRH)
20.12.743440706348303704240685056.3	x^20 - 5x^18 - 14x^16 + 97x^14 - 84x^12 - 147x^10 + 168x^8 + 37x^6 - 46x^4 - 9x^2 + 1	\( 2^{24}\cdot 83^{4}\cdot 983^{4} \)	20T964	Trivial (GRH)
20.12.743440706348303704240685056.4	x^20 - 5x^19 + 5x^18 + 11x^17 - 23x^16 + 30x^15 - 122x^14 + 264x^13 - 230x^12 - 56x^11 + 516x^10 - 688x^9 - x^8 + 653x^7 - 279x^6 - 193x^5 + 128x^4 + 9x^3 - 23x^2 + x + 1	\( 2^{24}\cdot 83^{4}\cdot 983^{4} \)	20T964	Trivial (GRH)
20.0.2486366931153398287534391296.1	x^20 + 5x^18 - 2x^16 - 25x^14 + x^12 + 59x^10 + 78x^8 + 66x^6 + 38x^4 + 11x^2 + 1	\( 2^{20}\cdot 149^{4}\cdot 1481^{4} \)	20T964	Trivial (GRH)
20.12.2486366931153398287534391296.1	x^20 - 5x^18 - 2x^16 + 25x^14 + x^12 - 59x^10 + 78x^8 - 66x^6 + 38x^4 - 11x^2 + 1	\( 2^{20}\cdot 149^{4}\cdot 1481^{4} \)	20T964	Trivial (GRH)
20.4.2486366931153398287534391296.1	x^20 + 3x^18 - 7x^14 - 21x^12 - 13x^10 + 60x^8 + 16x^6 - 62x^4 + 21x^2 + 1	\( 2^{20}\cdot 149^{4}\cdot 1481^{4} \)	20T964	Trivial (GRH)
20.8.2486366931153398287534391296.1	x^20 - 4x^18 - 4x^16 + 29x^14 - 10x^12 - 49x^10 + 28x^8 + 20x^4 - 13x^2 + 1	\( 2^{20}\cdot 149^{4}\cdot 1481^{4} \)	20T964	Trivial (GRH)
20.8.2486366931153398287534391296.2	x^20 - 11x^18 + 50x^16 - 129x^14 + 206x^12 - 180x^10 + 55x^8 + 23x^6 - 17x^4 + 1	\( 2^{20}\cdot 149^{4}\cdot 1481^{4} \)	20T964	Trivial (GRH)
20.0.2676556907318115605247164416.1	x^20 + 5x^18 - 4x^16 - 31x^14 + 21x^12 + 153x^10 + 183x^8 + 124x^6 + 58x^4 + 13x^2 + 1	\( 2^{20}\cdot 53^{4}\cdot 4241^{4} \)	20T964	Trivial (GRH)
20.12.2676556907318115605247164416.1	x^20 - 5x^18 - 4x^16 + 31x^14 + 21x^12 - 153x^10 + 183x^8 - 124x^6 + 58x^4 - 13x^2 + 1	\( 2^{20}\cdot 53^{4}\cdot 4241^{4} \)	20T964	Trivial (GRH)
20.0.13083641515520609586402820096.1	x^20 + 14x^18 + 55x^16 + 46x^14 + 61x^12 + 754x^10 + 1706x^8 + 2982x^6 + 3168x^4 + 1036x^2 + 49	\( 2^{30}\cdot 7^{2}\cdot 137^{4}\cdot 163^{4} \)	20T964	$[2]$ (GRH)
20.12.13083641515520609586402820096.1	x^20 - 14x^18 + 55x^16 - 46x^14 + 61x^12 - 754x^10 + 1706x^8 - 2982x^6 + 3168x^4 - 1036x^2 + 49	\( 2^{30}\cdot 7^{2}\cdot 137^{4}\cdot 163^{4} \)	20T964	Trivial (GRH)
20.8.18992006556968186030670741504.1	x^20 - 2x^19 - 9x^18 + 52x^17 - 136x^16 + 174x^15 + x^14 - 466x^13 + 1138x^12 - 1746x^11 + 2176x^10 - 2446x^9 + 2470x^8 - 1998x^7 + 878x^6 + 286x^5 - 634x^4 + 262x^3 - 83x^2 + 4x + 1	\( 2^{20}\cdot 3^{6}\cdot 17^{4}\cdot 4153^{4} \)	20T964	Trivial (GRH)
20.12.190320820825165748285615374336.3	x^20 + 5x^18 - 26x^16 - 47x^14 + 251x^12 - 70x^10 - 640x^8 + 874x^6 - 397x^4 + 49x^2 + 1	\( 2^{32}\cdot 83^{4}\cdot 983^{4} \)	20T964	Trivial (GRH)
20.16.190320820825165748285615374336.3	x^20 - 15x^18 + 82x^16 - 203x^14 + 190x^12 + 101x^10 - 310x^8 + 127x^6 + 72x^4 - 45x^2 + 1	\( 2^{32}\cdot 83^{4}\cdot 983^{4} \)	20T964	Trivial (GRH)
20.4.190320820825165748285615374336.3	x^20 + 9x^18 + 24x^16 - 3x^14 - 105x^12 - 128x^10 + 30x^8 + 134x^6 + 75x^4 + 15x^2 + 1	\( 2^{32}\cdot 83^{4}\cdot 983^{4} \)	20T964	Trivial (GRH)
20.8.190320820825165748285615374336.3	x^20 - x^18 - 31x^16 - 36x^14 + 97x^12 + 131x^10 - 51x^8 - 120x^6 - 43x^4 - x^2 + 1	\( 2^{32}\cdot 83^{4}\cdot 983^{4} \)	20T964	Trivial (GRH)
20.12.190320820825165748285615374336.4	x^20 + 5x^18 - 14x^16 - 79x^14 + 63x^12 + 342x^10 - 156x^8 - 250x^6 + 167x^4 - 27x^2 + 1	\( 2^{32}\cdot 83^{4}\cdot 983^{4} \)	20T964	Trivial (GRH)
20.16.190320820825165748285615374336.4	x^20 - 5x^18 - 10x^16 + 83x^14 - 71x^12 - 242x^10 + 544x^8 - 426x^6 + 147x^4 - 21x^2 + 1	\( 2^{32}\cdot 83^{4}\cdot 983^{4} \)	20T964	Trivial (GRH)
20.4.190320820825165748285615374336.4	x^20 + 5x^18 - 16x^16 - 109x^14 - 51x^12 + 506x^10 + 1024x^8 + 790x^6 + 271x^4 + 37x^2 + 1	\( 2^{32}\cdot 83^{4}\cdot 983^{4} \)	20T964	Trivial (GRH)
20.4.119483533089645699448237893615616.1	x^20 - 4x^19 + 16x^18 - 26x^17 + 5x^16 - 132x^15 + 460x^14 - 2570x^13 + 4080x^12 + 4392x^11 - 37114x^10 + 143566x^9 - 307861x^8 + 514608x^7 - 627434x^6 + 266044x^5 + 1004251x^4 - 2356262x^3 + 2982810x^2 - 1667462x + 411919	\( 2^{30}\cdot 13^{8}\cdot 97^{2}\cdot 347^{4} \)	20T964	$[2, 2]$ (GRH)
20.8.119483533089645699448237893615616.1	x^20 - 2x^19 - 24x^18 + 60x^17 + 9x^16 - 74x^15 + 684x^14 - 3218x^13 + 2566x^12 + 3642x^11 + 9758x^10 - 33834x^9 - 49005x^8 + 350106x^7 - 813040x^6 + 1115350x^5 - 856931x^4 + 514434x^3 - 474364x^2 - 266062x + 646351	\( 2^{30}\cdot 13^{8}\cdot 97^{2}\cdot 347^{4} \)	20T964	$[2]$ (GRH)
20.4.119483533089645699448237893615616.2	x^20 - 10x^19 + 44x^18 - 104x^17 + 54x^16 + 504x^15 - 1958x^14 + 2690x^13 + 495x^12 - 6330x^11 + 8600x^10 - 8080x^9 + 39757x^8 - 61260x^7 - 36548x^6 - 123760x^5 - 532103x^4 - 752018x^3 - 1449910x^2 - 631886x - 61427	\( 2^{30}\cdot 13^{8}\cdot 97^{2}\cdot 347^{4} \)	20T964	$[2]$ (GRH)
20.8.119483533089645699448237893615616.2	x^20 - 10x^19 + 42x^18 - 86x^17 - 9x^16 + 568x^15 - 1704x^14 + 3072x^13 - 4335x^12 + 3210x^11 + 16392x^10 - 56168x^9 + 35465x^8 + 40900x^7 + 85034x^6 - 789730x^5 + 1886124x^4 - 692568x^3 - 3501172x^2 + 3682192x - 199967	\( 2^{30}\cdot 13^{8}\cdot 97^{2}\cdot 347^{4} \)	20T964	$[2]$ (GRH)
20.0.144516905723267215365502945884368797696.1	x^20 + 117x^18 + 5400x^16 + 130685x^14 + 1837652x^12 + 15602353x^10 + 80109940x^8 + 240789391x^6 + 390385852x^4 + 280747417x^2 + 47458321	\( 2^{36}\cdot 83^{8}\cdot 983^{4} \)	20T964	$[2, 2, 47536]$ (GRH)
20.12.144516905723267215365502945884368797696.1	x^20 - 99x^18 + 3390x^16 - 40437x^14 - 104470x^12 + 3979611x^10 - 760612x^8 - 65887143x^6 - 454674x^4 + 277316695x^2 + 47458321	\( 2^{36}\cdot 83^{8}\cdot 983^{4} \)	20T964	Trivial (GRH)