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 matches 1-50 of 140)

Label	Polynomial	Discriminant	Galois group	Class group
22.10.1622619348151146292612416109.1	x^22 - 5x^21 + 4x^20 + 19x^19 - 39x^18 + 11x^17 - 8x^16 + 47x^15 + 183x^14 - 603x^13 + 274x^12 + 853x^11 - 1093x^10 - 146x^9 + 897x^8 - 256x^7 - 277x^6 + 109x^5 + 47x^4 - 10x^3 - 11x^2 + x + 1	\( 29101\cdot 372881^{2}\cdot 633263^{2} \)	22T53	Trivial (GRH)
22.10.70442637605798451973179258449.1	x^22 - 11x^21 + 43x^20 - 45x^19 - 147x^18 + 411x^17 + 19x^16 - 1070x^15 + 605x^14 + 1553x^13 - 1312x^12 - 1553x^11 + 1432x^10 + 1195x^9 - 928x^8 - 712x^7 + 352x^6 + 291x^5 - 71x^4 - 67x^3 + 7x^2 + 7x - 1	\( 71^{2}\cdot 1282529\cdot 3300850529^{2} \)	22T53	Trivial (GRH)
22.10.73443346282868916473942769664.1	x^22 - 13x^20 + 75x^18 - 255x^16 + 572x^14 - 895x^12 + 999x^10 - 790x^8 + 425x^6 - 140x^4 + 21x^2 - 1	\( 2^{22}\cdot 211441^{2}\cdot 625831^{2} \)	22T51	Trivial (GRH)
22.10.117045760309296676701139369984.1	x^22 - 2x^20 + x^16 - 7x^14 + 14x^12 - x^10 - 9x^8 + 15x^6 - 22x^4 + 10x^2 - 1	\( 2^{22}\cdot 2089^{2}\cdot 79966751^{2} \)	22T51	Trivial (GRH)
22.10.349316852822940057561884852224.1	x^22 - 9x^20 + 34x^18 - 69x^16 + 75x^14 - 25x^12 - 38x^10 + 52x^8 - 24x^6 - 4x^4 + 9x^2 - 1	\( 2^{16}\cdot 349^{2}\cdot 6615221297^{2} \)	22T51	Trivial (GRH)
22.10.854993079356720164347705078125.1	x^22 - 2x^21 - 4x^20 + 14x^18 + 27x^17 - 40x^16 - 66x^15 + 4x^14 + 154x^13 + 292x^12 - 44x^11 - 237x^10 + 44x^9 + 22x^8 - 93x^7 - 3x^6 + 33x^5 - 4x^4 - 2x^3 + 7x^2 - x - 1	\( 5^{11}\cdot 211441^{2}\cdot 625831^{2} \)	22T47	Trivial (GRH)
22.10.1211544925921916910574267578125.1	x^22 - x^21 - 4x^20 - x^19 - 6x^18 + 7x^17 + 10x^16 + 54x^15 + 178x^14 + 64x^13 - 301x^12 - 359x^11 - 56x^10 + 64x^9 + 32x^8 + 45x^7 + 27x^6 + 16x^5 - 4x^4 - 12x^3 + 4x^2 + 2x - 1	\( 5^{11}\cdot 19457^{2}\cdot 8095783^{2} \)	22T47	Trivial (GRH)
22.10.1562900555060447098970765787136.1	x^22 + 7x^20 + 15x^18 + 4x^16 - 28x^14 - 36x^12 + 7x^10 + 49x^8 - 5x^6 - 24x^4 + 10x^2 - 1	\( 2^{22}\cdot 610429790897^{2} \)	22T51	Trivial (GRH)
22.10.3790988231418101231518884499009.1	x^22 - 9x^21 + 30x^20 - 42x^19 - 6x^18 + 128x^17 - 208x^16 + 41x^15 + 302x^14 - 426x^13 + 86x^12 + 571x^11 - 569x^10 - 541x^9 + 986x^8 - 5x^7 - 712x^6 + 381x^5 + 144x^4 - 180x^3 + 16x^2 + 14x - 1	\( 23^{20}\cdot 47^{2} \)	22T23	Trivial (GRH)
22.10.3790988231418101231518884499009.2	x^22 - 2x^21 - 10x^20 + 30x^19 + 20x^18 - 150x^17 + 9x^16 + 368x^15 + 116x^14 - 520x^13 - 753x^12 + 353x^11 + 1135x^10 + 407x^9 - 467x^8 - 1035x^7 - 43x^6 + 309x^5 + 310x^4 + 160x^3 - 227x^2 - 59x + 47	\( 23^{20}\cdot 47^{2} \)	22T23	Trivial (GRH)
22.10.237871803919090816246272099352576.1	x^22 + x^20 - 6x^18 - 5x^16 + 10x^14 + 8x^12 - 5x^8 - 10x^6 + 2x^4 + 4x^2 - 1	\( 2^{22}\cdot 29^{2}\cdot 131^{2}\cdot 5399^{2}\cdot 367163^{2} \)	22T51	Trivial (GRH)
22.10.1288033148279983900699565800554496.1	x^22 - 3x^20 - x^18 + 7x^16 - 2x^14 + 4x^12 - 2x^10 - 16x^8 + 4x^6 + 9x^4 - x^2 - 1	\( 2^{22}\cdot 17524013040643^{2} \)	22T51	Trivial (GRH)
22.10.4098058278162967431271914143428729.1	x^22 - 4x^21 - 7x^20 + 51x^19 - 66x^18 - 127x^17 + 255x^16 + 429x^15 - 934x^14 - 1094x^13 + 2996x^12 - 93x^11 - 5194x^10 - 3466x^9 + 9862x^8 + 3976x^7 - 11948x^6 - 2532x^5 + 6218x^4 + 3280x^3 + 565x^2 + 40x + 1	\( 23^{21}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.10.4098058278162967431271914143428729.2	x^22 - 2x^21 + 4x^20 - 31x^19 + 16x^18 - 9x^17 + 271x^16 + 378x^15 - 1469x^14 - 6x^13 - 3622x^12 + 12005x^11 + 853x^10 - 21762x^9 + 26642x^8 - 55561x^7 + 72873x^6 + 1477x^5 - 82097x^4 + 74034x^3 - 28997x^2 + 5416x - 367	\( 23^{21}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.10.4098058278162967431271914143428729.3	x^22 - 2x^21 + 4x^20 - 8x^19 - 30x^18 + 14x^17 - 166x^16 - 59x^15 - 135x^14 - 650x^13 + 196x^12 + 68x^11 + 1428x^10 + 4895x^9 + 8081x^8 + 8908x^7 + 10658x^6 + 7273x^5 - 1252x^4 - 1429x^3 + 121x^2 + 34x + 1	\( 23^{21}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.10.4098058278162967431271914143428729.4	x^22 - 4x^21 - 7x^20 + 51x^19 - 66x^18 - 12x^17 + 232x^16 - 859x^15 + 2125x^14 - 4636x^13 + 4698x^12 + 14121x^11 - 59796x^10 + 97872x^9 - 63140x^8 - 96327x^7 + 342689x^6 - 501195x^5 + 415894x^4 - 177615x^3 + 22323x^2 + 2961x + 47	\( 23^{21}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.10.4098058278162967431271914143428729.5	x^22 - 9x^21 + 35x^20 - 62x^19 - 17x^18 + 429x^17 - 1469x^16 + 2710x^15 - 1068x^14 - 8995x^13 + 24766x^12 - 21230x^11 - 17678x^10 + 54245x^9 - 48721x^8 + 10505x^7 + 21927x^6 - 21117x^5 + 10009x^4 - 3601x^3 + 1290x^2 - 800x + 139	\( 23^{21}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.10.4098058278162967431271914143428729.6	x^22 - 8x^21 + 18x^20 + 17x^19 - 113x^18 + 30x^17 + 335x^16 + 218x^15 - 3607x^14 + 9536x^13 - 14993x^12 + 19365x^11 - 31525x^10 + 66337x^9 - 124953x^8 + 178846x^7 - 184444x^6 + 124670x^5 - 38191x^4 - 12470x^3 + 14913x^2 - 4212x + 277	\( 23^{21}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.10.4098058278162967431271914143428729.7	x^22 - 5x^21 + 2x^20 + 36x^19 - 157x^18 + 302x^17 + 31x^16 - 431x^15 - 145x^14 - 126x^13 - 106x^12 - 3955x^11 + 10115x^10 + 5177x^9 - 3345x^8 - 7080x^7 + 9157x^6 - 14850x^5 - 37415x^4 + 1350x^3 + 12892x^2 + 1090x - 229	\( 23^{21}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.10.7198079267989980836471065337135104.1	x^22 + x^20 - 33x^18 - 55x^16 + 243x^14 + 373x^12 - 608x^10 - 633x^8 + 334x^6 + 222x^4 + 17x^2 - 1	\( 2^{22}\cdot 23^{20} \)	22T23	Trivial (GRH)
22.10.7198079267989980836471065337135104.2	x^22 - 11x^20 + 9x^18 + 180x^16 - 153x^14 - 945x^12 - 550x^10 + 245x^8 + 165x^6 - 9x^4 - 12x^2 - 1	\( 2^{22}\cdot 23^{20} \)	22T23	Trivial (GRH)
22.10.7198079267989980836471065337135104.3	x^22 + 2x^20 - 17x^18 - 26x^16 + 93x^14 + 114x^12 - 157x^10 - 202x^8 + 13x^6 + 44x^4 - 3x^2 - 1	\( 2^{22}\cdot 23^{20} \)	22T23	Trivial (GRH)
22.10.7198079267989980836471065337135104.4	x^22 + 8x^20 - 19x^18 - 215x^16 - 66x^14 + 1115x^12 + 905x^10 - 282x^8 - 205x^6 + 43x^4 + 5x^2 - 1	\( 2^{22}\cdot 23^{20} \)	22T23	Trivial (GRH)
22.10.7198079267989980836471065337135104.5	x^22 + 9x^20 + 18x^18 - 29x^16 - 83x^14 + 40x^12 + 108x^10 - 25x^8 - 51x^6 + 7x^4 + 7x^2 - 1	\( 2^{22}\cdot 23^{20} \)	22T23	Trivial (GRH)
22.10.7198079267989980836471065337135104.6	x^22 + 2x^20 - 17x^18 - 26x^16 + 93x^14 + 91x^12 - 180x^10 - 87x^8 + 59x^6 + 21x^4 - 3x^2 - 1	\( 2^{22}\cdot 23^{20} \)	22T23	Trivial (GRH)
22.10.7198079267989980836471065337135104.7	x^22 + 4x^20 - 22x^18 - 70x^16 + 108x^14 + 198x^12 - 250x^10 - 73x^8 + 108x^6 + 11x^4 - 13x^2 - 1	\( 2^{22}\cdot 23^{20} \)	22T23	Trivial (GRH)
22.10.7198079267989980836471065337135104.8	x^22 + 8x^20 + 4x^18 - 54x^16 - 20x^14 + 103x^12 + 31x^10 - 75x^8 - 21x^6 + 20x^4 + 5x^2 - 1	\( 2^{22}\cdot 23^{20} \)	22T23	Trivial (GRH)
22.10.7198079267989980836471065337135104.9	x^22 + 8x^20 + 4x^18 - 100x^16 - 181x^14 + 287x^12 + 767x^10 + 132x^8 - 274x^6 + 43x^4 + 5x^2 - 1	\( 2^{22}\cdot 23^{20} \)	22T23	Trivial (GRH)
22.10.7198079267989980836471065337135104.10	x^22 + 3x^20 - 44x^18 - 59x^16 + 409x^14 + 318x^12 - 965x^10 - 415x^8 + 417x^6 + 109x^4 - 2x^2 - 1	\( 2^{22}\cdot 23^{20} \)	22T23	Trivial (GRH)
22.10.12701184200335173359101913935642624.1	x^22 + 4x^20 - 4x^18 - 31x^16 - 8x^14 + 81x^12 + 48x^10 - 88x^8 - 60x^6 + 35x^4 + 22x^2 - 1	\( 2^{22}\cdot 55029067682009^{2} \)	22T51	Trivial (GRH)
22.10.12701184200335173359101913935642624.2	x^22 + 7x^20 + 11x^18 - 20x^16 - 54x^14 + 17x^12 + 80x^10 - 11x^8 - 43x^6 + 9x^4 + 5x^2 - 1	\( 2^{22}\cdot 55029067682009^{2} \)	22T51	Trivial (GRH)
22.10.17471883970840462300304775614373553.1	x^22 - 2x^21 - 2x^20 + 24x^19 - 83x^18 - 30x^17 + 161x^16 + 292x^15 + 431x^14 - 4032x^13 + 7422x^12 - 3707x^11 - 11808x^10 + 25440x^9 - 18429x^8 + 765x^7 + 7197x^6 - 4873x^5 + 1431x^4 - 165x^3 - 15x^2 + 8x - 1	\( 1297^{11} \)	22T29	Trivial (GRH)
22.10.17471883970840462300304775614373553.2	x^22 - 4x^21 - 12x^20 + 79x^19 - 46x^18 - 417x^17 + 999x^16 - 364x^15 - 2461x^14 + 6453x^13 - 7803x^12 + 1855x^11 + 10460x^10 - 21218x^9 + 23963x^8 - 17867x^7 + 7632x^6 - 1285x^5 - 15x^4 + 157x^3 - 73x^2 - 10x + 1	\( 1297^{11} \)	22T29	Trivial (GRH)
22.10.165555823163769559238834502754107392.1	x^22 - 92x^18 + 69x^16 + 1702x^14 - 1748x^12 - 7429x^10 + 3634x^8 + 7590x^6 + 2645x^4 + 184x^2 - 23	\( 2^{22}\cdot 23^{21} \)	22T28	Trivial (GRH)
22.10.165555823163769559238834502754107392.2	x^22 + 23x^20 + 161x^18 + 368x^16 - 207x^14 - 1472x^12 - 207x^10 + 2001x^8 + 23x^6 - 966x^4 + 299x^2 - 23	\( 2^{22}\cdot 23^{21} \)	22T28	Trivial (GRH)
22.10.165555823163769559238834502754107392.3	x^22 - 46x^18 - 92x^16 + 299x^14 + 713x^12 - 575x^10 - 1495x^8 + 368x^6 + 759x^4 - 138x^2 - 23	\( 2^{22}\cdot 23^{21} \)	22T28	Trivial (GRH)
22.10.165555823163769559238834502754107392.4	x^22 - 46x^18 + 69x^16 + 299x^14 - 253x^12 - 598x^10 + 253x^8 + 483x^6 - 46x^4 - 138x^2 - 23	\( 2^{22}\cdot 23^{21} \)	22T28	Trivial (GRH)
22.10.165555823163769559238834502754107392.5	x^22 - 69x^18 + 115x^16 + 736x^14 - 667x^12 - 2415x^10 + 644x^8 + 2277x^6 + 529x^4 - 161x^2 - 23	\( 2^{22}\cdot 23^{21} \)	22T28	Trivial (GRH)
22.10.22661033510180079603495293971842498241.1	x^22 - 2x^21 - 21x^20 + 53x^19 - 10x^18 + 194x^17 - 407x^16 - 1527x^15 + 6220x^14 - 4654x^13 - 629x^12 - 17002x^11 + 27165x^10 + 61220x^9 - 186927x^8 + 181221x^7 - 68565x^6 - 17301x^5 + 21983x^4 + 305x^3 - 3623x^2 + 368x + 89	\( 1297^{12} \)	22T30	Trivial (GRH)
22.10.22661033510180079603495293971842498241.2	x^22 - x^21 - 15x^20 + 49x^19 + 44x^18 - 485x^17 + 631x^16 + 1475x^15 - 5443x^14 + 3138x^13 + 10542x^12 - 20731x^11 + 9385x^10 - 1329x^9 + 26060x^8 - 12671x^7 - 46031x^6 + 81808x^5 - 90460x^4 + 26591x^3 + 21718x^2 - 4276x - 289	\( 1297^{12} \)	22T30	$[2]$ (GRH)
22.10.22661033510180079603495293971842498241.3	x^22 - x^21 - x^20 + 60x^19 - 104x^18 - 389x^17 + 930x^16 + 1131x^15 - 4806x^14 - 200x^13 + 14407x^12 - 16040x^11 - 4755x^10 + 43121x^9 - 59207x^8 - 13398x^7 + 79635x^6 - 16708x^5 - 39710x^4 - 1394x^3 + 28884x^2 - 12840x + 1343	\( 1297^{12} \)	22T30	Trivial (GRH)
22.10.22661033510180079603495293971842498241.4	x^22 - 35x^20 - 72x^19 + 349x^18 + 1479x^17 + 303x^16 - 6784x^15 - 5684x^14 + 33196x^13 + 87806x^12 + 64287x^11 - 46217x^10 - 105124x^9 - 72109x^8 - 28967x^7 + 30762x^6 + 56113x^5 - 4944x^4 - 27192x^3 - 1892x^2 + 3210x + 509	\( 1297^{12} \)	22T30	Trivial (GRH)
22.10.22661033510180079603495293971842498241.5	x^22 - 5x^21 + 6x^20 + 16x^19 - 102x^18 + 158x^17 + 126x^16 - 120x^15 + 3303x^14 - 15009x^13 - 7047x^12 + 123140x^11 - 153297x^10 - 373493x^9 + 984859x^8 + 258716x^7 - 2326169x^6 + 706632x^5 + 2505600x^4 - 1023169x^3 - 1195624x^2 + 155028x + 13045	\( 1297^{12} \)	22T30	Trivial (GRH)
22.10.22661033510180079603495293971842498241.6	x^22 - 5x^21 + x^20 + 45x^19 - 310x^18 + 927x^17 - 1531x^16 + 1204x^15 + 2550x^14 - 9408x^13 + 18565x^12 - 24332x^11 + 23469x^10 + 9560x^9 - 46190x^8 + 69717x^7 - 91965x^6 + 67098x^5 - 36153x^4 + 9787x^3 + 1002x^2 - 474x - 25	\( 1297^{12} \)	22T30	$[2]$ (GRH)
22.10.24111231168499845791571893752356143104.1	x^22 - 11x^20 + 33x^18 - 11x^16 - 22x^14 - 22x^12 - 80x^11 - 22x^10 - 22x^8 - 11x^6 + 33x^4 - 11x^2 + 1	\( 2^{20}\cdot 7^{10}\cdot 11^{22} \)	22T34	Trivial (GRH)
22.10.56501459388151144478039723653407440896.1	x^22 - 5x^20 - 97x^18 - 162x^16 + 392x^14 + 639x^12 - 299x^10 - 637x^8 - 27x^6 + 178x^4 + 43x^2 - 1	\( 2^{22}\cdot 1297^{10} \)	22T30	Trivial (GRH)
22.10.56501459388151144478039723653407440896.2	x^22 - 2x^20 - 56x^18 + 245x^16 + 126x^14 - 1903x^12 + 1997x^10 + 1141x^8 - 1026x^6 - 464x^4 - 41x^2 - 1	\( 2^{22}\cdot 1297^{10} \)	22T30	Trivial (GRH)
22.10.56501459388151144478039723653407440896.3	x^22 + 3x^20 - 62x^18 - 30x^16 + 1121x^14 - 1695x^12 - 1287x^10 + 2870x^8 - 170x^6 - 456x^4 - 65x^2 - 1	\( 2^{22}\cdot 1297^{10} \)	22T30	Trivial (GRH)
22.10.56501459388151144478039723653407440896.4	x^22 + 4x^20 - 69x^18 - 366x^16 + 420x^14 + 3456x^12 + 424x^10 - 3247x^8 - 1390x^6 - 35x^4 + 28x^2 - 1	\( 2^{22}\cdot 1297^{10} \)	22T30	Trivial (GRH)
22.10.56501459388151144478039723653407440896.5	x^22 + 19x^20 + 30x^18 - 427x^16 - 1235x^14 + 833x^12 + 3553x^10 - 222x^8 - 2608x^6 - 298x^4 + 42x^2 - 1	\( 2^{22}\cdot 1297^{10} \)	22T30	Trivial (GRH)