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 50 matches)

Label	Polynomial	Discriminant	Galois group	Class group
22.8.14799420881562079578038490499.1	x^22 - 11x^21 + 44x^20 - 55x^19 - 112x^18 + 381x^17 - 87x^16 - 834x^15 + 674x^14 + 1020x^13 - 1213x^12 - 834x^11 + 1220x^10 + 511x^9 - 776x^8 - 247x^7 + 323x^6 + 85x^5 - 89x^4 - 18x^3 + 16x^2 + x - 1	\( -\,97\cdot 2381^{2}\cdot 2467\cdot 104446171^{2} \)	22T53	Trivial (GRH)
22.8.80659324072725558117423074447.1	x^22 - 9x^21 + 29x^20 - 38x^19 - 4x^18 + 86x^17 - 143x^16 + 138x^15 - 79x^14 - 37x^13 + 184x^12 - 257x^11 + 184x^10 - 37x^9 - 79x^8 + 138x^7 - 143x^6 + 86x^5 - 4x^4 - 38x^3 + 29x^2 - 9x + 1	\( -\,23^{20}\cdot 47 \)	22T28	Trivial (GRH)
22.8.104070916689387515610916716544.1	x^22 - 2x^20 - x^18 - 2x^16 + 18x^12 - 24x^10 - 3x^8 + 36x^6 - 27x^4 + 4x^2 + 1	\( -\,2^{22}\cdot 19457^{2}\cdot 8095783^{2} \)	22T53	Trivial (GRH)
22.8.1562900555060447098970765787136.1	x^22 - x^20 - 4x^18 + x^16 + 5x^14 + 7x^12 - 7x^10 - 5x^8 + 7x^6 - 3x^4 - x^2 + 1	\( -\,2^{22}\cdot 610429790897^{2} \)	22T53	Trivial (GRH)
22.8.2741869623221317890608793124864.1	x^22 - 2x^20 - x^18 + 4x^16 - x^14 - 5x^12 - x^10 + 8x^8 + 3x^6 - 5x^4 - x^2 + 1	\( -\,2^{22}\cdot 43^{2}\cdot 547^{2}\cdot 34374601^{2} \)	22T53	Trivial (GRH)
22.8.87192729322616328324934343477207.1	x^22 - x^21 + x^20 - x^19 - 22x^18 + 22x^17 - 91x^16 + 68x^15 - 229x^14 - 162x^13 + 484x^12 - 1105x^11 + 852x^10 - 461x^9 - 114x^8 + 1264x^7 - 735x^6 + 574x^5 + 622x^4 + 298x^3 - 459x^2 - 162x + 47	\( -\,23^{21}\cdot 47^{2} \)	22T28	Trivial (GRH)
22.8.87192729322616328324934343477207.2	x^22 - 4x^21 - 7x^20 + 51x^19 - 43x^18 - 150x^17 + 416x^16 - 192x^15 - 1256x^14 + 1988x^13 + 2076x^12 - 5521x^11 - 1238x^10 + 8241x^9 - 2466x^8 - 6627x^7 + 5601x^6 + 2988x^5 - 5397x^4 + 566x^3 + 3417x^2 - 2306x - 1609	\( -\,23^{21}\cdot 47^{2} \)	22T28	Trivial (GRH)
22.8.178176446876650757881387571453423.1	x^22 - 2x^21 - 14x^20 + 31x^19 + 70x^18 - 232x^17 - 279x^16 + 727x^15 + 777x^14 - 691x^13 - 405x^12 + 301x^11 - 1802x^10 - 2957x^9 + 1747x^8 + 4390x^7 + 52x^6 - 990x^5 - 739x^4 - 86x^3 + 40x^2 + 61x - 47	\( -\,23^{20}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.8.237871803919090816246272099352576.1	x^22 - x^20 - 6x^18 + 5x^16 + 10x^14 - 8x^12 + 5x^8 - 10x^6 - 2x^4 + 4x^2 + 1	\( -\,2^{22}\cdot 29^{2}\cdot 131^{2}\cdot 5399^{2}\cdot 367163^{2} \)	22T53	Trivial (GRH)
22.8.1288033148279983900699565800554496.1	x^22 + 3x^20 - x^18 - 7x^16 - 2x^14 - 4x^12 - 2x^10 + 16x^8 + 4x^6 - 9x^4 - x^2 + 1	\( -\,2^{22}\cdot 17524013040643^{2} \)	22T53	Trivial (GRH)
22.8.7198079267989980836471065337135104.1	x^22 + 7x^20 - 7x^18 - 166x^16 - 458x^14 - 375x^12 + 144x^10 + 285x^8 + 29x^6 - 51x^4 - 9x^2 + 1	\( -\,2^{22}\cdot 23^{20} \)	22T28	Trivial (GRH)
22.8.7198079267989980836471065337135104.2	x^22 + 10x^20 + 35x^18 + 39x^16 - 42x^14 - 112x^12 - 14x^10 + 85x^8 + 24x^6 - 22x^4 - 4x^2 + 1	\( -\,2^{22}\cdot 23^{20} \)	22T28	Trivial (GRH)
22.8.7198079267989980836471065337135104.3	x^22 + 5x^20 - 20x^18 - 113x^16 + 75x^14 + 721x^12 + 196x^10 - 1492x^8 - 981x^6 + 372x^4 + 84x^2 + 1	\( -\,2^{22}\cdot 23^{20} \)	22T28	Trivial (GRH)
22.8.7198079267989980836471065337135104.4	x^22 - 4x^20 - 45x^18 - 45x^16 + 223x^14 + 469x^12 + 26x^10 - 571x^8 - 421x^6 - 34x^4 + 33x^2 + 1	\( -\,2^{22}\cdot 23^{20} \)	22T28	Trivial (GRH)
22.8.13844017509319141075535476685799424.1	x^22 + 11x^20 + 43x^18 + 62x^16 - 16x^14 - 116x^12 - 53x^10 + 56x^8 + 32x^6 - 10x^4 - 4x^2 + 1	\( -\,2^{22}\cdot 233^{2}\cdot 246572816873^{2} \)	22T53	Trivial (GRH)
22.8.17213757945874230471135911350559867.1	x^22 - 11x^21 + 62x^20 - 235x^19 + 656x^18 - 1401x^17 + 2307x^16 - 2850x^15 + 2370x^14 - 664x^13 - 1547x^12 + 2938x^11 - 2660x^10 + 1125x^9 + 394x^8 - 967x^7 + 681x^6 - 193x^5 - 53x^4 + 68x^3 - 22x^2 + x + 1	\( -\,137^{2}\cdot 293^{2}\cdot 11093^{2}\cdot 216649^{2}\cdot 1849643 \)	22T53	Trivial (GRH)
22.8.19750127333914657004021168648045757632.1	x^22 - 3x^21 - 2x^20 + 17x^19 - 15x^18 - 29x^17 + 62x^16 - x^15 - 98x^14 + 77x^13 + 66x^12 - 131x^11 + 24x^10 + 98x^9 - 81x^8 - 17x^7 + 57x^6 - 25x^5 - 12x^4 + 14x^3 - 3x^2 - 2x + 1	\( -\,2^{6}\cdot 673\cdot 683\cdot 4730027\cdot 141935338646968028959691 \)	22T59	Trivial (GRH)
22.8.56501459388151144478039723653407440896.1	x^22 + 16x^20 + 62x^18 - 216x^16 - 1948x^14 - 3000x^12 + 4363x^10 + 9892x^8 - 2285x^6 - 747x^4 + 4x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.8.56501459388151144478039723653407440896.2	x^22 + 16x^20 + 46x^18 - 346x^16 - 2536x^14 - 5981x^12 - 4843x^10 + 1475x^8 + 2688x^6 - 302x^4 - 144x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.8.56501459388151144478039723653407440896.3	x^22 + 9x^20 - 34x^18 - 335x^16 + 207x^14 + 3414x^12 + 981x^10 - 8064x^8 + 51x^6 + 3070x^4 + 710x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.8.56501459388151144478039723653407440896.4	x^22 + 9x^20 - 9x^18 - 259x^16 - 351x^14 + 1960x^12 + 4198x^10 - 1414x^8 - 4092x^6 - 774x^4 + 197x^2 + 25	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.8.56501459388151144478039723653407440896.5	x^22 - 7x^20 - 72x^18 - 36x^16 + 711x^14 + 1469x^12 - 353x^10 - 3136x^8 - 2011x^6 + 858x^4 + 1172x^2 + 289	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.8.56501459388151144478039723653407440896.6	x^22 + 6x^20 - 87x^18 - 904x^16 - 2836x^14 - 3349x^12 - 591x^10 + 1601x^8 + 959x^6 + 43x^4 - 47x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.8.56501459388151144478039723653407440896.7	x^22 + x^20 - 89x^18 + 172x^16 + 1434x^14 - 3373x^12 - 5614x^10 + 7890x^8 + 12675x^6 + 3940x^4 + 219x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.8.56501459388151144478039723653407440896.8	x^22 + 4x^20 - 67x^18 - 65x^16 + 801x^14 + 697x^12 - 3324x^10 - 3913x^8 + 3601x^6 + 7419x^4 + 3784x^2 + 625	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.8.168074113321603771232534997081756591796875.1	x^22 + 49x^20 + 685x^18 + 1815x^16 - 17505x^14 - 55752x^12 + 164457x^10 + 203115x^8 - 250965x^6 - 61270x^4 + 1001x^2 + 44	\( -\,3^{20}\cdot 5^{20}\cdot 11^{17} \)	22T36	Trivial (GRH)
22.8.1580153645858805893796455628954412194463744.1	x^22 + 22x^20 - 66x^18 - 1892x^16 + 2684x^14 + 50908x^12 - 77924x^10 - 384824x^8 + 646272x^6 + 36080x^4 + 660x^2 + 4	\( -\,2^{36}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.8.6320614583435223575185822515817648777854976.1	x^22 + 22x^20 - 22x^18 - 1738x^16 + 1100x^14 + 22000x^12 + 4840x^10 - 87120x^8 - 57596x^6 + 104544x^4 + 94380x^2 + 484	\( -\,2^{38}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.8.15646172003756569249283257910156250000000000.1	x^22 + 26x^20 - 110x^18 - 3315x^16 - 14415x^14 - 13548x^12 + 20277x^10 + 30555x^8 + 10620x^6 + 670x^4 - 94x^2 + 1	\( -\,2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.8.15646172003756569249283257910156250000000000.2	x^22 - 19x^20 - 170x^18 + 3015x^16 + 10980x^14 - 127398x^12 - 271758x^10 + 1040880x^8 + 1659690x^6 + 598255x^4 + 77051x^2 + 3136	\( -\,2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.8.15646172003756569249283257910156250000000000.3	x^22 + 26x^20 - 20x^18 - 3330x^16 - 12255x^14 + 78192x^12 + 447987x^10 + 277980x^8 - 1318755x^6 - 2129930x^4 - 884209x^2 + 8836	\( -\,2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.8.15646172003756569249283257910156250000000000.4	x^22 - 19x^20 - 395x^18 + 615x^16 + 20850x^14 + 16842x^12 - 223773x^10 - 144525x^8 + 284565x^6 + 250165x^4 + 38861x^2 + 1	\( -\,2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.8.15646172003756569249283257910156250000000000.5	x^22 + 44x^20 + 415x^18 - 2265x^16 - 52410x^14 - 232827x^12 + 61662x^10 + 2529105x^8 + 4141035x^6 - 550070x^4 + 15791x^2 + 64	\( -\,2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.8.22085756220567549162579756126980406366726963.1	x^22 - 33x^20 - 66x^19 - 165x^17 - 1584x^16 - 5379x^15 + 11517x^14 + 66462x^13 + 1452x^12 - 124158x^11 + 531795x^10 + 1346697x^9 - 72006x^8 - 136224x^7 + 4245747x^6 + 2948682x^5 - 3930531x^4 - 687159x^3 + 4962870x^2 + 314622x - 2099481	\( -\,3^{21}\cdot 11^{32} \)	22T36	Trivial (GRH)
22.8.25282458333740894300743290063270595111419904.1	x^22 - 11x^20 - 297x^18 + 1639x^16 + 20130x^14 + 39776x^12 + 10890x^10 - 19096x^8 - 10527x^6 + 231x^4 + 715x^2 + 49	\( -\,2^{40}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.8.28617804644466364808600171614542123126263348.1	x^22 - 4x^21 - 8x^20 + 47x^19 + 7x^18 - 218x^17 + 124x^16 + 494x^15 - 557x^14 - 508x^13 + 1073x^12 + 9x^11 - 1074x^10 + 507x^9 + 535x^8 - 513x^7 - 87x^6 + 233x^5 - 23x^4 - 50x^3 + 10x^2 + 5x - 1	\( -\,2^{2}\cdot 7154451161116591202150042903635530781565837 \)	22T59	Trivial (GRH)
22.8.44244302084046565026300757610723541444984832.1	x^22 + 44x^20 + 330x^18 - 1122x^16 - 10428x^14 - 9548x^12 + 33044x^10 + 58124x^8 + 25432x^6 + 748x^4 - 836x^2 + 28	\( -\,2^{38}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.8.176977208336186260105203030442894165779939328.1	x^22 - 440x^18 + 1760x^16 + 29216x^14 - 54208x^12 - 381568x^10 + 2816x^8 + 1143296x^6 + 1216512x^4 + 405504x^2 + 28672	\( -\,2^{40}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.8.4129233136056857981979443884256982828952059904.1	x^22 + 13x^20 - 175x^18 - 443x^16 + 4918x^14 + 5154x^12 - 30529x^10 - 31931x^8 - 8640x^6 - 37x^4 + 149x^2 + 9	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.8.4129233136056857981979443884256982828952059904.2	x^22 - 7x^20 - 305x^18 + 1628x^16 + 16707x^14 - 32324x^12 - 356150x^10 - 370911x^8 + 918618x^6 + 1408022x^4 + 86679x^2 + 729	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.8.4129233136056857981979443884256982828952059904.3	x^22 - 10x^20 - 462x^18 + 3723x^16 + 44062x^14 - 61606x^12 - 1444979x^10 - 4726237x^8 - 6044709x^6 - 2432660x^4 + 446695x^2 + 52441	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.8.4129233136056857981979443884256982828952059904.4	x^22 + 53x^20 + 1013x^18 + 7634x^16 + 4909x^14 - 175743x^12 - 326231x^10 + 1362553x^8 + 1192125x^6 - 2661192x^4 - 168308x^2 + 109561	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.8.4129233136056857981979443884256982828952059904.5	x^22 + 10x^20 - 224x^18 - 1796x^16 + 5190x^14 + 71141x^12 + 187010x^10 + 147260x^8 + 4176x^6 - 5361x^4 - 167x^2 + 1	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.8.4129233136056857981979443884256982828952059904.6	x^22 + 13x^20 - 136x^18 - 1229x^16 + 6421x^14 + 15324x^12 - 43922x^10 - 84593x^8 - 33311x^6 - 3209x^4 + 35x^2 + 9	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.8.33342566148849566152016281600000000000000000000.1	x^22 + 11x^20 - 495x^18 - 7865x^16 - 24585x^14 + 129107x^12 + 801867x^10 + 572385x^8 - 2731740x^6 - 3375130x^4 - 45419x^2 + 1681	\( -\,2^{32}\cdot 5^{20}\cdot 11^{22} \)	22T37	$[2]$ (GRH)
22.8.33342566148849566152016281600000000000000000000.2	x^22 - 55x^20 - 110x^19 + 1265x^18 + 5390x^17 - 12155x^16 - 108680x^15 - 54615x^14 + 1156650x^13 + 2584725x^12 - 6092700x^11 - 26435475x^10 + 3812050x^9 + 118802475x^8 + 110680350x^7 - 162157050x^6 - 354485450x^5 - 248457000x^4 - 122510850x^3 - 86390975x^2 - 35201100x - 4085775	\( -\,2^{32}\cdot 5^{20}\cdot 11^{22} \)	22T37	$[2]$ (GRH)
22.8.24986117063726489111930820723283680074515474022619927764789155841703936.1	x^22 - 3x^20 - 36x^18 + 60x^16 + 213x^14 - 9x^12 - 114x^10 - 180x^8 - 108x^6 + 6x^4 + 36x^2 + 54	\( -\,2^{45}\cdot 3^{29}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16} \)	22T52	Trivial (GRH)
22.8.333148227516353188159077609643782400993539653634932370197188744556052480.1	x^22 - 8x^20 - 11x^18 + 234x^16 - 633x^14 + 30x^12 + 2835x^10 - 5934x^8 + 5448x^6 - 2104x^4 + 8x^2 + 80	\( -\,2^{48}\cdot 3^{28}\cdot 5\cdot 7^{4}\cdot 23^{4}\cdot 137^{16} \)	22T52	Trivial (GRH)
22.8.31549754154938736139605034462596274469412770924031278962771396260567384323209653421425695172275073152188416.1	x^22 - 11x^21 + 73x^20 - 345x^19 - 4261x^18 + 45987x^17 - 307032x^16 + 1383522x^15 + 3961947x^14 - 48148705x^13 + 366194477x^12 - 1522409545x^11 + 1221051993x^10 + 6576607873x^9 - 104670123606x^8 + 364667664168x^7 - 921763556307x^6 + 1531016892369x^5 + 1216236277569x^4 - 4579083727977x^3 + 13843027641789x^2 - 11356029443979x + 7476951174594	\( -\,2^{48}\cdot 3^{20}\cdot 79\cdot 337^{8}\cdot 25537\cdot 310501^{8}\cdot 1108640890417 \)	22T44	n/a
22.8.58418948490087900856198784513049139500595201522971777317979130633702859321491007685912328702163396402872320.1	x^22 + 40x^20 - 4821x^18 - 209496x^16 + 5285400x^14 + 302815992x^12 + 922756032x^10 - 93270702624x^8 - 1132846722171x^6 - 2066536069936x^4 + 13681132452239x^2 + 35545793447880	\( -\,2^{71}\cdot 3^{21}\cdot 5\cdot 337^{8}\cdot 1543\cdot 310501^{8}\cdot 21330377 \)	22T44	n/a