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
22.6.1447402975463751668017578125.1	x^22 - 2x^21 - x^20 + 18x^19 - 17x^18 - 44x^17 + 110x^16 - 3x^15 - 254x^14 + 59x^13 + 240x^12 - 102x^11 - 552x^10 - 230x^9 + 307x^8 + 320x^7 - 3x^6 - 154x^5 - 62x^4 + 18x^3 + 19x^2 + 2x - 1	\( 5^{11}\cdot 7^{4}\cdot 83^{4}\cdot 127^{4} \)	22T46	Trivial (GRH)
22.0.15257581934366008831157764375.1	x^22 - 4x^21 + 18x^20 - 48x^19 + 125x^18 - 249x^17 + 478x^16 - 766x^15 + 1216x^14 - 1618x^13 + 2242x^12 - 2454x^11 + 2995x^10 - 2616x^9 + 2692x^8 - 1937x^7 + 1684x^6 - 1102x^5 + 757x^4 - 253x^3 + 163x^2 + 2x + 1	\( -\,5^{4}\cdot 7^{11}\cdot 83^{4}\cdot 127^{4} \)	22T46	Trivial (GRH)
22.0.45853693993707071407334096896.1	x^22 + 2x^20 + 3x^18 - 2x^16 - 7x^14 - 5x^12 + 4x^10 + 11x^8 - 2x^6 - 6x^4 + x^2 + 1	\( -\,2^{28}\cdot 11^{4}\cdot 19^{4}\cdot 547^{4} \)	22T46	Trivial (GRH)
22.6.32352556342113252227121422532608.1	x^22 - 10x^20 + 20x^18 + 38x^16 + 30x^14 - 676x^12 + 645x^10 + 720x^8 - 79x^6 - 2438x^4 + 2236x^2 - 648	\( 2^{43}\cdot 43793^{4} \)	22T46	Trivial (GRH)
22.0.11914309055197948986020479547159042393930184375104869730372026368.1	x^22 - 3x^21 + 45x^20 - 12x^19 + 1263x^18 - 891x^17 + 11013x^16 + 12294x^15 + 42993x^14 + 18555x^13 + 42921x^12 + 71280x^11 + 36558x^10 + 25902x^9 + 32238x^8 + 31986x^7 + 15876x^6 + 6156x^5 + 13644x^4 + 11880x^3 + 972x^2 + 1944x + 2916	\( -\,2^{24}\cdot 3^{29}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16} \)	22T46	Trivial (GRH)
22.0.1016687706043558313473747588024238284282042400008948883658412916736.1	x^22 + 81x^20 + 2082x^18 + 19218x^16 + 53361x^14 + 19161x^12 - 39240x^10 - 1188x^8 + 6588x^6 - 11628x^4 + 648x^2 + 2916	\( -\,2^{32}\cdot 3^{28}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16} \)	22T46	Trivial (GRH)
22.14.3050063118130674940421242764072714852846127200026846650975238750208.1	x^22 - 6x^21 - 96x^20 + 516x^19 + 3315x^18 - 15678x^17 - 58926x^16 + 239076x^15 + 605475x^14 - 2137974x^13 - 3792132x^12 + 12206088x^11 + 14763681x^10 - 46019430x^9 - 34917642x^8 + 112918896x^7 + 44592120x^6 - 169280496x^5 - 19547856x^4 + 127652544x^3 + 2781648x^2 - 33869664x - 3859488	\( 2^{32}\cdot 3^{29}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16} \)	22T46	Trivial (GRH)
22.14.8328705687908829703976940241094560024838491340873309254929718613901312.1	x^22 - 6x^21 - 85x^20 + 456x^19 + 2554x^18 - 11784x^17 - 38526x^16 + 144516x^15 + 323265x^14 - 990414x^13 - 1608525x^12 + 4228056x^11 + 4901112x^10 - 11919636x^9 - 9151008x^8 + 22004508x^7 + 9743124x^6 - 25064112x^5 - 3630980x^4 + 14132688x^3 + 1997240x^2 - 2436432x - 530108	\( 2^{45}\cdot 3^{28}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16} \)	22T46	Trivial (GRH)