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 8 matches)

Label	Polynomial	Discriminant	Galois group	Class group
22.0.5354138939812686410506736146606791.1	x^22 + 22x^20 + 209x^18 + 1122x^16 + 3740x^14 + 8008x^12 - x^11 + 11011x^10 - 11x^9 + 9438x^8 - 44x^7 + 4719x^6 - 77x^5 + 1210x^4 - 55x^3 + 121x^2 - 11x + 1	\( -\,3^{11}\cdot 11^{22}\cdot 13^{5} \)	22T20	Trivial (GRH)
22.0.8866351725365604006246875731591168.1	x^22 - 22x^20 + 209x^18 - 1122x^16 + 3740x^14 - 8008x^12 - 6x^11 + 11011x^10 + 66x^9 - 9438x^8 - 264x^7 + 4719x^6 + 462x^5 - 1210x^4 - 330x^3 + 121x^2 + 66x + 10	\( -\,2^{32}\cdot 11^{18}\cdot 13^{5} \)	22T20	Trivial (GRH)
22.12.640136435131832537454172869677734375.1	x^22 - 22x^20 + 209x^18 - 1122x^16 + 3740x^14 - 8008x^12 - 3x^11 + 11011x^10 + 33x^9 - 9438x^8 - 132x^7 + 4719x^6 + 231x^5 - 1210x^4 - 165x^3 + 121x^2 + 33x + 1	\( -\,5^{11}\cdot 11^{27} \)	22T20	Trivial (GRH)
22.12.9841858708691628205709619862255859375.1	x^22 - 22x^20 + 209x^18 - 1122x^16 + 3740x^14 - 8008x^12 - 5x^11 + 11011x^10 + 55x^9 - 9438x^8 - 220x^7 + 4719x^6 + 385x^5 - 1210x^4 - 275x^3 + 121x^2 + 55x + 5	\( -\,5^{11}\cdot 11^{22}\cdot 19^{5} \)	22T20	Trivial (GRH)
22.2.81526558675934032193346333780712890625.1	x^22 + 22x^20 + 209x^18 + 1122x^16 + 3740x^14 + 8008x^12 - x^11 + 11011x^10 - 11x^9 + 9438x^8 - 44x^7 + 4719x^6 - 77x^5 + 1210x^4 - 55x^3 + 121x^2 - 11x - 1	\( 5^{11}\cdot 11^{22}\cdot 29^{5} \)	22T20	Trivial (GRH)
22.2.81011787339596536319747972164688577298432.1	x^22 + 22x^20 + 209x^18 + 1122x^16 + 3740x^14 + 8008x^12 - 2x^11 + 11011x^10 - 22x^9 + 9438x^8 - 88x^7 + 4719x^6 - 154x^5 + 1210x^4 - 110x^3 + 121x^2 - 22x - 1	\( 2^{33}\cdot 11^{22}\cdot 41^{5} \)	22T20	Trivial (GRH)
22.22.984311297528998947620977146874832596749227182758485402624.1	x^22 - 44x^20 + 836x^18 - 8976x^16 + 59840x^14 - 256256x^12 - 9x^11 + 704704x^10 + 198x^9 - 1208064x^8 - 1584x^7 + 1208064x^6 + 5544x^5 - 619520x^4 - 7920x^3 + 123904x^2 + 3168x + 16	\( 2^{10}\cdot 11^{22}\cdot 17^{11}\cdot 3217^{5} \)	22T20	Trivial (GRH)
22.22.881393093933942014560136225812507608113495413655720744560124493824.1	x^22 - 44x^20 + 836x^18 - 8976x^16 + 59840x^14 - 256256x^12 - 8x^11 + 704704x^10 + 176x^9 - 1208064x^8 - 1408x^7 + 1208064x^6 + 4928x^5 - 619520x^4 - 7040x^3 + 123904x^2 + 2816x + 8	\( 2^{43}\cdot 7^{5}\cdot 11^{22}\cdot 137^{5}\cdot 1087^{5} \)	22T20	Trivial (GRH)