Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 27 matches)

Label	Polynomial	Discriminant	Galois group	Class group
22.16.87192729322616328324934343477207.1	x^22 - 8x^21 + 18x^20 + 40x^19 - 297x^18 + 513x^17 + 450x^16 - 3255x^15 + 4443x^14 + 2314x^13 - 13613x^12 + 11338x^11 + 9530x^10 - 21040x^9 + 5227x^8 + 11912x^7 - 8172x^6 - 1577x^5 + 2749x^4 - 372x^3 - 267x^2 + 66x + 1	\( -\,23^{21}\cdot 47^{2} \)	22T28	Trivial (GRH)
22.16.178176446876650757881387571453423.1	x^22 - 11x^21 + 51x^20 - 125x^19 + 128x^18 + 216x^17 - 1077x^16 + 1782x^15 - 804x^14 - 2284x^13 + 4953x^12 - 3588x^11 - 1546x^10 + 5279x^9 - 3904x^8 - 185x^7 + 2226x^6 - 1217x^5 - 74x^4 + 213x^3 - 24x^2 - 10x + 1	\( -\,23^{20}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.16.178176446876650757881387571453423.2	x^22 - 4x^21 - 9x^20 + 52x^19 + x^18 - 163x^17 - 117x^16 + 266x^15 + 1582x^14 - 1236x^13 - 6092x^12 + 5618x^11 + 10042x^10 - 10618x^9 - 7547x^8 + 8528x^7 + 2464x^6 - 2769x^5 - 255x^4 + 289x^3 + 24x^2 - 9x - 1	\( -\,23^{20}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.16.178176446876650757881387571453423.3	x^22 - 5x^21 - 11x^20 + 93x^19 - 25x^18 - 607x^17 + 616x^16 + 2224x^15 - 4041x^14 - 2772x^13 + 11203x^12 - 4782x^11 - 11283x^10 + 14512x^9 - 1218x^8 - 9343x^7 + 6225x^6 + 273x^5 - 1230x^4 + 85x^3 + 86x^2 + x - 1	\( -\,23^{20}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.16.289690752824370116310308034941759.1	x^22 - 11x^21 + 43x^20 - 45x^19 - 152x^18 + 456x^17 - 114x^16 - 1026x^15 + 1114x^14 + 790x^13 - 1814x^12 + 120x^11 + 1304x^10 - 464x^9 - 493x^8 + 217x^7 + 170x^6 - 46x^5 - 77x^4 + 9x^3 + 18x^2 - 1	\( -\,809\cdot 4759\cdot 8674315276967^{2} \)	22T53	Trivial (GRH)
22.16.1288033148279983900699565800554496.1	x^22 - 14x^20 + 84x^18 - 284x^16 + 596x^14 - 794x^12 + 632x^10 - 220x^8 - 53x^6 + 65x^4 - 15x^2 + 1	\( -\,2^{22}\cdot 17524013040643^{2} \)	22T53	Trivial (GRH)
22.16.12701184200335173359101913935642624.1	x^22 - 15x^20 + 91x^18 - 278x^16 + 410x^14 - 123x^12 - 404x^10 + 417x^8 - 19x^6 - 77x^4 - 3x^2 + 1	\( -\,2^{22}\cdot 55029067682009^{2} \)	22T53	Trivial (GRH)
22.16.13844017509319141075535476685799424.1	x^22 - 11x^20 + 43x^18 - 52x^16 - 96x^14 + 332x^12 - 229x^10 - 230x^8 + 408x^6 - 186x^4 + 20x^2 + 1	\( -\,2^{22}\cdot 233^{2}\cdot 246572816873^{2} \)	22T53	Trivial (GRH)
22.16.56501459388151144478039723653407440896.1	x^22 - 17x^20 + 76x^18 + 4x^16 - 654x^14 + 958x^12 + 990x^10 - 2740x^8 + 855x^6 + 1065x^4 - 556x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.16.56501459388151144478039723653407440896.2	x^22 - 17x^20 + 74x^18 + 62x^16 - 919x^14 + 1316x^12 + 196x^10 - 1389x^8 + 887x^6 - 194x^4 + 7x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.16.56501459388151144478039723653407440896.3	x^22 - 17x^20 + 56x^18 + 103x^16 - 578x^14 + 31x^12 + 1647x^10 - 963x^8 - 1208x^6 + 1034x^4 - 112x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.16.56501459388151144478039723653407440896.4	x^22 - 14x^20 + 39x^18 + 167x^16 - 805x^14 - 22x^12 + 3282x^10 - 2173x^8 - 3246x^6 + 3447x^4 - 852x^2 + 25	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.16.4849461357032540054012505516531188236288.1	x^22 - 4x^21 - 14x^20 + 64x^19 + 85x^18 - 434x^17 - 310x^16 + 1626x^15 + 804x^14 - 3674x^13 - 1589x^12 + 5118x^11 + 2305x^10 - 4288x^9 - 2238x^8 + 1974x^7 + 1299x^6 - 372x^5 - 387x^4 - 22x^3 + 42x^2 + 12x + 1	\( -\,2^{33}\cdot 31\cdot 2287\cdot 372719\cdot 21364574876217246673 \)	22T57	Trivial (GRH)
22.16.43207326253951723658496833604222208442368.1	x^22 - 33x^20 - 66x^19 + 231x^18 + 1144x^17 + 1529x^16 - 4928x^15 - 22154x^14 - 1936x^13 + 88242x^12 - 17636x^11 - 365706x^10 + 218944x^9 + 1743610x^8 + 775632x^7 - 2869999x^6 - 3158496x^5 + 575311x^4 + 2206182x^3 + 942403x^2 + 77528x + 1789	\( -\,2^{28}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.16.47139885424515679279908496898278071205888.1	x^22 - 4x^21 - 16x^20 + 70x^19 + 116x^18 - 516x^17 - 533x^16 + 2066x^15 + 1752x^14 - 4808x^13 - 4036x^12 + 6422x^11 + 5961x^10 - 4476x^9 - 5101x^8 + 1158x^7 + 2240x^6 + 184x^5 - 405x^4 - 106x^3 + 19x^2 + 10x + 1	\( -\,2^{33}\cdot 7^{3}\cdot 31\cdot 89\cdot 1033\cdot 5613742962947696588359 \)	22T57	Trivial (GRH)
22.16.67897226970495565749066452806634898980864.1	x^22 - 55x^20 - 22x^19 + 957x^18 + 198x^17 - 7293x^16 + 1914x^15 + 24794x^14 - 25828x^13 - 28380x^12 + 85584x^11 - 13596x^10 - 105028x^9 + 73260x^8 + 53592x^7 - 84535x^6 - 11374x^5 + 43571x^4 + 264x^3 - 10241x^2 + 572x + 1115	\( -\,2^{28}\cdot 7^{10}\cdot 11^{23} \)	22T37	Trivial (GRH)
22.16.98759602866175368362278476809650762153984.1	x^22 - 44x^20 + 814x^18 - 8426x^16 - 176x^15 + 54912x^14 + 4752x^13 - 239844x^12 - 52324x^11 + 715836x^10 + 302192x^9 - 1393920x^8 - 959640x^7 + 1505240x^6 + 1551528x^5 - 514272x^4 - 984368x^3 - 174856x^2 + 115280x + 32136	\( -\,2^{32}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.16.168074113321603771232534997081756591796875.1	x^22 - 7x^21 - 35x^20 + 270x^19 + 645x^18 - 4209x^17 - 9252x^16 + 31050x^15 + 96990x^14 - 65105x^13 - 614131x^12 - 561998x^11 + 1988085x^10 + 4067340x^9 - 2442075x^8 - 9864030x^7 - 410850x^6 + 10078335x^5 + 2192040x^4 - 3755745x^3 - 571725x^2 + 123390x - 4545	\( -\,3^{20}\cdot 5^{20}\cdot 11^{17} \)	22T36	Trivial (GRH)
22.16.172829305015806894633987334416888833769472.1	x^22 - 33x^20 + 429x^18 - 176x^17 - 4081x^16 + 5852x^15 + 47674x^14 - 68332x^13 - 459998x^12 + 333988x^11 + 2587090x^10 - 470580x^9 - 7832726x^8 - 1357004x^7 + 11956197x^6 + 4761548x^5 - 7915633x^4 - 4092132x^3 + 1244177x^2 + 607860x + 45207	\( -\,2^{30}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.16.840370566608018856162674985408782958984375.1	x^22 - 25x^20 + 130x^18 + 975x^16 - 8280x^14 - 5580x^12 + 129810x^10 - 86460x^8 - 586080x^6 + 671935x^4 - 203995x^2 + 10780	\( -\,3^{20}\cdot 5^{21}\cdot 11^{17} \)	22T36	$[2]$ (GRH)
22.16.426683540939887793863697221184000740328041448.1	x^22 - 4x^21 - 15x^20 + 67x^19 + 99x^18 - 474x^17 - 395x^16 + 1838x^15 + 1092x^14 - 4243x^13 - 2161x^12 + 5933x^11 + 2919x^10 - 4899x^9 - 2465x^8 + 2230x^7 + 1163x^6 - 500x^5 - 264x^4 + 52x^3 + 27x^2 - 2x - 1	\( -\,2^{3}\cdot 7\cdot 13\cdot 109\cdot 947\cdot 211723\cdot 26818222844318783613352699392179 \)	22T59	Trivial (GRH)
22.16.818969006264990311635207859283133228738235532.1	x^22 - 4x^21 - 15x^20 + 67x^19 + 99x^18 - 474x^17 - 395x^16 + 1838x^15 + 1092x^14 - 4243x^13 - 2161x^12 + 5933x^11 + 2919x^10 - 4899x^9 - 2465x^8 + 2231x^7 + 1163x^6 - 501x^5 - 264x^4 + 52x^3 + 27x^2 - 2x - 1	\( -\,2^{2}\cdot 878489\cdot 33910867246172209\cdot 6872776964574058806283 \)	22T59	Trivial (GRH)
22.16.4129233136056857981979443884256982828952059904.1	x^22 - 29x^20 + 57x^18 + 3633x^16 - 22667x^14 - 43524x^12 + 516399x^10 - 732335x^8 - 444902x^6 + 959879x^4 - 44962x^2 + 441	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.16.4129233136056857981979443884256982828952059904.2	x^22 - 18x^20 - 120x^18 + 3945x^16 - 21338x^14 - 14989x^12 + 369623x^10 - 648901x^8 - 637282x^6 + 2623736x^4 - 2281873x^2 + 588289	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.16.4129233136056857981979443884256982828952059904.3	x^22 - 6x^20 - 335x^18 + 5050x^16 - 18019x^14 - 101105x^12 + 982641x^10 - 2621147x^8 + 1562236x^6 + 2051432x^4 - 26350x^2 + 9	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.16.4129233136056857981979443884256982828952059904.4	x^22 - 20x^20 - 141x^18 + 6373x^16 - 58122x^14 + 200198x^12 - 37877x^10 - 1451515x^8 + 3467174x^6 - 2913736x^4 + 806773x^2 + 3969	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.16.27758443257594324914983363876184067664865764900320098627846512840261521316613154967560690069271834754285568.1	x^22 - 180x^20 + 9179x^18 + 58284x^16 - 16217640x^14 + 321816792x^12 + 2957044992x^10 - 135890353824x^8 + 871502095749x^6 + 4468447202724x^4 - 44093388187521x^2 + 46916659556700	\( -\,2^{70}\cdot 3^{21}\cdot 67\cdot 337^{8}\cdot 2851\cdot 310501^{8}\cdot 818717 \)	22T44	n/a