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 86)

Label	Polynomial	Discriminant	Galois group	Class group
20.2.357932753285354148069376.1	x^20 - 4x^18 - 12x^17 - 7x^16 + 16x^15 + 48x^14 + 40x^13 - 26x^12 - 124x^11 - 168x^10 - 124x^9 - 26x^8 + 40x^7 + 48x^6 + 16x^5 - 7x^4 - 12x^3 - 4x^2 + 1	\( -\,2^{20}\cdot 13^{10}\cdot 19^{5} \)	20T989	Trivial
20.0.1698943469934323523649536.1	x^20 + 2x^18 + 13x^16 + 28x^14 + 26x^12 + 24x^10 + 30x^8 + 24x^6 + 33x^4 + 42x^2 + 21	\( 2^{30}\cdot 3^{23}\cdot 7^{5} \)	20T989	Trivial
20.0.1793075893656120387960832.1	x^20 - 4x^19 + 4x^18 + 8x^17 - 12x^16 - 24x^15 + 56x^14 + 4x^13 - 18x^12 - 92x^11 + 104x^10 + 4x^9 + 46x^8 - 100x^7 + 32x^6 - 20x^5 + 36x^4 - 16x^3 + 4x^2 - 4x + 2	\( 2^{40}\cdot 277^{5} \)	20T989	Trivial (GRH)
20.2.5726924052565666369110016.1	x^20 + 2x^18 + 9x^16 + 20x^14 + 26x^12 + 48x^10 - 6x^8 - 196x^6 - 235x^4 - 114x^2 - 19	\( -\,2^{24}\cdot 13^{10}\cdot 19^{5} \)	20T989	Trivial
20.2.17537157059432067986358272.1	x^20 - x^19 - 4x^18 + x^17 + 17x^16 - 2x^15 - 63x^14 + 15x^13 + 136x^12 + 67x^11 - 75x^10 - 58x^9 + 307x^8 + 111x^7 + 28x^6 - 109x^5 + 202x^4 + 43x^3 - x^2 - 10x - 4	\( -\,2^{18}\cdot 19^{8}\cdot 83^{5} \)	20T989	Trivial (GRH)
20.6.17537157059432067986358272.1	x^20 - 10x^19 + 46x^18 - 128x^17 + 222x^16 - 182x^15 - 183x^14 + 903x^13 - 1724x^12 + 2232x^11 - 2147x^10 + 1501x^9 - 608x^8 - 122x^7 + 474x^6 - 480x^5 + 309x^4 - 142x^3 + 45x^2 - 9x + 1	\( -\,2^{18}\cdot 19^{8}\cdot 83^{5} \)	20T989	Trivial (GRH)
20.2.34700415561107942970228736.1	x^20 - 2x^19 + 2x^18 - 6x^17 - 6x^15 + 26x^14 + 12x^13 + 56x^12 - 16x^11 - 76x^10 - 84x^9 + 22x^8 + 136x^7 - 48x^6 + 128x^5 + 28x^4 + 40x^3 + 16x^2 - 4x + 2	\( -\,2^{34}\cdot 13^{8}\cdot 19^{5} \)	20T989	Trivial (GRH)
20.6.34700415561107942970228736.1	x^20 - 2x^19 + 2x^18 + 4x^17 - 7x^16 - 18x^15 - 26x^14 + 6x^13 + 94x^11 + 54x^10 + 138x^9 + 280x^8 - 2x^7 + 166x^6 + 62x^5 - 177x^4 + 20x^3 - 12x^2 + 2x + 1	\( -\,2^{34}\cdot 13^{8}\cdot 19^{5} \)	20T989	Trivial (GRH)
20.0.199526484064428162466095321.1	x^20 - 10x^19 + 51x^18 - 174x^17 + 448x^16 - 932x^15 + 1637x^14 - 2493x^13 + 3336x^12 - 3935x^11 + 4109x^10 - 3842x^9 + 3206x^8 - 2293x^7 + 1399x^6 - 813x^5 + 424x^4 - 130x^3 + 14x^2 - 3x + 9	\( 3^{2}\cdot 17^{5}\cdot 97^{5}\cdot 42641^{2} \)	20T989	Trivial (GRH)
20.0.591987413523782063351660544.1	x^20 + 8x^18 - 6x^17 + 23x^16 - 52x^15 + 54x^14 - 128x^13 + 164x^12 - 116x^11 + 432x^10 - 116x^9 + 492x^8 - 248x^7 + 286x^6 + 72x^5 + 245x^4 + 160x^3 + 124x^2 + 54x + 9	\( 2^{36}\cdot 3^{21}\cdot 7^{7} \)	20T989	Trivial (GRH)
20.4.591987413523782063351660544.1	x^20 - 4x^19 - 2x^18 + 22x^17 + 10x^16 - 100x^15 + 18x^14 + 236x^13 - 224x^12 - 164x^11 + 522x^10 - 348x^9 - 294x^8 + 652x^7 - 388x^6 - 164x^5 + 510x^4 - 480x^3 + 272x^2 - 96x + 18	\( 2^{36}\cdot 3^{21}\cdot 7^{7} \)	20T989	Trivial (GRH)
20.6.622306464875034504147763200.1	x^20 - 4x^19 + 6x^18 - 19x^16 + 32x^15 - 61x^14 + 20x^13 - 18x^12 + 76x^11 - 321x^10 + 162x^9 - 216x^8 + 20x^7 + 85x^6 + 116x^5 + 159x^4 - 82x^3 + 44x^2 - 102x + 13	\( -\,2^{20}\cdot 3^{16}\cdot 5^{2}\cdot 223^{5} \)	20T989	Trivial (GRH)
20.4.1136314786920743836803137536.1	x^20 - 15x^18 + 115x^16 - 579x^14 + 2037x^12 - 5165x^10 + 9631x^8 - 12997x^6 + 11846x^4 - 6436x^2 + 1609	\( 2^{20}\cdot 317^{2}\cdot 1609^{5} \)	20T989	Trivial (GRH)
20.6.5600758183875310537329868800.1	x^20 - 10x^19 + 37x^18 - 48x^17 - 63x^16 + 300x^15 - 342x^14 - 204x^13 + 990x^12 - 688x^11 - 1292x^10 + 3242x^9 - 2595x^8 - 774x^7 + 3891x^6 - 4302x^5 + 2649x^4 - 972x^3 + 202x^2 - 22x + 1	\( -\,2^{20}\cdot 3^{18}\cdot 5^{2}\cdot 223^{5} \)	20T989	Trivial (GRH)
20.4.8733767413172976390878789632.2	x^20 + 7x^18 - 10x^17 + 4x^15 - 11x^14 - 2x^13 + 43x^12 + 30x^11 - 111x^10 + 82x^9 - 289x^8 - 356x^7 + 707x^6 - 386x^5 + 118x^4 + 344x^3 - 351x^2 + 18x + 41	\( 2^{20}\cdot 61^{5}\cdot 397^{5} \)	20T989	Trivial (GRH)
20.8.8733767413172976390878789632.2	x^20 - x^18 - 4x^17 - 15x^16 - 16x^15 - 47x^14 + 78x^13 + x^12 + 120x^11 + 229x^10 + 104x^9 - 264x^8 - 444x^7 - 207x^6 + 134x^5 + 230x^4 + 96x^3 - 17x^2 - 20x - 1	\( 2^{20}\cdot 61^{5}\cdot 397^{5} \)	20T989	Trivial (GRH)
20.4.8733767413172976390878789632.3	x^20 - 4x^19 + 5x^18 + 18x^17 - 88x^16 + 190x^15 - 200x^14 + 30x^13 + 256x^12 - 324x^11 + 183x^10 + 100x^9 - 2x^8 + 52x^7 + 40x^6 + 172x^5 + 165x^4 + 98x^3 + 40x^2 + 10x + 1	\( 2^{20}\cdot 61^{5}\cdot 397^{5} \)	20T989	Trivial (GRH)
20.8.8733767413172976390878789632.3	x^20 - 4x^19 - 2x^18 + 20x^17 + 11x^16 + 58x^15 - 380x^14 + 160x^13 + 499x^12 - 424x^11 + 682x^10 - 1802x^9 + 1636x^8 - 398x^7 + 42x^6 - 24x^5 - 143x^4 + 286x^3 - 270x^2 + 52x + 23	\( 2^{20}\cdot 61^{5}\cdot 397^{5} \)	20T989	Trivial (GRH)
20.4.8733767413172976390878789632.4	x^20 - 4x^19 + 6x^18 + 4x^17 - 58x^16 + 148x^15 - 272x^14 + 332x^13 - 331x^12 + 390x^11 - 577x^10 + 754x^9 - 434x^8 - 230x^7 - 73x^6 + 816x^5 + 67x^4 - 502x^3 - 247x^2 + 152x + 83	\( 2^{20}\cdot 61^{5}\cdot 397^{5} \)	20T989	Trivial (GRH)
20.4.8733767413172976390878789632.5	x^20 - 6x^19 + 10x^18 + 32x^17 - 146x^16 + 186x^15 + 152x^14 - 932x^13 + 1617x^12 - 1064x^11 - 1200x^10 + 3748x^9 - 4951x^8 + 5140x^7 - 5590x^6 + 6252x^5 - 5963x^4 + 4280x^3 - 2160x^2 + 702x - 109	\( 2^{20}\cdot 61^{5}\cdot 397^{5} \)	20T989	Trivial (GRH)
20.0.46045894455076759556429185024.1	x^20 - 2x^19 + 4x^18 - 23x^17 - x^16 - 61x^15 + 73x^14 + 126x^13 + 758x^12 + 1090x^11 + 2420x^10 + 2518x^9 + 3720x^8 + 2806x^7 + 3030x^6 + 1586x^5 + 1290x^4 + 398x^3 + 274x^2 + 24x + 32	\( 2^{20}\cdot 33769^{5} \)	20T989	Trivial (GRH)
20.4.46045894455076759556429185024.1	x^20 - 5x^19 + 9x^18 - x^17 - 38x^16 + 91x^15 - 29x^14 - 308x^13 + 943x^12 - 1429x^11 + 561x^10 + 1732x^9 - 5135x^8 + 5889x^7 - 4099x^6 + 736x^5 + 704x^4 - 302x^3 - 22x^2 + 9x + 1	\( 2^{20}\cdot 33769^{5} \)	20T989	Trivial (GRH)
20.4.46045894455076759556429185024.2	x^20 - 4x^19 + 2x^18 + 28x^17 - 116x^16 + 262x^15 - 380x^14 + 154x^13 + 1423x^12 - 6870x^11 + 20878x^10 - 49378x^9 + 94784x^8 - 149592x^7 + 195884x^6 - 211688x^5 + 182288x^4 - 117288x^3 + 51648x^2 - 13648x + 1616	\( 2^{20}\cdot 33769^{5} \)	20T989	Trivial (GRH)
20.8.46045894455076759556429185024.3	x^20 - x^19 - 9x^18 + 3x^17 - 10x^16 + 97x^15 + 92x^14 - 267x^13 - 93x^12 - 324x^11 + 594x^10 + 785x^9 - 783x^8 + 21x^7 - 639x^6 + 52x^5 + 944x^4 - 309x^3 - 324x^2 + 202x - 31	\( 2^{20}\cdot 33769^{5} \)	20T989	Trivial (GRH)
20.8.46045894455076759556429185024.4	x^20 - 6x^19 + 5x^18 + 45x^17 - 104x^16 - 100x^15 + 574x^14 - 323x^13 - 1362x^12 + 2824x^11 - 1202x^10 - 3007x^9 + 5526x^8 - 3956x^7 + 532x^6 + 1461x^5 - 1425x^4 + 606x^3 - 73x^2 - 22x + 4	\( 2^{20}\cdot 33769^{5} \)	20T989	Trivial (GRH)
20.10.375319694708943511165994008576.1	x^20 - 10x^18 - 16x^17 - 60x^16 - 20x^15 + 192x^14 - 132x^13 + 112x^12 + 336x^11 - 628x^10 + 748x^9 - 594x^8 + 84x^7 + 104x^6 - 204x^5 + 96x^4 + 8x^3 - 12x^2 + 12x + 2	\( -\,2^{40}\cdot 13^{10}\cdot 19^{5} \)	20T989	Trivial (GRH)
20.2.375319694708943511165994008576.1	x^20 + 10x^18 - 4x^17 + 63x^16 - 32x^15 + 108x^14 - 20x^13 - 196x^12 + 88x^11 - 260x^10 - 160x^9 + 938x^8 - 1044x^7 + 1596x^6 - 1524x^5 + 725x^4 - 68x^3 - 26x^2 - 1	\( -\,2^{40}\cdot 13^{10}\cdot 19^{5} \)	20T989	$[2]$ (GRH)
20.6.375319694708943511165994008576.1	x^20 - 10x^18 - 8x^17 + 26x^16 - 4x^15 - 100x^14 + 164x^13 + 830x^12 + 736x^11 - 624x^10 - 2160x^9 - 3606x^8 - 2940x^7 + 4156x^6 + 10988x^5 + 5112x^4 - 6160x^3 - 7672x^2 - 2716x - 214	\( -\,2^{40}\cdot 13^{10}\cdot 19^{5} \)	20T989	Trivial (GRH)
20.10.375319694708943511165994008576.2	x^20 - 20x^18 - 16x^17 + 136x^16 + 204x^15 - 312x^14 - 808x^13 + 180x^12 + 1668x^11 - 268x^10 - 4624x^9 - 3716x^8 + 3116x^7 + 7564x^6 + 5988x^5 + 2328x^4 + 288x^3 - 88x^2 - 20x + 2	\( -\,2^{40}\cdot 13^{10}\cdot 19^{5} \)	20T989	Trivial (GRH)
20.2.375319694708943511165994008576.2	x^20 - 4x^19 + 12x^18 - 32x^17 + 73x^16 - 124x^15 + 108x^14 + 204x^13 - 1008x^12 + 2864x^11 - 7356x^10 + 16132x^9 - 28266x^8 + 39096x^7 - 44516x^6 + 44216x^5 - 37389x^4 + 23088x^3 - 7252x^2 - 628x + 863	\( -\,2^{40}\cdot 13^{10}\cdot 19^{5} \)	20T989	$[2]$ (GRH)
20.6.375319694708943511165994008576.2	x^20 - 4x^19 + 12x^18 - 12x^17 - 38x^16 + 272x^15 - 740x^14 + 1020x^13 - 104x^12 - 2180x^11 + 3380x^10 - 872x^9 - 3648x^8 + 4860x^7 - 1944x^6 - 92x^5 - 340x^4 + 664x^3 - 276x^2 + 28x + 2	\( -\,2^{40}\cdot 13^{10}\cdot 19^{5} \)	20T989	Trivial (GRH)
20.4.614181896762472025726248091648.1	x^20 - 2x^19 - 8x^18 + 11x^17 + 29x^16 - 46x^15 - 76x^14 + 134x^13 + 106x^12 - 350x^11 - 78x^10 + 564x^9 - 45x^8 - 738x^7 + 276x^6 + 741x^5 - 538x^4 - 420x^3 + 512x^2 - 93x - 17	\( 2^{16}\cdot 11^{8}\cdot 157^{5}\cdot 677^{2} \)	20T989	Trivial (GRH)
20.0.1643730849252059749049366422528.1	x^20 + x^18 - 3x^17 + 53x^16 - 92x^15 + 140x^14 - 151x^13 + 788x^12 - 2408x^11 + 4727x^10 - 5446x^9 + 3408x^8 + 116x^7 - 1384x^6 + 329x^5 + 704x^4 - 373x^3 + 147x^2 - 27x + 5	\( 2^{10}\cdot 61^{5}\cdot 397^{5}\cdot 439^{2} \)	20T989	Trivial (GRH)
20.0.1643730849252059749049366422528.2	x^20 - 4x^19 + 13x^18 - 18x^17 + 27x^16 - 3x^15 - 38x^14 + 50x^13 + 127x^12 - 987x^11 + 3149x^10 - 7123x^9 + 14266x^8 - 23184x^7 + 32577x^6 - 41008x^5 + 43122x^4 - 37130x^3 + 30158x^2 - 19821x + 7453	\( 2^{10}\cdot 61^{5}\cdot 397^{5}\cdot 439^{2} \)	20T989	Trivial (GRH)
20.4.1697562448531136375219997900800.1	x^20 - 10x^19 + 49x^18 - 140x^17 + 242x^16 - 258x^15 + 211x^14 - 302x^13 + 193x^12 + 424x^11 - 1560x^10 + 1132x^9 - 342x^8 - 136x^7 - 1289x^6 + 878x^5 - 1271x^4 + 1678x^3 + 196x^2 + 60x + 423	\( 2^{20}\cdot 5^{2}\cdot 36497^{5} \)	20T989	Trivial (GRH)
20.12.1697562448531136375219997900800.2	x^20 - 4x^19 - 14x^18 + 96x^17 - 44x^16 - 716x^15 + 1461x^14 + 1274x^13 - 6892x^12 + 4206x^11 + 9489x^10 - 11622x^9 - 3572x^8 + 6582x^7 + 993x^6 + 164x^5 - 1534x^4 + 90x^3 + 580x^2 - 50x - 25	\( 2^{20}\cdot 5^{2}\cdot 36497^{5} \)	20T989	Trivial (GRH)
20.16.2946937245124912611611467841536.1	x^20 - 8x^19 + 15x^18 + 16x^17 - 94x^16 + 247x^15 - 384x^14 - 399x^13 + 1965x^12 - 1773x^11 + 230x^10 + 1969x^9 - 6699x^8 + 5415x^7 + 4790x^6 - 6455x^5 - 790x^4 + 2033x^3 + 173x^2 - 217x - 37	\( 2^{26}\cdot 33769^{5} \)	20T989	Trivial (GRH)
20.4.2946937245124912611611467841536.1	x^20 - 5x^19 + 15x^18 - 16x^17 - 18x^16 + 115x^15 - 107x^14 - 263x^13 + 983x^12 - 1826x^11 - 390x^10 + 3022x^9 - 10770x^8 + 7644x^7 - 2212x^6 - 23316x^5 + 41244x^4 - 30332x^3 + 30980x^2 - 2908x - 404	\( 2^{26}\cdot 33769^{5} \)	20T989	Trivial (GRH)
20.8.2946937245124912611611467841536.1	x^20 - 7x^19 + 32x^18 - 95x^17 + 196x^16 - 242x^15 - 223x^14 + 1763x^13 - 4717x^12 + 8050x^11 - 8117x^10 - 503x^9 + 17749x^8 - 25864x^7 + 23471x^6 + 167x^5 - 26570x^4 + 15915x^3 - 6673x^2 - 318x + 503	\( 2^{26}\cdot 33769^{5} \)	20T989	Trivial (GRH)
20.8.5993774335551541600171439685632.1	x^20 - 4x^19 - 8x^18 + 78x^17 - 105x^16 - 346x^15 + 1286x^14 - 468x^13 - 4080x^12 + 5930x^11 + 4515x^10 - 14414x^9 + 4073x^8 + 12070x^7 - 13703x^6 + 5324x^5 + 3799x^4 - 7978x^3 + 5668x^2 - 1878x + 241	\( 2^{20}\cdot 89417^{5} \)	20T989	Trivial (GRH)
20.0.5993774335551541600171439685632.2	x^20 - 9x^18 - 8x^17 + 40x^16 + 128x^15 + 354x^14 + 394x^13 + 283x^12 + 900x^11 + 1027x^10 + 2846x^9 + 4889x^8 - 398x^7 + 9398x^6 - 3986x^5 + 14867x^4 + 4812x^3 + 1274x^2 + 468x + 99	\( 2^{20}\cdot 89417^{5} \)	20T989	$[2]$ (GRH)
20.12.8943377831089127824259880583168.1	x^20 - 10x^19 + 20x^18 + 72x^17 - 213x^16 - 260x^15 + 626x^14 + 1044x^13 + 201x^12 - 3322x^11 - 5772x^10 + 3088x^9 + 14032x^8 + 8560x^7 - 9340x^6 - 17722x^5 - 6289x^4 + 4552x^3 + 3234x^2 + 570x + 29	\( 2^{30}\cdot 61^{5}\cdot 397^{5} \)	20T989	Trivial (GRH)
20.12.8943377831089127824259880583168.2	x^20 - 6x^19 - 8x^18 + 60x^17 + 134x^16 - 278x^15 - 1368x^14 + 1606x^13 + 5063x^12 - 7296x^11 - 7426x^10 + 14632x^9 + 4490x^8 - 12360x^7 - 472x^6 + 4468x^5 - 1504x^4 - 2358x^3 + 706x^2 + 1232x + 185	\( 2^{30}\cdot 61^{5}\cdot 397^{5} \)	20T989	Trivial (GRH)
20.0.15809782301365736641176025390625.1	x^20 - 3x^19 + 16x^17 - 27x^16 - 26x^15 + 192x^14 - 32x^13 - 1547x^12 + 4304x^11 - 2756x^10 - 10715x^9 + 33479x^8 - 45065x^7 + 31547x^6 - 12708x^5 + 12206x^4 - 11246x^3 - 2135x^2 + 3195x + 1741	\( 5^{12}\cdot 36497^{5} \)	20T989	$[2]$ (GRH)
20.0.15809782301365736641176025390625.2	x^20 - 3x^19 + 8x^18 - 10x^17 + 17x^16 + 68x^15 - 117x^14 + 416x^13 - 74x^12 - 432x^11 + 3365x^10 - 3312x^9 + 1908x^8 + 6724x^7 - 8547x^6 + 9431x^5 + 234x^4 - 4595x^3 + 10011x^2 - 6831x + 3159	\( 5^{12}\cdot 36497^{5} \)	20T989	$[2]$ (GRH)
20.16.32498348544416645150459976220672.1	x^20 - 6x^19 - 5x^18 + 110x^17 - 235x^16 - 296x^15 + 2114x^14 - 2988x^13 - 1469x^12 + 8568x^11 - 14458x^10 + 24196x^9 - 10590x^8 - 51064x^7 + 85957x^6 - 49886x^5 + 9847x^4 + 766x^3 - 456x^2 + 32x + 1	\( 2^{20}\cdot 61^{7}\cdot 397^{5} \)	20T989	Trivial (GRH)
20.4.32498348544416645150459976220672.1	x^20 + 5x^18 - 13x^16 - 78x^15 - 147x^14 - 604x^13 - 400x^12 - 1346x^11 - 1429x^10 + 2530x^9 - 6571x^8 + 11964x^7 - 9432x^6 + 14560x^5 + 7637x^4 + 9288x^3 + 16717x^2 + 4456x + 4241	\( 2^{20}\cdot 61^{7}\cdot 397^{5} \)	20T989	Trivial (GRH)
20.8.32498348544416645150459976220672.1	x^20 - 10x^17 - 36x^16 + 4x^15 - 228x^14 + 356x^13 - 301x^12 + 696x^11 + 3684x^10 - 40x^9 + 12558x^8 + 11194x^7 - 52236x^6 - 64746x^5 + 20711x^4 + 53720x^3 + 15069x^2 - 154x + 1037	\( 2^{20}\cdot 61^{7}\cdot 397^{5} \)	20T989	Trivial (GRH)
20.4.32498348544416645150459976220672.2	x^20 - 6x^19 + 3x^18 + 70x^17 - 298x^16 + 630x^15 - 1110x^14 + 2728x^13 - 5549x^12 + 6780x^11 - 4793x^10 + 3658x^9 - 1643x^8 + 180x^7 - 644x^6 + 2878x^5 + 989x^4 + 270x^3 - 200x^2 - 52x - 23	\( 2^{20}\cdot 61^{7}\cdot 397^{5} \)	20T989	Trivial (GRH)
20.8.32498348544416645150459976220672.2	x^20 - 10x^19 + 39x^18 - 62x^17 - 48x^16 + 516x^15 - 1248x^14 + 758x^13 + 2552x^12 - 5866x^11 + 5089x^10 - 838x^9 - 8095x^8 + 16220x^7 - 10742x^6 + 962x^5 + 4451x^4 - 6266x^3 + 3315x^2 - 5108x + 4091	\( 2^{20}\cdot 61^{7}\cdot 397^{5} \)	20T989	Trivial (GRH)