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 26 matches)

Label	Polynomial	Discriminant	Galois group	Class group
22.14.1848815246537641483557884967899322509765625.1	x^22 - x^21 - 17x^20 + 165x^19 - 465x^18 - 2217x^17 + 13152x^16 - 18246x^15 - 88965x^14 + 460975x^13 + 80417x^12 - 3206822x^11 + 1243761x^10 + 11369550x^9 - 5283585x^8 - 23052156x^7 + 8795046x^6 + 26559657x^5 - 6629445x^4 - 15684075x^3 + 2137059x^2 + 3574746x - 256383	\( 3^{20}\cdot 5^{20}\cdot 11^{18} \)	22T33	Trivial (GRH)
22.6.1848815246537641483557884967899322509765625.1	x^22 - 7x^21 + x^20 + 75x^19 - 315x^18 + 1521x^17 - 7332x^16 + 27996x^15 - 55200x^14 + 80260x^13 - 143239x^12 + 243448x^11 - 301974x^10 + 245025x^9 - 351450x^8 + 319011x^7 + 83028x^6 + 214731x^5 + 190575x^4 - 577170x^3 - 104544x^2 - 362637x + 178596	\( 3^{20}\cdot 5^{20}\cdot 11^{18} \)	22T33	Trivial (GRH)
22.14.7361918740189183054193252042326802122242321.1	x^22 - 66x^19 - 231x^18 + 1485x^16 + 10494x^15 + 17820x^14 - 37125x^13 - 139689x^12 - 1242x^11 + 3267x^10 - 2339172x^9 - 3977424x^8 + 6373620x^7 + 23097690x^6 + 23541111x^5 + 9752886x^4 + 812592x^3 - 477576x^2 - 109593x - 6399	\( 3^{20}\cdot 11^{32} \)	22T33	Trivial (GRH)
22.14.7361918740189183054193252042326802122242321.2	x^22 - 44x^20 - 66x^19 + 649x^18 + 2112x^17 - 1815x^16 - 20064x^15 - 31317x^14 + 33396x^13 + 179157x^12 + 228075x^11 + 12771x^10 - 323499x^9 - 376893x^8 + 26664x^7 + 352836x^6 + 134178x^5 - 129811x^4 - 61842x^3 + 21263x^2 + 7128x - 1552	\( 3^{20}\cdot 11^{32} \)	22T33	Trivial (GRH)
22.10.15646172003756569249283257910156250000000000.1	x^22 + x^20 - 170x^18 - 555x^16 + 6885x^14 + 30117x^12 - 60543x^10 - 412455x^8 - 405180x^6 + 147845x^4 + 98801x^2 - 9604	\( 2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T33	Trivial (GRH)
22.14.15646172003756569249283257910156250000000000.1	x^22 - 24x^20 + 90x^18 + 1170x^16 - 4725x^14 - 26028x^12 + 42282x^10 + 208170x^8 + 12150x^6 - 201690x^4 + 94041x^2 - 11664	\( 2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T33	Trivial (GRH)
22.18.15646172003756569249283257910156250000000000.1	x^22 - 36x^20 + 45x^18 + 7290x^16 - 90045x^14 + 482778x^12 - 1333233x^10 + 1837620x^8 - 984150x^6 - 46170x^4 + 102141x^2 - 1296	\( 2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T33	Trivial (GRH)
22.6.15646172003756569249283257910156250000000000.1	x^22 + 46x^20 + 685x^18 + 2205x^16 - 31830x^14 - 268983x^12 - 577818x^10 + 110985x^8 + 831555x^6 + 80420x^4 - 203959x^2 - 20164	\( 2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T33	Trivial (GRH)
22.10.15646172003756569249283257910156250000000000.2	x^22 - 5x^20 - 185x^18 + 1380x^16 + 1395x^14 - 16575x^12 + 75x^10 + 38475x^8 + 6600x^6 - 2875x^4 - 625x^2 - 25	\( 2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T33	Trivial (GRH)
22.6.15646172003756569249283257910156250000000000.2	x^22 + 34x^20 - 740x^18 - 8385x^16 - 18285x^14 + 22008x^12 + 76707x^10 + 62055x^8 + 18855x^6 + 1310x^4 - 199x^2 - 1	\( 2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T33	Trivial (GRH)
22.10.15646172003756569249283257910156250000000000.3	x^22 - 14x^20 - 170x^18 + 2265x^16 + 8340x^14 - 102513x^12 - 94713x^10 + 975090x^8 + 900525x^6 - 1409725x^4 - 537079x^2 - 9604	\( 2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T33	Trivial (GRH)
22.10.15646172003756569249283257910156250000000000.4	x^22 - x^21 - 15x^20 + 35x^19 + 25x^18 - 702x^17 + 3432x^16 + 15225x^15 - 61200x^14 - 188900x^13 + 464426x^12 + 1329204x^11 - 2392015x^10 - 5062310x^9 + 10204785x^8 + 9013785x^7 - 33166500x^6 + 4116735x^5 + 69240535x^4 - 86769655x^3 + 33467790x^2 + 2877980x - 3125465	\( 2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T33	Trivial (GRH)
22.10.15646172003756569249283257910156250000000000.5	x^22 + 9x^20 - 195x^18 - 1530x^16 + 2475x^14 + 16803x^12 + 5427x^10 - 27945x^8 - 9450x^6 + 14175x^4 - 729x^2 - 81	\( 2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T33	Trivial (GRH)
22.10.15646172003756569249283257910156250000000000.6	x^22 + 46x^20 + 190x^18 - 6375x^16 - 10215x^14 + 216612x^12 - 238743x^10 - 440280x^8 + 83280x^6 + 151040x^4 + 14336x^2 - 1024	\( 2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T33	Trivial (GRH)
22.10.15646172003756569249283257910156250000000000.7	x^22 + x^20 - 335x^18 - 1770x^16 + 13635x^14 + 79467x^12 - 119778x^10 - 838335x^8 - 798495x^6 + 220985x^4 + 319841x^2 - 40804	\( 2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T33	Trivial (GRH)
22.10.15646172003756569249283257910156250000000000.8	x^22 - 9x^20 - 555x^18 + 4740x^16 + 27645x^14 - 132543x^12 - 456858x^10 + 655515x^8 + 1193310x^6 - 1246410x^4 - 98919x^2 - 1764	\( 2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T33	Trivial (GRH)
22.10.15646172003756569249283257910156250000000000.9	x^22 + 15x^20 - 540x^18 - 3075x^16 + 21600x^14 + 168705x^12 + 247050x^10 - 375750x^8 - 988650x^6 - 338175x^4 + 19800x^2 - 225	\( 2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T33	Trivial (GRH)
22.10.15646172003756569249283257910156250000000000.10	x^22 + 6x^20 - 1065x^18 - 300x^16 + 41040x^14 + 53082x^12 - 78633x^10 - 70200x^8 + 37485x^6 + 9360x^4 - 2259x^2 - 9	\( 2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T33	Trivial (GRH)
22.10.62584688015026276997133031640625000000000000.1	x^22 - 24x^20 - 75x^18 + 4920x^16 - 19785x^14 - 180108x^12 + 895572x^10 + 2214000x^8 - 8958555x^6 - 6484860x^4 - 1038609x^2 - 2304	\( 2^{12}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T33	Trivial (GRH)
22.14.62584688015026276997133031640625000000000000.1	x^22 - 29x^20 + 250x^18 - 45x^16 - 7890x^14 + 18072x^12 + 68622x^10 - 146790x^8 - 167430x^6 + 39395x^4 + 4751x^2 - 4	\( 2^{12}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T33	Trivial (GRH)
22.18.62584688015026276997133031640625000000000000.1	x^22 - 29x^20 - 35x^18 + 7965x^16 - 79140x^14 + 140187x^12 + 1374597x^10 - 6587220x^8 + 8430720x^6 - 2011840x^4 + 141056x^2 - 1024	\( 2^{12}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T33	Trivial (GRH)
22.6.62584688015026276997133031640625000000000000.1	x^22 - 39x^20 - 75x^18 + 3420x^16 + 15615x^14 + 7587x^12 - 64638x^10 - 131625x^8 - 100305x^6 - 35235x^4 - 5589x^2 - 324	\( 2^{12}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T33	Trivial (GRH)
22.14.62584688015026276997133031640625000000000000.2	x^22 - 11x^20 - 410x^18 + 9030x^16 - 66270x^14 + 194118x^12 - 95253x^10 - 446805x^8 + 374250x^6 + 219080x^4 - 120829x^2 - 42436	\( 2^{12}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T33	Trivial (GRH)
22.2.1893186812454544879163274207128906250000000000.1	x^22 - 5x^21 - 29x^20 + 360x^19 - 990x^18 + 1875x^17 - 5670x^16 + 22785x^15 - 97815x^14 + 308825x^13 - 409888x^12 - 264895x^11 + 1426017x^10 - 79980x^9 - 3413490x^8 + 3818490x^7 + 4882185x^6 + 58738635x^5 + 99523260x^4 - 161912160x^3 - 446673024x^2 - 327824640x - 82658304	\( 2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{18} \)	22T33	$[4]$ (GRH)
22.2.16021680131846726911266056100000000000000000000.1	x^22 + 46x^20 + 820x^18 + 7185x^16 + 30045x^14 + 18222x^12 - 381873x^10 - 1771215x^8 - 3659430x^6 - 3811900x^4 - 1759504x^2 - 218089	\( 2^{20}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T33	$[2]$ (GRH)
22.22.1938623295953453956263192788100000000000000000000.1	x^22 - 95x^20 + 3775x^18 - 82560x^16 + 1100625x^14 - 9320475x^12 + 50405850x^10 - 169469025x^8 + 330598125x^6 - 324638875x^4 + 121062425x^2 - 12390400	\( 2^{20}\cdot 3^{20}\cdot 5^{20}\cdot 11^{18} \)	22T33	Trivial (GRH)