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 7 matches)

Label	Polynomial	Discriminant	Galois group	Class group
22.2.716463968651672990739595264.1	x^22 + 4x^20 + x^18 - 20x^16 - 7x^14 + 93x^12 + 46x^10 - 121x^8 - 80x^6 - 34x^4 - 9x^2 - 1	\( 2^{22}\cdot 11^{4}\cdot 19^{4}\cdot 547^{4} \)	22T49	Trivial (GRH)
22.2.2865855874606691962958381056.1	x^22 - 5x^20 + 9x^18 - 6x^16 - 12x^14 + 37x^12 - 45x^10 + 75x^8 - 54x^6 - 17x^4 + 44x^2 - 16	\( 2^{24}\cdot 11^{4}\cdot 19^{4}\cdot 547^{4} \)	22T49	Trivial (GRH)
22.6.18415764278243178646713405625.1	x^22 - 7x^21 + 16x^20 - 3x^19 - 51x^18 + 101x^17 - 62x^16 - 50x^15 + 49x^14 + 124x^13 - 271x^12 + 166x^11 + 113x^10 - 102x^9 - 51x^8 - 34x^7 + 128x^6 - 78x^5 - 37x^4 + 36x^3 + 14x^2 - 8x + 1	\( 5^{4}\cdot 7^{4}\cdot 83^{4}\cdot 127^{4}\cdot 997^{2} \)	22T49	Trivial (GRH)
22.6.45853693993707071407334096896.1	x^22 - 12x^20 + 59x^18 - 154x^16 + 229x^14 - 193x^12 + 96x^10 - 57x^8 + 54x^6 - 24x^4 + x^2 - 1	\( 2^{28}\cdot 11^{4}\cdot 19^{4}\cdot 547^{4} \)	22T49	Trivial (GRH)
22.6.63542981627722394592109224251514892767627650000559305228650807296.1	x^22 + 111x^20 + 4230x^18 + 329346x^16 - 2553795x^14 - 1664102961x^12 - 50639346936x^10 + 35043156036x^8 + 17771158853280x^6 + 85652947987596x^4 - 1530431923623624x^2 - 6261750295213284	\( 2^{28}\cdot 3^{28}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16} \)	22T49	Trivial (GRH)
22.10.254171926510889578368436897006059571070510600002237220914603229184.1	x^22 - 4x^21 - 92x^20 + 978x^19 - 23031x^18 + 208542x^17 + 3327324x^16 - 36397800x^15 - 19963545x^14 - 406653528x^13 - 16539946488x^12 + 256034067942x^11 + 682357346031x^10 - 13494358927986x^9 + 9822827363220x^8 + 261815058820176x^7 - 813912422758992x^6 - 647257611403968x^5 + 8751031478070272x^4 - 24165278101734848x^3 + 30990808995877088x^2 - 13115399746724928x - 2634468582334464	\( 2^{30}\cdot 3^{28}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16} \)	22T49	Trivial (GRH)
22.14.1275054393023762909963506622668395857607199180560057153446822299847849103680658423408180099481492815135308821561344.1	x^22 - 242454x^20 - 66254755944x^18 + 9988149125214624x^16 + 2412251307077297217168x^14 - 97126283753436220637656848x^12 - 36043439335840553783024429840880x^10 - 968324930877205693808500678923025440x^8 + 411693823788000055227773052463075223008512x^6 - 14674638475171337576102371060253129696887988224x^4 + 164949721485379801300637463025582558350584505753600x^2 - 571411117069770362003780702945732790998630818613760000	\( 2^{44}\cdot 3^{28}\cdot 7^{4}\cdot 13^{10}\cdot 23^{4}\cdot 137^{16}\cdot 2161^{10} \)	22T49	n/a