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 20 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.4519908793361499099136.1	x^20 - 8x^16 + 15x^14 + 30x^12 - 6x^10 + 10x^8 + 20x^6 - 11x^4 + x^2 + 1	\( 2^{12}\cdot 32411^{4} \)	20T567	Trivial
20.4.61453477994727278116864.1	x^20 - 7x^18 + 19x^16 - 37x^14 + 69x^12 - 98x^10 + 94x^8 - 71x^6 + 46x^4 - 18x^2 + 1	\( 2^{26}\cdot 5501^{4} \)	20T567	Trivial (GRH)
20.4.66045000696445844586496.1	x^20 - 4x^18 + 2x^16 + 4x^14 + 10x^12 - 21x^10 - 3x^8 + 28x^4 - 20x^2 + 4	\( 2^{24}\cdot 89^{8} \)	20T567	Trivial (GRH)
20.4.395060246754808891597056.1	x^20 + 7x^18 + 17x^16 + 12x^14 - 20x^12 - 43x^10 - 20x^8 + 12x^6 + 17x^4 + 7x^2 + 1	\( 2^{8}\cdot 3^{4}\cdot 66067^{4} \)	20T567	Trivial (GRH)
20.0.444622235903180809437184.2	x^20 - 2x^19 + 2x^18 - 2x^17 + 12x^16 - 38x^15 + 70x^14 - 78x^13 + 83x^12 - 80x^11 + 136x^10 - 226x^9 + 248x^8 - 258x^7 + 176x^6 - 180x^5 + 208x^4 - 208x^3 + 200x^2 - 92x + 47	\( 2^{30}\cdot 13^{4}\cdot 347^{4} \)	20T567	Trivial (GRH)
20.4.1860495326773308902342656.1	x^20 + x^18 - x^14 - x^12 - x^10 - x^8 - x^6 + x^2 + 1	\( 2^{20}\cdot 36497^{4} \)	20T567	Trivial (GRH)
20.4.1860495326773308902342656.2	x^20 - 4x^18 + 7x^16 - x^14 - 3x^12 - 2x^10 + 25x^8 - 19x^6 + 9x^4 - 5x^2 + 1	\( 2^{20}\cdot 36497^{4} \)	20T567	Trivial (GRH)
20.4.1860495326773308902342656.3	x^20 - 4x^18 + 7x^16 + 10x^14 - 11x^12 + 19x^10 + 31x^8 - 30x^6 + 34x^4 - 11x^2 + 1	\( 2^{20}\cdot 36497^{4} \)	20T567	Trivial (GRH)
20.4.2320349626175642005405696.1	x^20 - x^12 - x^10 - x^8 + 1	\( 2^{20}\cdot 38569^{4} \)	20T567	Trivial (GRH)
20.4.2438032999196926988517376.1	x^20 - 2x^18 - 8x^16 + 11x^12 - 8x^10 + 6x^8 - 4x^6 - 14x^4 - 8x^2 + 1	\( 2^{20}\cdot 17^{4}\cdot 2297^{4} \)	20T567	Trivial (GRH)
20.0.222578998094306639295545344.1	x^20 - 2x^19 - 6x^18 + 9x^17 + 6x^16 + 8x^15 + 56x^14 - 113x^13 - 146x^12 + 388x^11 + 88x^10 - 671x^9 + 101x^8 + 722x^7 + 2x^6 - 556x^5 - 167x^4 + 296x^3 + 122x^2 - 33x + 7	\( 2^{18}\cdot 170701^{4} \)	20T567	Trivial (GRH)
20.0.369301640628035174640123904.1	x^20 - 6x^19 + 12x^18 + 2x^17 - 42x^16 + 22x^15 + 154x^14 - 250x^13 + 9x^12 + 142x^11 - 190x^10 - 110x^9 + 1836x^8 - 1308x^7 - 994x^6 + 540x^5 + 1280x^4 - 1520x^3 + 744x^2 - 190x + 25	\( 2^{30}\cdot 61^{4}\cdot 397^{4} \)	20T567	Trivial (GRH)
20.12.626072689707529169661853696.1	x^20 - 9x^18 + 19x^16 + 29x^14 - 101x^12 - 52x^10 + 254x^8 - 165x^6 + 31x^4 - 7x^2 + 1	\( 2^{20}\cdot 7^{4}\cdot 137^{4}\cdot 163^{4} \)	20T567	Trivial (GRH)
20.12.743440706348303704240685056.1	x^20 - 5x^19 + 55x^17 - 145x^16 + 56x^15 + 374x^14 - 646x^13 - 88x^12 + 1224x^11 - 568x^10 - 1182x^9 + 657x^8 + 701x^7 - 242x^6 - 211x^5 + 32x^4 + 13x^3 - 20x^2 - 9x - 1	\( 2^{24}\cdot 83^{4}\cdot 983^{4} \)	20T567	Trivial (GRH)
20.12.743440706348303704240685056.2	x^20 - 5x^19 + 41x^17 - 67x^16 - 72x^15 + 292x^14 - 136x^13 - 435x^12 + 527x^11 + 318x^10 - 801x^9 + 11x^8 + 624x^7 - 250x^6 - 174x^5 + 171x^4 - 21x^3 - 30x^2 + 11x - 1	\( 2^{24}\cdot 83^{4}\cdot 983^{4} \)	20T567	Trivial (GRH)
20.8.2110222950774242892296749056.1	x^20 - 4x^18 + x^16 + 32x^14 - 165x^12 + 427x^10 - 601x^8 + 474x^6 - 198x^4 + 31x^2 + 1	\( 2^{20}\cdot 3^{4}\cdot 17^{4}\cdot 4153^{4} \)	20T567	Trivial (GRH)
20.8.2110222950774242892296749056.2	x^20 + 3x^18 - 22x^16 + 59x^14 - 93x^12 + 59x^10 + 67x^8 - 133x^6 + 72x^4 - 15x^2 + 1	\( 2^{20}\cdot 3^{4}\cdot 17^{4}\cdot 4153^{4} \)	20T567	Trivial (GRH)
20.12.12698855679630747098335412224.1	x^20 - 12x^18 - 12x^17 + 3x^16 + 180x^15 + 170x^14 - 766x^13 - 101x^12 + 1814x^11 - 1144x^10 - 2410x^9 + 2259x^8 + 1314x^7 - 1538x^6 - 288x^5 + 458x^4 + 58x^3 - 44x^2 - 4x + 1	\( 2^{30}\cdot 13^{8}\cdot 347^{4} \)	20T567	Trivial (GRH)
20.20.694161316497577089027749764022640050176.1	x^20 - x^19 - 154x^18 + 75x^17 + 10051x^16 - 2x^15 - 361954x^14 - 157978x^13 + 7832688x^12 + 6292522x^11 - 103951264x^10 - 112550514x^9 + 829070309x^8 + 1036532987x^7 - 3753286546x^6 - 4728386579x^5 + 8751855594x^4 + 8947530117x^3 - 8595162260x^2 - 2950847201x + 2032171457	\( 2^{24}\cdot 83^{4}\cdot 983^{8} \)	20T567	Trivial (GRH)
20.20.694161316497577089027749764022640050176.2	x^20 - 9x^19 - 129x^18 + 1144x^17 + 6145x^16 - 55673x^15 - 136555x^14 + 1355486x^13 + 1391729x^12 - 18053417x^11 - 3132925x^10 + 134002170x^9 - 55598389x^8 - 532500985x^7 + 464927625x^6 + 983198086x^5 - 1305212247x^4 - 458891619x^3 + 1222599377x^2 - 387824762x - 46005884	\( 2^{24}\cdot 83^{4}\cdot 983^{8} \)	20T567	Trivial (GRH)