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 60)

Label	Polynomial	Discriminant	Galois group	Class group
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)
22.14.1855164453672687836700730712281.1	x^22 - 3x^21 - 14x^20 + 42x^19 + 81x^18 - 220x^17 - 283x^16 + 596x^15 + 627x^14 - 1145x^13 - 429x^12 + 1655x^11 - 1009x^10 - 1021x^9 + 1683x^8 - 196x^7 - 608x^6 + 283x^5 - 44x^4 - 6x^3 + 18x^2 - 8x + 1	\( 23^{21}\cdot 47 \)	22T28	Trivial (GRH)
22.12.87192729322616328324934343477207.1	x^22 - 4x^21 - 7x^20 + 74x^19 - 135x^18 - 196x^17 + 1152x^16 - 1457x^15 - 1072x^14 + 5185x^13 - 5192x^12 - 461x^11 + 5455x^10 - 5559x^9 + 2042x^8 + 1469x^7 + 196x^6 - 5039x^5 + 4907x^4 - 446x^3 - 1666x^2 + 891x - 137	\( -\,23^{21}\cdot 47^{2} \)	22T28	Trivial (GRH)
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)
22.8.87192729322616328324934343477207.1	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)
22.12.87192729322616328324934343477207.2	x^22 - 3x^21 - 14x^20 + 65x^19 + 12x^18 - 404x^17 + 384x^16 + 1079x^15 - 1857x^14 - 1536x^13 + 4746x^12 + 574x^11 - 8668x^10 + 4752x^9 + 8353x^8 - 11765x^7 + 174x^6 + 9989x^5 - 6254x^4 - 2191x^3 + 3353x^2 - 560x - 229	\( -\,23^{21}\cdot 47^{2} \)	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)
22.12.178176446876650757881387571453423.1	x^22 - x^21 + 8x^20 + x^19 - 10x^18 + 79x^17 - 234x^16 + 293x^15 - 293x^14 - 441x^13 + 1283x^12 - 1700x^11 + 1629x^10 + 2222x^9 - 4511x^8 - 315x^7 + 2661x^6 - 55x^5 - 669x^4 - 21x^3 + 68x^2 + 7x - 1	\( -\,23^{20}\cdot 47^{3} \)	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)
22.4.178176446876650757881387571453423.1	x^22 - 3x^21 - 4x^20 + 21x^19 - 34x^18 - 64x^17 + 209x^16 - 79x^15 - 626x^14 + 986x^13 + 469x^12 - 2461x^11 + 890x^10 + 2535x^9 - 360x^8 - 4500x^7 - 1390x^6 + 7497x^5 - 2384x^4 - 6847x^3 + 1939x^2 + 3881x - 2897	\( -\,23^{20}\cdot 47^{3} \)	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)
22.12.178176446876650757881387571453423.2	x^22 - 9x^21 + 23x^20 + 32x^19 - 251x^18 + 219x^17 + 915x^16 - 1739x^15 - 1820x^14 + 6548x^13 + 969x^12 - 16878x^11 + 9906x^10 + 22070x^9 - 29522x^8 - 3288x^7 + 25694x^6 - 12946x^5 - 3524x^4 + 4687x^3 - 1081x^2 - 6x + 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)
22.12.178176446876650757881387571453423.3	x^22 - 8x^21 + 12x^20 + 46x^19 - 109x^18 - 114x^17 + 165x^16 + 756x^15 + 9x^14 - 3299x^13 - 666x^12 + 8067x^11 + 4331x^10 - 16061x^9 - 4342x^8 + 13658x^7 + 3196x^6 - 4458x^5 - 1074x^4 + 552x^3 + 42x^2 - 12x - 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)
22.12.178176446876650757881387571453423.4	x^22 - 5x^21 - 10x^20 + 78x^19 + 30x^18 - 586x^17 + 91x^16 + 3136x^15 - 3117x^14 - 7084x^13 + 12319x^12 + 6022x^11 - 23809x^10 + 9384x^9 + 15063x^8 - 18488x^7 + 10061x^6 - 2016x^5 - 5851x^4 + 8564x^3 - 4987x^2 + 1340x - 137	\( -\,23^{20}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.12.178176446876650757881387571453423.5	x^22 - 7x^21 + 10x^20 + 16x^19 - 10x^18 - 184x^17 + 468x^16 - 58x^15 - 1272x^14 + 816x^13 + 2227x^12 - 2216x^11 - 2463x^10 + 2895x^9 + 2624x^8 - 1329x^7 - 2547x^6 - 368x^5 + 990x^4 + 174x^3 - 144x^2 + 9x + 1	\( -\,23^{20}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.12.178176446876650757881387571453423.6	x^22 - 10x^21 + 42x^20 - 88x^19 + 26x^18 + 460x^17 - 1667x^16 + 3076x^15 - 2650x^14 - 1948x^13 + 9671x^12 - 13923x^11 + 7597x^10 + 7283x^9 - 18181x^8 + 15029x^7 - 2411x^6 - 6693x^5 + 6866x^4 - 3122x^3 + 705x^2 - 65x + 1	\( -\,23^{20}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.12.178176446876650757881387571453423.7	x^22 - 7x^21 + 8x^20 + 58x^19 - 243x^18 + 346x^17 + 333x^16 - 2299x^15 + 3786x^14 - 920x^13 - 7580x^12 + 14118x^11 - 5659x^10 - 17342x^9 + 33608x^8 - 19265x^7 - 19737x^6 + 44371x^5 - 35838x^4 + 14864x^3 - 2259x^2 - 482x + 139	\( -\,23^{20}\cdot 47^{3} \)	22T28	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)
22.14.4098058278162967431271914143428729.1	x^22 - 4x^21 - 7x^20 + 51x^19 - 43x^18 - 173x^17 + 600x^16 - 652x^15 - 2636x^14 + 6381x^13 + 6768x^12 - 16676x^11 - 7057x^10 + 24180x^9 + 2364x^8 - 20611x^7 - 494x^6 + 7657x^5 - 659x^4 - 998x^3 + 289x^2 - 29x + 1	\( 23^{21}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.18.4098058278162967431271914143428729.1	x^22 - 3x^21 - 14x^20 + 42x^19 + 35x^18 - 82x^17 - 76x^16 - 508x^15 + 1938x^14 - 984x^13 - 5144x^12 + 9774x^11 + 1291x^10 - 17627x^9 + 8445x^8 + 12822x^7 - 10291x^6 - 3443x^5 + 4487x^4 - 121x^3 - 672x^2 + 130x + 1	\( 23^{21}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.6.4098058278162967431271914143428729.1	x^22 - x^21 + x^20 - x^19 - 22x^18 - x^17 - 114x^16 + 160x^15 - 22x^14 + 390x^13 + 806x^12 + 712x^11 + 1174x^10 - 5015x^9 - 2690x^8 - 5866x^7 + 10213x^6 - 2646x^5 + 2232x^4 - 12927x^3 + 6786x^2 - 806x + 47	\( 23^{21}\cdot 47^{3} \)	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)
22.14.4098058278162967431271914143428729.2	x^22 - 3x^21 - 14x^20 + 65x^19 - 57x^18 - 197x^17 + 729x^16 - 508x^15 - 1121x^14 + 1546x^13 - 935x^12 + 160x^11 + 1889x^10 - 975x^9 + 579x^8 + 80x^7 - 700x^6 + 99x^5 - 159x^4 - 75x^3 + 41x^2 + 15x + 1	\( 23^{21}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.6.4098058278162967431271914143428729.2	x^22 - 5x^21 + 2x^20 + 36x^19 - 111x^18 + 141x^17 - 107x^16 + 558x^15 - 1962x^14 + 3577x^13 - 3027x^12 - 2023x^11 + 17912x^10 - 42755x^9 + 54822x^8 - 37877x^7 + 18311x^6 - 12826x^5 + 673x^4 + 3420x^3 + 4336x^2 - 3280x + 47	\( 23^{21}\cdot 47^{3} \)	22T28	$[2]$ (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)
22.6.4098058278162967431271914143428729.3	x^22 - 5x^21 + 2x^20 + 36x^19 - 88x^18 + 95x^17 - 15x^16 - 224x^15 + 108x^14 + 58x^13 + 1642x^12 - 5082x^11 + 6435x^10 + 1474x^9 - 21998x^8 + 40783x^7 - 25274x^6 - 17265x^5 + 57828x^4 - 81220x^3 + 54660x^2 - 19173x + 7499	\( 23^{21}\cdot 47^{3} \)	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)
22.12.7198079267989980836471065337135104.1	x^22 - 2x^20 - 17x^18 + 26x^16 + 93x^14 - 91x^12 - 180x^10 + 87x^8 + 59x^6 - 21x^4 - 3x^2 + 1	\( -\,2^{22}\cdot 23^{20} \)	22T28	Trivial (GRH)
22.20.7198079267989980836471065337135104.1	x^22 - 24x^20 + 220x^18 - 980x^16 + 2267x^14 - 2696x^12 + 1324x^10 + 265x^8 - 563x^6 + 215x^4 - 29x^2 + 1	\( -\,2^{22}\cdot 23^{20} \)	22T28	Trivial (GRH)
22.4.7198079267989980836471065337135104.1	x^22 + 17x^20 + 100x^18 + 265x^16 + 265x^14 - 217x^12 - 833x^10 - 861x^8 - 405x^6 - 79x^4 - x^2 + 1	\( -\,2^{22}\cdot 23^{20} \)	22T28	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)
22.12.7198079267989980836471065337135104.2	x^22 - x^20 - 33x^18 + 55x^16 + 243x^14 - 373x^12 - 608x^10 + 633x^8 + 334x^6 - 222x^4 + 17x^2 + 1	\( -\,2^{22}\cdot 23^{20} \)	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)
22.12.7198079267989980836471065337135104.3	x^22 + 7x^20 - 7x^18 - 97x^16 + 48x^14 + 476x^12 - 454x^10 - 704x^8 + 1317x^6 - 718x^4 + 129x^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)
22.2.13079147944053004756241817943013989.1	x^22 - 11x^21 + 78x^20 - 395x^19 + 1595x^18 - 5292x^17 + 14883x^16 - 35934x^15 + 75375x^14 - 138055x^13 + 221616x^12 - 311835x^11 + 383985x^10 - 411930x^9 + 382260x^8 - 303600x^7 + 203205x^6 - 112125x^5 + 49335x^4 - 16445x^3 + 3795x^2 - 506x + 23	\( 23^{20}\cdot 7621189 \)	22T28	$[3]$ (GRH)
22.20.165555823163769559238834502754107392.1	x^22 - 23x^20 + 207x^18 - 897x^16 + 1679x^14 + 483x^12 - 7636x^10 + 13041x^8 - 9660x^6 + 3312x^4 - 483x^2 + 23	\( -\,2^{22}\cdot 23^{21} \)	22T28	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)
22.14.165555823163769559238834502754107392.1	x^22 - 69x^18 + 115x^16 + 1265x^14 - 3680x^12 - 1426x^10 + 9752x^8 - 4646x^6 - 2369x^4 + 943x^2 - 23	\( 2^{22}\cdot 23^{21} \)	22T28	Trivial (GRH)
22.18.165555823163769559238834502754107392.1	x^22 - 23x^20 + 184x^18 - 598x^16 + 437x^14 + 1840x^12 - 4324x^10 + 2875x^8 + 253x^6 - 828x^4 + 253x^2 - 23	\( 2^{22}\cdot 23^{21} \)	22T28	Trivial (GRH)
22.2.165555823163769559238834502754107392.1	x^22 + 23x^20 + 207x^18 + 897x^16 + 1679x^14 - 483x^12 - 7636x^10 - 13041x^8 - 9660x^6 - 3312x^4 - 483x^2 - 23	\( 2^{22}\cdot 23^{21} \)	22T28	Trivial (GRH)
22.6.165555823163769559238834502754107392.1	x^22 - 46x^18 - 69x^16 + 529x^14 + 1242x^12 - 1196x^10 - 5336x^8 - 4922x^6 - 1932x^4 - 345x^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)
22.14.165555823163769559238834502754107392.2	x^22 - 69x^18 + 207x^16 + 368x^14 - 1863x^12 + 920x^10 + 3036x^8 - 4186x^6 + 1794x^4 - 184x^2 - 23	\( 2^{22}\cdot 23^{21} \)	22T28	Trivial (GRH)