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 16 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.30679705675697817124864.1	x^20 - 2x^18 + 5x^16 - 8x^14 + 14x^12 - 4x^10 + 14x^8 - 8x^6 + 5x^4 - 2x^2 + 1	\( 2^{42}\cdot 17^{8} \)	20T230	Trivial (GRH)
20.4.490875290811165073997824.1	x^20 - 2x^19 + 7x^18 - 6x^17 - 3x^16 + 40x^15 - 74x^14 + 48x^13 - 44x^12 + 64x^11 + 2x^10 - 80x^9 + 58x^8 - 16x^7 - 4x^6 + 32x^5 - 14x^4 - 20x^3 + 10x^2 + 4x - 2	\( 2^{46}\cdot 17^{8} \)	20T230	Trivial
20.0.490875290811165073997824.2	x^20 + 4x^16 - 6x^12 + 16x^8 - 15x^4 + 4	\( 2^{46}\cdot 17^{8} \)	20T230	Trivial (GRH)
20.4.35201711859446669696303104.1	x^20 - 10x^18 + 44x^16 - 128x^14 + 328x^12 - 600x^10 + 1112x^8 - 1472x^6 + 996x^4 - 280x^2 + 16	\( 2^{46}\cdot 29^{8} \)	20T230	Trivial (GRH)
20.0.21822182114965484993955979209.1	x^20 + 8x^18 + 52x^16 + 142x^14 + 358x^12 + 205x^10 + 881x^8 + 666x^6 + 923x^4 - 30x^2 + 1	\( 3^{10}\cdot 883^{8} \)	20T230	$[4]$ (GRH)
20.0.21822182114965484993955979209.2	x^20 - 3x^19 + 9x^18 + 6x^17 - 14x^16 + 39x^15 + 56x^14 - 57x^13 + 124x^12 + 201x^11 - 181x^10 + 402x^9 + 496x^8 - 456x^7 + 896x^6 + 1248x^5 - 896x^4 + 768x^3 + 2304x^2 - 1536x + 1024	\( 3^{10}\cdot 883^{8} \)	20T230	$[2, 2]$ (GRH)
20.0.21822182114965484993955979209.3	x^20 - 2x^19 + 11x^18 - 4x^17 + 63x^16 - 56x^15 + 99x^14 - 89x^13 + 96x^12 - 153x^11 + 77x^10 - 153x^9 + 96x^8 - 89x^7 + 99x^6 - 56x^5 + 63x^4 - 4x^3 + 11x^2 - 2x + 1	\( 3^{10}\cdot 883^{8} \)	20T230	$[2, 2]$ (GRH)
20.0.1098418932986448505871281640625.1	x^20 - 2x^19 + 16x^18 - 38x^17 + 202x^16 - 401x^15 + 927x^14 - 933x^13 + 1347x^12 - 772x^11 + 1331x^10 - 772x^9 + 1347x^8 - 933x^7 + 927x^6 - 401x^5 + 202x^4 - 38x^3 + 16x^2 - 2x + 1	\( 3^{20}\cdot 5^{8}\cdot 73^{8} \)	20T230	$[5]$ (GRH)
20.4.11898465795995295047760009765625.1	x^20 - 10x^19 + 65x^18 - 300x^17 + 1085x^16 - 3172x^15 + 7670x^14 - 15520x^13 + 26400x^12 - 37760x^11 + 45121x^10 - 44485x^9 + 35340x^8 - 21640x^7 + 9260x^6 - 1915x^5 - 540x^4 + 550x^3 - 150x^2 + 5	\( 5^{26}\cdot 41^{8} \)	20T230	Trivial (GRH)
20.4.27460473324661212646782041015625.1	x^20 - 5x^18 + 12x^16 - 266x^14 + 1966x^12 - 5979x^10 + 8784x^8 - 7488x^6 + 23949x^4 - 78570x^2 + 77841	\( 3^{20}\cdot 5^{10}\cdot 73^{8} \)	20T230	Trivial (GRH)
20.12.73828490224822538451051656249344.1	x^20 + 8x^18 - 20x^17 - 23x^16 - 16x^15 - 104x^14 + 296x^13 - 341x^12 + 112x^11 + 2576x^10 - 1060x^9 - 1329x^8 + 4128x^7 - 328x^6 - 4768x^5 - 736x^4 + 1280x^3 + 184x^2 - 112x - 4	\( 2^{42}\cdot 11^{8}\cdot 23^{8} \)	20T230	Trivial (GRH)
20.12.211886368245842690175787353515625.1	x^20 - 21x^18 + 68x^16 + 42x^14 - 44x^12 - 117x^10 - 44x^8 + 42x^6 + 68x^4 - 21x^2 + 1	\( 3^{16}\cdot 5^{14}\cdot 73^{8} \)	20T230	Trivial (GRH)
20.0.382427325615169748862424594776064.1	x^20 + 140x^16 + 2560x^12 + 9316x^8 + 8944x^4 + 64	\( 2^{26}\cdot 11^{8}\cdot 113^{8} \)	20T230	$[2, 70]$ (GRH)
20.0.1378292916885385650670001824763904.1	x^20 + 14x^18 + 135x^16 + 660x^14 + 2317x^12 + 4630x^10 + 6589x^8 + 4340x^6 + 2019x^4 + 46x^2 + 1	\( 2^{12}\cdot 3^{10}\cdot 11^{8}\cdot 113^{8} \)	20T230	$[6, 18]$ (GRH)
20.20.6234865940162794507742264996921344.1	x^20 - 10x^19 + 5x^18 + 240x^17 - 616x^16 - 1804x^15 + 7652x^14 + 3506x^13 - 39328x^12 + 12394x^11 + 102554x^10 - 63382x^9 - 149398x^8 + 102876x^7 + 127665x^6 - 73218x^5 - 62725x^4 + 19586x^3 + 14486x^2 - 484x - 673	\( 2^{34}\cdot 881^{8} \)	20T230	Trivial (GRH)
20.20.14064174967249198299016802500000000.1	x^20 - x^19 - 48x^18 + 42x^17 + 825x^16 - 379x^15 - 7051x^14 - 278x^13 + 31929x^12 + 16492x^11 - 71110x^10 - 67360x^9 + 58815x^8 + 89029x^7 - 4166x^6 - 45082x^5 - 13867x^4 + 6319x^3 + 4107x^2 + 678x + 29	\( 2^{8}\cdot 5^{10}\cdot 17^{8}\cdot 73^{8} \)	20T230	Trivial (GRH)