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 109)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.3937574412547571424825.1	x^20 - 5x^19 + 11x^18 - 9x^17 - 9x^16 + 34x^15 - 42x^14 + 21x^13 + 18x^12 - 46x^11 + 42x^10 - 16x^9 - 13x^8 + 25x^7 - 12x^6 - 4x^5 + 22x^4 - 21x^3 + 15x^2 - 6x + 1	\( 3^{10}\cdot 5^{2}\cdot 7\cdot 43^{2}\cdot 151\cdot 36943^{2} \)	20T1045	Trivial (GRH)
20.0.6092127302465063639061.1	x^20 - 3x^19 - x^18 + 15x^17 - 17x^16 - 16x^15 + 56x^14 - 48x^13 - 12x^12 + 77x^11 - 107x^10 + 87x^9 - 8x^8 - 109x^7 + 201x^6 - 214x^5 + 158x^4 - 84x^3 + 32x^2 - 8x + 1	\( 3^{10}\cdot 73^{2}\cdot 13921^{2}\cdot 99901 \)	20T1045	Trivial (GRH)
20.2.30774019386159912109375.1	x^20 - 7x^19 + 26x^18 - 68x^17 + 133x^16 - 195x^15 + 204x^14 - 106x^13 - 115x^12 + 413x^11 - 699x^10 + 881x^9 - 917x^8 + 819x^7 - 636x^6 + 430x^5 - 248x^4 + 118x^3 - 43x^2 + 11x - 1	\( -\,5^{12}\cdot 199^{2}\cdot 1471^{3} \)	20T1045	Trivial (GRH)
20.0.82665094518185166015625.1	x^20 - 2x^19 + 2x^18 + x^17 + 2x^15 + 3x^14 - 2x^13 + 6x^12 - 20x^11 + 37x^10 + 28x^9 - 26x^8 - 35x^7 + 42x^6 - 19x^5 - 3x^4 + 5x^3 + 6x^2 + 2x + 1	\( 5^{10}\cdot 31^{2}\cdot 89^{2}\cdot 199^{2}\cdot 28081 \)	20T1045	Trivial (GRH)
20.2.153870096930799560546875.1	x^20 - 3x^19 + 7x^18 - 12x^17 + 20x^16 - 27x^15 + 40x^14 - 66x^13 + 63x^12 - 91x^11 + 69x^10 - 9x^9 + 50x^8 + 15x^7 - 14x^6 - 17x^5 - 31x^4 - 13x^3 - 10x^2 - 2x - 1	\( -\,5^{13}\cdot 199^{2}\cdot 1471^{3} \)	20T1045	Trivial (GRH)
20.0.255091649759845126953125.1	x^20 - 10x^19 + 52x^18 - 183x^17 + 484x^16 - 1016x^15 + 1751x^14 - 2535x^13 + 3136x^12 - 3359x^11 + 3147x^10 - 2596x^9 + 1888x^8 - 1203x^7 + 660x^6 - 302x^5 + 111x^4 - 32x^3 + 10x^2 - 4x + 1	\( 5^{10}\cdot 41\cdot 71^{2}\cdot 4861\cdot 5099^{2} \)	20T1045	Trivial (GRH)
20.6.301326738635234130859375.1	x^20 - 2x^19 - 7x^18 + 21x^17 + 2x^16 - 71x^15 + 88x^14 + 62x^13 - 251x^12 + 140x^11 + 180x^10 - 135x^9 - 230x^8 + 259x^7 + 7x^6 - 78x^5 - 8x^4 + 24x^3 + x^2 - 5x + 1	\( -\,5^{12}\cdot 1039^{3}\cdot 1049^{2} \)	20T1045	Trivial (GRH)
20.4.304226899738556884765625.1	x^20 - x^19 - 2x^18 + 6x^17 + 2x^16 - 7x^15 - 7x^14 + 17x^13 - 5x^12 + x^11 + 6x^10 - 28x^9 - 54x^8 + 28x^7 + 95x^6 + 14x^5 - 48x^4 - 34x^3 + 11x^2 + 3x + 1	\( 5^{12}\cdot 1039^{2}\cdot 1049^{3} \)	20T1045	Trivial (GRH)
20.4.417549019713061806640625.1	x^20 - 10x^19 + 55x^18 - 210x^17 + 614x^16 - 1444x^15 + 2814x^14 - 4628x^13 + 6500x^12 - 7852x^11 + 8186x^10 - 7364x^9 + 5687x^8 - 3726x^7 + 2019x^6 - 860x^5 + 253x^4 - 28x^3 - 14x^2 + 7x - 1	\( 5^{10}\cdot 31\cdot 61^{2}\cdot 839\cdot 21019^{2} \)	20T1045	Trivial (GRH)
20.8.1208667589881678916015625.1	x^20 - 8x^18 - 5x^17 + 24x^16 + 14x^15 - 54x^14 - 7x^13 + 138x^12 + 57x^11 - 201x^10 - 171x^9 + 159x^8 + 207x^7 - 95x^6 - 166x^5 + 24x^4 + 77x^3 + 14x^2 - 6x - 1	\( 5^{10}\cdot 109\cdot 149\cdot 2760559^{2} \)	20T1045	Trivial (GRH)
20.4.1444745460180146494140625.1	x^20 - 10x^19 + 55x^18 - 210x^17 + 614x^16 - 1444x^15 + 2812x^14 - 4614x^13 + 6443x^12 - 7692x^11 + 7850x^10 - 6817x^9 + 4987x^8 - 3020x^7 + 1465x^6 - 531x^5 + 114x^4 + 8x^3 - 17x^2 + 6x + 1	\( 5^{10}\cdot 29\cdot 31\cdot 2099\cdot 280001^{2} \)	20T1045	Trivial (GRH)
20.2.1506633693176170654296875.1	x^20 - 4x^19 + 15x^17 - 9x^16 - 11x^15 + x^14 - 17x^13 + 46x^12 - x^11 - 73x^10 + 104x^9 + 18x^8 - 143x^7 + 150x^6 - 136x^5 + 37x^4 - 12x^3 - 11x^2 + 5x - 1	\( -\,5^{13}\cdot 1039^{3}\cdot 1049^{2} \)	20T1045	Trivial (GRH)
20.4.1521134498692784423828125.1	x^20 - 2x^19 - 6x^18 + 17x^17 + 14x^16 - 30x^15 - 33x^14 - 15x^13 + 119x^12 - 20x^11 - 123x^10 + 188x^9 - 154x^8 + x^7 + 89x^6 - 107x^5 + 102x^4 - 58x^3 + 26x^2 - 9x + 1	\( 5^{13}\cdot 1039^{2}\cdot 1049^{3} \)	20T1045	Trivial (GRH)
20.4.1578257679223144345703125.1	x^20 - 10x^19 + 54x^18 - 201x^17 + 568x^16 - 1280x^15 + 2365x^14 - 3641x^13 + 4708x^12 - 5121x^11 + 4661x^10 - 3500x^9 + 2105x^8 - 949x^7 + 261x^6 + 11x^5 - 53x^4 + 27x^3 - 6x^2 + 1	\( 5^{10}\cdot 619\cdot 1399\cdot 432001^{2} \)	20T1045	Trivial (GRH)
20.2.3919998265087984677734375.1	x^20 - 10x^19 + 51x^18 - 174x^17 + 438x^16 - 852x^15 + 1306x^14 - 1576x^13 + 1448x^12 - 888x^11 + 99x^10 + 599x^9 - 971x^8 + 980x^7 - 757x^6 + 474x^5 - 245x^4 + 103x^3 - 34x^2 + 8x - 1	\( -\,5^{10}\cdot 38231\cdot 3240299^{2} \)	20T1045	Trivial (GRH)
20.6.6719704070016640000000000.1	x^20 - 6x^18 + 12x^16 - 4x^14 - 25x^12 + 57x^10 - 66x^8 + 51x^6 - 26x^4 + 8x^2 - 1	\( -\,2^{16}\cdot 5^{10}\cdot 3240299^{2} \)	20T1045	Trivial (GRH)
20.2.12164157316311040000000000.2	x^20 - 2x^18 - 2x^16 + 9x^14 + x^12 - 11x^10 + x^8 + 7x^6 + x^4 - 3x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 1039^{2}\cdot 1049^{2} \)	20T1045	Trivial (GRH)
20.6.12164157316311040000000000.2	x^20 + 2x^18 - 2x^16 - 9x^14 + x^12 + 11x^10 + x^8 - 7x^6 + x^4 + 3x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 1039^{2}\cdot 1049^{2} \)	20T1045	Trivial (GRH)
20.4.18709453898395662900390625.1	x^20 - 10x^19 + 55x^18 - 210x^17 + 613x^16 - 1436x^15 + 2776x^14 - 4502x^13 + 6178x^12 - 7194x^11 + 7084x^10 - 5836x^9 + 3928x^8 - 2052x^7 + 721x^6 - 60x^5 - 121x^4 + 94x^3 - 39x^2 + 10x - 1	\( 5^{10}\cdot 29\cdot 8669\cdot 2760559^{2} \)	20T1045	Trivial (GRH)
20.2.34812983677427964951171875.1	x^20 - x^19 + x^18 - 6x^17 + 5x^16 - 10x^15 + 24x^14 + 8x^13 - 25x^12 - 69x^11 + 152x^10 - 89x^9 + 6x^8 - 83x^7 + 187x^6 - 260x^5 + 516x^4 - 813x^3 + 803x^2 - 457x + 109	\( -\,5^{10}\cdot 29\cdot 81799\cdot 1225879^{2} \)	20T1045	Trivial (GRH)
20.6.57538948540426240000000000.2	x^20 + x^16 - 9x^14 + 2x^12 - 16x^10 + 18x^8 - 3x^6 + 34x^4 + 4x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 2370451^{2} \)	20T1045	Trivial (GRH)
20.8.97156282846886820595703125.1	x^20 - 10x^19 + 34x^18 - 21x^17 - 134x^16 + 256x^15 + 140x^14 - 666x^13 + 59x^12 + 946x^11 - 236x^10 - 905x^9 + 191x^8 + 596x^7 - 32x^6 - 240x^5 - 40x^4 + 38x^3 + 17x^2 + 6x + 1	\( 5^{10}\cdot 61\cdot 108529\cdot 1225879^{2} \)	20T1045	Trivial (GRH)
20.2.97355529125679302500000000.1	x^20 + 12x^18 + 60x^16 + 162x^14 + 251x^12 + 201x^10 + 15x^8 - 117x^6 - 87x^4 - 18x^2 - 1	\( -\,2^{8}\cdot 5^{10}\cdot 11^{4}\cdot 1630891^{2} \)	20T1045	Trivial (GRH)
20.6.276787479753533440000000000.3	x^20 + x^18 - x^16 - 4x^14 - 4x^12 + 5x^10 + 2x^8 - x^6 + 4x^4 - x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 31^{2}\cdot 167711^{2} \)	20T1045	Trivial (GRH)
20.6.276787479753533440000000000.4	x^20 - x^18 - x^16 + 4x^14 - 4x^12 - 5x^10 + 2x^8 + x^6 + 4x^4 + x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 31^{2}\cdot 167711^{2} \)	20T1045	Trivial (GRH)
20.0.747973000399882240000000000.1	x^20 + 4x^18 + 9x^16 + 38x^14 + 116x^12 + 232x^10 + 410x^8 + 615x^6 + 598x^4 + 305x^2 + 61	\( 2^{20}\cdot 5^{10}\cdot 61^{3}\cdot 17939^{2} \)	20T1045	Trivial (GRH)
20.10.1254027648371107840000000000.1	x^20 - 6x^18 + 10x^16 - 4x^14 + 7x^12 - 12x^10 - 14x^8 + 18x^6 + 7x^4 - 5x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11066329^{2} \)	20T1045	Trivial (GRH)
20.2.1254027648371107840000000000.1	x^20 + 6x^18 + 10x^16 + 4x^14 + 7x^12 + 12x^10 - 14x^8 - 18x^6 + 7x^4 + 5x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11066329^{2} \)	20T1045	Trivial (GRH)
20.10.1287675250344566243662109375.1	x^20 - 10x^19 + 35x^18 - 30x^17 - 107x^16 + 244x^15 + 49x^14 - 533x^13 + 171x^12 + 651x^11 - 306x^10 - 544x^9 + 218x^8 + 329x^7 - 53x^6 - 142x^5 - 12x^4 + 39x^3 + 5x^2 - 5x - 1	\( -\,5^{10}\cdot 19\cdot 61\cdot 929\cdot 11066329^{2} \)	20T1045	Trivial (GRH)
20.10.1818446924078203240000000000.1	x^20 - 10x^18 + 37x^16 - 57x^14 + 11x^12 + 67x^10 - 59x^8 - 6x^6 + 16x^4 - 1	\( -\,2^{12}\cdot 5^{10}\cdot 491^{2}\cdot 434249^{2} \)	20T1045	Trivial (GRH)
20.10.2355133645630848640000000000.1	x^20 - 15x^18 + 96x^16 - 342x^14 + 741x^12 - 1002x^10 + 837x^8 - 410x^6 + 97x^4 - x^2 - 1	\( -\,2^{16}\cdot 5^{10}\cdot 60662149^{2} \)	20T1045	Trivial (GRH)
20.0.3196665012803057372744140625.1	x^20 - 10x^19 + 63x^18 - 282x^17 + 1004x^16 - 2932x^15 + 7270x^14 - 15492x^13 + 28800x^12 - 46908x^11 + 67392x^10 - 85330x^9 + 95374x^8 - 93518x^7 + 80175x^6 - 59214x^5 + 37267x^4 - 19294x^3 + 7985x^2 - 2351x + 439	\( 5^{10}\cdot 1759\cdot 61511\cdot 1739359^{2} \)	20T1045	Trivial (GRH)
20.10.5991589106524593640000000000.1	x^20 - 4x^18 + 11x^14 - x^12 - 4x^10 - 9x^8 - 9x^6 + 10x^4 + 7x^2 - 1	\( -\,2^{12}\cdot 5^{10}\cdot 29^{2}\cdot 13345751^{2} \)	20T1045	Trivial (GRH)
20.14.7753892385981245440000000000.1	x^20 - 11x^18 + 44x^16 - 71x^14 + 11x^12 + 92x^10 - 84x^8 + 16x^6 - 2x^4 + 4x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 27517559^{2} \)	20T1045	Trivial (GRH)
20.2.7753892385981245440000000000.1	x^20 + 11x^18 + 44x^16 + 71x^14 + 11x^12 - 92x^10 - 84x^8 - 16x^6 - 2x^4 - 4x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 27517559^{2} \)	20T1045	Trivial (GRH)
20.6.7753892385981245440000000000.2	x^20 + 2x^18 - x^16 - x^12 - 12x^10 - x^8 + 12x^6 + 3x^4 - 3x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 27517559^{2} \)	20T1045	Trivial (GRH)
20.6.8239247507322480640000000000.2	x^20 + x^18 - 11x^16 - 20x^14 + 12x^12 + 55x^10 + 42x^8 - 15x^6 - 34x^4 - 11x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3169^{2}\cdot 8951^{2} \)	20T1045	Trivial (GRH)
20.12.10534289551208156654064369664.1	x^20 - 10x^19 + 29x^18 + 24x^17 - 258x^16 + 228x^15 + 818x^14 - 1352x^13 - 1254x^12 + 3208x^11 + 966x^10 - 4198x^9 - 383x^8 + 3254x^7 + 177x^6 - 1460x^5 - 136x^4 + 330x^3 + 40x^2 - 24x + 1	\( 2^{30}\cdot 143569\cdot 8266513^{2} \)	20T1045	Trivial (GRH)
20.12.13977528553593540191650390625.1	x^20 - 10x^19 + 35x^18 - 30x^17 - 105x^16 + 228x^15 + 90x^14 - 540x^13 + 40x^12 + 800x^11 - 177x^10 - 815x^9 + 190x^8 + 560x^7 - 100x^6 - 247x^5 + 35x^4 + 60x^3 - 10x^2 - 5x + 1	\( 5^{20}\cdot 61^{2}\cdot 601^{2}\cdot 109049 \)	20T1045	Trivial (GRH)
20.0.17033456355953858560000000000.1	x^20 + 14x^18 + 86x^16 + 319x^14 + 818x^12 + 1563x^10 + 2320x^8 + 2489x^6 + 1661x^4 + 579x^2 + 79	\( 2^{20}\cdot 5^{10}\cdot 79\cdot 4588681^{2} \)	20T1045	Trivial (GRH)
20.16.17423096031535445218837890625.1	x^20 - 10x^19 + 31x^18 + 6x^17 - 213x^16 + 276x^15 + 461x^14 - 1121x^13 - 307x^12 + 2011x^11 - 225x^10 - 2071x^9 + 453x^8 + 1359x^7 - 279x^6 - 562x^5 + 98x^4 + 120x^3 - 20x^2 - 8x + 1	\( 5^{10}\cdot 11^{2}\cdot 135049\cdot 10448989^{2} \)	20T1045	Trivial (GRH)
20.4.36082669406290176321903394816.1	x^20 - 10x^19 + 49x^18 - 156x^17 + 354x^16 - 588x^15 + 698x^14 - 512x^13 + 34x^12 + 472x^11 - 666x^10 + 442x^9 - 35x^8 - 226x^7 + 221x^6 - 80x^5 - 20x^4 + 34x^3 - 12x^2 + 1	\( 2^{30}\cdot 47\cdot 10463\cdot 8266513^{2} \)	20T1045	Trivial (GRH)
20.2.37682138330093578240000000000.2	x^20 + 15x^18 + 96x^16 + 342x^14 + 741x^12 + 1002x^10 + 837x^8 + 410x^6 + 97x^4 + x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 60662149^{2} \)	20T1045	$[2]$ (GRH)
20.8.43959768010245351744384765625.1	x^20 - 10x^19 + 53x^18 - 192x^17 + 515x^16 - 1060x^15 + 1685x^14 - 2017x^13 + 1656x^12 - 563x^11 - 730x^10 + 1455x^9 - 1268x^8 + 529x^7 + 95x^6 - 275x^5 + 160x^4 - 29x^3 - 12x^2 + 7x - 1	\( 5^{13}\cdot 1039^{2}\cdot 7229\cdot 67931^{2} \)	20T1045	Trivial (GRH)
20.8.73780388329188759543642578125.1	x^20 - 10x^19 + 52x^18 - 183x^17 + 474x^16 - 936x^15 + 1415x^14 - 1583x^13 + 1154x^12 - 203x^11 - 752x^10 + 1125x^9 - 792x^8 + 171x^7 + 221x^6 - 241x^5 + 94x^4 + 6x^3 - 21x^2 + 8x - 1	\( 5^{10}\cdot 41^{2}\cdot 521^{2}\cdot 16921^{2}\cdot 57829 \)	20T1045	Trivial (GRH)
20.0.83090679921935322045009765625.1	x^20 - 10x^19 + 65x^18 - 300x^17 + 1108x^16 - 3356x^15 + 8641x^14 - 19097x^13 + 36774x^12 - 61875x^11 + 91524x^10 - 118771x^9 + 135257x^8 - 134179x^7 + 115282x^6 - 84424x^5 + 51870x^4 - 25800x^3 + 9968x^2 - 2678x + 419	\( 5^{10}\cdot 29\cdot 241\cdot 9941\cdot 11066329^{2} \)	20T1045	Trivial (GRH)
20.8.91397098909479510139150390625.1	x^20 - 10x^19 + 51x^18 - 174x^17 + 435x^16 - 828x^15 + 1207x^14 - 1303x^13 + 908x^12 - 105x^11 - 693x^10 + 1028x^9 - 776x^8 + 233x^7 + 168x^6 - 246x^5 + 123x^4 - 7x^3 - 23x^2 + 11x - 1	\( 5^{10}\cdot 29\cdot 149^{2}\cdot 24781\cdot 765899^{2} \)	20T1045	Trivial (GRH)
20.4.99675368705307102203369140625.1	x^20 - 10x^19 + 55x^18 - 210x^17 + 615x^16 - 1452x^15 + 2850x^14 - 4740x^13 + 6760x^12 - 8320x^11 + 8847x^10 - 8095x^9 + 6300x^8 - 4080x^7 + 2100x^6 - 771x^5 + 125x^4 + 60x^3 - 50x^2 + 15x - 1	\( 5^{20}\cdot 61^{2}\cdot 601^{2}\cdot 777641 \)	20T1045	Trivial (GRH)
20.2.117251634365529281807249309696.1	x^20 - 10x^19 + 59x^18 - 246x^17 + 795x^16 - 2076x^15 + 4490x^14 - 8156x^13 + 12522x^12 - 16268x^11 + 17796x^10 - 16210x^9 + 12043x^8 - 7030x^7 + 3003x^6 - 782x^5 + 41x^4 + 30x^3 + 10x^2 - 12x + 1	\( -\,2^{30}\cdot 449\cdot 3559\cdot 8266513^{2} \)	20T1045	$[3]$ (GRH)
20.4.158045650939267594240000000000.1	x^20 + 8x^18 + 23x^16 + 48x^14 + 90x^12 - 96x^10 - 834x^8 - 1392x^6 + 149x^4 + 2456x^2 + 571	\( 2^{20}\cdot 5^{10}\cdot 31^{2}\cdot 571\cdot 167711^{2} \)	20T1045	Trivial (GRH)