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 100)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.4102645060079682024636416.1	x^20 - 4x^17 - 4x^16 - 4x^15 + 16x^14 - 16x^13 + 76x^12 - 76x^11 + 64x^10 - 88x^9 + 24x^8 - 16x^7 - 64x^6 + 8x^5 + 48x^4 + 96x^3 + 104x^2 + 48x + 8	\( 2^{32}\cdot 13^{12}\cdot 41 \)	20T633	Trivial (GRH)
20.0.35069066786369201873014017.1	x^20 - 10x^19 + 35x^18 - 30x^17 - 107x^16 + 244x^15 + 50x^14 - 540x^13 + 184x^12 + 664x^11 - 364x^10 - 540x^9 + 330x^8 + 286x^7 - 165x^6 - 82x^5 + 35x^4 + 10x^3 + x^2 - 2x + 1	\( 3^{10}\cdot 17^{12}\cdot 1019353 \)	20T633	Trivial (GRH)
20.2.794111980409569671890599936.1	x^20 - 6x^18 - 8x^17 + 48x^16 - 36x^15 - 2x^14 - 164x^13 + 554x^12 - 872x^11 + 1004x^10 - 1012x^9 + 844x^8 - 544x^7 + 284x^6 - 104x^5 - 12x^4 + 48x^3 - 34x^2 + 12x - 2	\( -\,2^{40}\cdot 13^{12}\cdot 31 \)	20T633	Trivial (GRH)
20.2.6710886400000000000000000000.1	x^20 + 10x^18 + 45x^16 + 130x^14 + 250x^12 + 298x^10 + 165x^8 - 20x^6 - 50x^4 - 1	\( -\,2^{46}\cdot 5^{20} \)	20T633	Trivial (GRH)
20.0.62914560000000000000000000000.1	x^20 + 10x^16 + 30x^14 - 50x^12 - 264x^10 + 1745x^8 - 2410x^6 + 1295x^4 + 620x^2 + 54	\( 2^{43}\cdot 3\cdot 5^{22} \)	20T633	$[2]$ (GRH)
20.4.62914560000000000000000000000.1	x^20 + 10x^16 - 30x^14 - 50x^12 + 264x^10 + 1745x^8 + 2410x^6 + 1295x^4 - 620x^2 + 54	\( 2^{43}\cdot 3\cdot 5^{22} \)	20T633	$[2]$ (GRH)
20.0.62914560000000000000000000000.2	x^20 + 10x^18 + 35x^16 + 40x^14 - 40x^12 - 122x^10 - 40x^8 + 100x^6 + 105x^4 + 40x^2 + 6	\( 2^{43}\cdot 3\cdot 5^{22} \)	20T633	$[2]$ (GRH)
20.4.62914560000000000000000000000.2	x^20 - 10x^18 + 35x^16 - 40x^14 - 40x^12 + 122x^10 - 40x^8 - 100x^6 + 105x^4 - 40x^2 + 6	\( 2^{43}\cdot 3\cdot 5^{22} \)	20T633	$[2]$ (GRH)
20.10.2307408033657796196615222984704.1	x^20 - 6x^19 + x^18 + 74x^17 - 194x^16 - 32x^15 + 997x^14 - 1836x^13 + 551x^12 + 2994x^11 - 5405x^10 + 3524x^9 + 1107x^8 - 4010x^7 + 3306x^6 - 1000x^5 - 487x^4 + 672x^3 - 328x^2 + 80x - 8	\( -\,2^{34}\cdot 7^{8}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.0.14315153843200000000000000000000.1	x^20 - 10x^19 + 25x^18 + 60x^17 - 285x^16 - 372x^15 + 2510x^14 + 160x^13 - 10325x^12 + 70x^11 + 36707x^10 - 17430x^9 - 56505x^8 + 29100x^7 + 90110x^6 - 125026x^5 + 80395x^4 - 45850x^3 + 23555x^2 - 6890x + 853	\( 2^{28}\cdot 5^{20}\cdot 7^{8}\cdot 97 \)	20T633	$[5]$ (GRH)
20.12.16151856235604573376306560892928.1	x^20 - 2x^19 - 15x^18 - 6x^17 + 160x^16 + 236x^15 - 1123x^14 - 1222x^13 + 4578x^12 + 2606x^11 - 11248x^10 + 82x^9 + 15410x^8 - 7606x^7 - 11495x^6 + 9464x^5 + 4378x^4 - 4286x^3 - 597x^2 + 638x - 47	\( 2^{34}\cdot 7^{9}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.8.16151856235604573376306560892928.1	x^20 + 18x^18 + 59x^16 - 364x^14 - 1139x^12 + 3304x^10 + 743x^8 - 1866x^6 - 347x^4 + 180x^2 + 28	\( 2^{34}\cdot 7^{9}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.14.49465059721539005964938842734592.1	x^20 - 4x^19 - 18x^18 + 86x^17 + 128x^16 - 762x^15 - 667x^14 + 4154x^13 + 3587x^12 - 17668x^11 - 13857x^10 + 57466x^9 + 31387x^8 - 118368x^7 - 44926x^6 + 123080x^5 + 37156x^4 - 44592x^3 - 4936x^2 + 4768x - 368	\( -\,2^{30}\cdot 7^{11}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.6.49465059721539005964938842734592.1	x^20 - 2x^18 - 54x^16 - 48x^15 - 152x^14 - 108x^13 + 1079x^12 + 1144x^11 + 2168x^10 + 6792x^9 + 2216x^8 - 12216x^7 - 11954x^6 + 2616x^5 + 4839x^4 - 5288x^3 - 8692x^2 - 4184x - 713	\( -\,2^{30}\cdot 7^{11}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.0.57260615372800000000000000000000.1	x^20 - 10x^18 - 10x^17 + 35x^16 + 188x^15 - 170x^14 - 880x^13 - 20x^12 + 7060x^11 - 8546x^10 - 28940x^9 + 103320x^8 - 140080x^7 + 90390x^6 - 8876x^5 - 21025x^4 + 7680x^3 + 860x^2 - 470x + 185	\( 2^{30}\cdot 5^{20}\cdot 7^{8}\cdot 97 \)	20T633	$[10]$ (GRH)
20.10.113062993649232013634145926250496.1	x^20 - 26x^18 + 211x^16 - 394x^14 - 1546x^12 + 3258x^10 + 3207x^8 - 1760x^6 - 2040x^4 - 560x^2 - 49	\( -\,2^{34}\cdot 7^{10}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.14.113062993649232013634145926250496.1	x^20 - 2x^18 - 89x^16 + 106x^14 + 1854x^12 - 3398x^10 - 9065x^8 + 31024x^6 - 32732x^4 + 14700x^2 - 2401	\( -\,2^{34}\cdot 7^{10}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.10.113062993649232013634145926250496.2	x^20 - 6x^19 + 5x^18 + 16x^17 - 45x^16 + 306x^15 - 425x^14 - 2172x^13 + 4427x^12 + 6108x^11 - 17635x^10 - 7992x^9 + 41092x^8 + 3656x^7 - 60698x^6 - 1574x^5 + 54896x^4 + 6644x^3 - 26143x^2 - 5298x + 4151	\( -\,2^{34}\cdot 7^{10}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.10.197860238886156023859755370938368.1	x^20 + 12x^18 - 100x^16 - 524x^14 + 2940x^12 - 698x^10 - 6328x^8 + 1512x^6 + 3920x^4 - 196x^2 - 343	\( -\,2^{32}\cdot 7^{11}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.10.258429699769673174020904974286848.2	x^20 - 2x^19 - 15x^18 + 16x^17 + 74x^16 - 60x^15 - 164x^14 + 676x^13 + 1070x^12 - 3036x^11 - 5832x^10 + 3332x^9 + 10889x^8 + 782x^7 - 9441x^6 - 2860x^5 + 5377x^4 + 1754x^3 - 1603x^2 + 160x + 350	\( -\,2^{38}\cdot 7^{9}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.10.258429699769673174020904974286848.3	x^20 - 2x^19 - 9x^18 + 20x^17 - 61x^16 - 54x^15 + 293x^14 + 924x^13 + 1861x^12 - 4186x^11 - 13695x^10 + 324x^9 + 25195x^8 + 18102x^7 - 5175x^6 - 8720x^5 - 7797x^4 - 12590x^3 - 2553x^2 + 7604x + 3262	\( -\,2^{38}\cdot 7^{9}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.10.258429699769673174020904974286848.4	x^20 - 90x^16 + 208x^14 + 1771x^12 - 6994x^10 + 3430x^8 + 8346x^6 - 2127x^4 - 2730x^2 - 343	\( -\,2^{38}\cdot 7^{9}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.10.258429699769673174020904974286848.5	x^20 + 4x^18 - 32x^17 - 43x^16 - 32x^15 + 256x^14 + 900x^13 + 202x^12 - 2032x^11 - 3154x^10 + 104x^9 + 4218x^8 + 256x^7 - 4996x^6 - 1404x^5 + 2329x^4 + 520x^3 - 910x^2 - 400x - 28	\( -\,2^{38}\cdot 7^{9}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.10.258429699769673174020904974286848.6	x^20 - 12x^18 - 100x^16 + 308x^14 + 1560x^12 - 666x^10 - 1856x^8 + 288x^6 + 468x^4 - 48x^2 - 7	\( -\,2^{38}\cdot 7^{9}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.10.258429699769673174020904974286848.7	x^20 - 2x^19 - 13x^18 + 24x^17 + 53x^16 - 78x^15 + 85x^14 - 876x^13 - 6153x^12 - 6006x^11 + 14363x^10 + 32860x^9 + 15617x^8 - 15958x^7 - 23401x^6 - 11212x^5 + 1007x^4 + 5374x^3 + 3193x^2 + 680x + 46	\( -\,2^{38}\cdot 7^{9}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.14.367090109903933844075668896484375.1	x^20 - 5x^19 - 3x^18 + 16x^17 - 14x^16 + 306x^15 - 267x^14 - 587x^13 - 682x^12 - 1621x^11 + 4604x^10 + 6116x^9 - 4753x^8 - 6366x^7 - 166x^6 + 2044x^5 + 1142x^4 - 428x^3 - 284x^2 + 117x - 11	\( -\,5^{11}\cdot 13^{12}\cdot 19^{9} \)	20T633	Trivial (GRH)
20.6.367090109903933844075668896484375.1	x^20 - 12x^18 - 7x^17 + 42x^16 + 15x^15 - 114x^14 - 17x^13 + 459x^12 + 961x^11 + 908x^10 + 601x^9 + 2364x^8 + 6542x^7 + 5008x^6 - 15256x^5 - 53136x^4 - 81440x^3 - 73115x^2 - 37500x - 8525	\( -\,5^{11}\cdot 13^{12}\cdot 19^{9} \)	20T633	$[2]$ (GRH)
20.6.389951957688167557227972684414976.1	x^20 - 14x^18 - 165x^16 - 338x^14 + 1118x^12 + 5798x^10 + 9347x^8 + 6084x^6 + 676x^4 - 676x^2 - 169	\( -\,2^{34}\cdot 7^{8}\cdot 13^{14} \)	20T633	Trivial (GRH)
20.14.590696456616395826333497084084224.1	x^20 + 4x^18 - 44x^16 - 12x^14 + 429x^12 - 410x^10 - 942x^8 + 1582x^6 - 579x^4 + 66x^2 - 1	\( -\,2^{42}\cdot 7^{8}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.6.590696456616395826333497084084224.1	x^20 + 18x^18 + 113x^16 + 232x^14 - 447x^12 - 2798x^10 - 4289x^8 - 1992x^6 + 119x^4 + 82x^2 - 1	\( -\,2^{42}\cdot 7^{8}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.10.590696456616395826333497084084224.2	x^20 - 6x^18 - 89x^16 + 470x^14 + 690x^12 - 5326x^10 + 6399x^8 - 172x^6 - 1992x^4 - 216x^2 - 1	\( -\,2^{42}\cdot 7^{8}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.14.590696456616395826333497084084224.2	x^20 - 18x^18 + 113x^16 - 232x^14 - 447x^12 + 2798x^10 - 4289x^8 + 1992x^6 + 119x^4 - 82x^2 - 1	\( -\,2^{42}\cdot 7^{8}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.6.590696456616395826333497084084224.2	x^20 + 12x^18 + 12x^16 - 290x^14 - 1090x^12 - 632x^10 + 2753x^8 + 4782x^6 + 2069x^4 - 204x^2 - 4	\( -\,2^{42}\cdot 7^{8}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.10.590696456616395826333497084084224.3	x^20 + 6x^18 - 89x^16 - 470x^14 + 690x^12 + 5326x^10 + 6399x^8 + 172x^6 - 1992x^4 + 216x^2 - 1	\( -\,2^{42}\cdot 7^{8}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.14.590696456616395826333497084084224.3	x^20 - 18x^18 + 75x^16 + 184x^14 - 1711x^12 + 1888x^10 + 6043x^8 - 11814x^6 - 63x^4 + 6632x^2 - 16	\( -\,2^{42}\cdot 7^{8}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.6.590696456616395826333497084084224.3	x^20 - 4x^18 - 44x^16 + 12x^14 + 429x^12 + 410x^10 - 942x^8 - 1582x^6 - 579x^4 - 66x^2 - 1	\( -\,2^{42}\cdot 7^{8}\cdot 13^{12} \)	20T633	$[2]$ (GRH)
20.14.590696456616395826333497084084224.4	x^20 - 12x^18 + 12x^16 + 290x^14 - 1090x^12 + 632x^10 + 2753x^8 - 4782x^6 + 2069x^4 + 204x^2 - 4	\( -\,2^{42}\cdot 7^{8}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.12.791440955544624095439021483753472.1	x^20 - 6x^19 - 5x^18 + 86x^17 - 96x^16 - 574x^15 + 1037x^14 + 2668x^13 - 3561x^12 - 8384x^11 + 3898x^10 + 15790x^9 + 6214x^8 - 10452x^7 - 13533x^6 - 3750x^5 + 4003x^4 + 2948x^3 + 69x^2 - 374x - 73	\( 2^{34}\cdot 7^{11}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.16.791440955544624095439021483753472.1	x^20 - 2x^19 - 25x^18 + 44x^17 + 268x^16 - 280x^15 - 2320x^14 + 2288x^13 + 10310x^12 - 10410x^11 - 24508x^10 + 23034x^9 + 32277x^8 - 26682x^7 - 22881x^6 + 16730x^5 + 7847x^4 - 5398x^3 - 894x^2 + 700x - 49	\( 2^{34}\cdot 7^{11}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.4.791440955544624095439021483753472.1	x^20 - 12x^18 - 14x^17 + 66x^16 + 122x^15 - 43x^14 - 1110x^13 - 2221x^12 - 3720x^11 - 1617x^10 + 9562x^9 + 14353x^8 + 10942x^7 + 12800x^6 + 11246x^5 + 5906x^4 - 392x^3 - 3848x^2 - 2748x - 1559	\( 2^{34}\cdot 7^{11}\cdot 13^{12} \)	20T633	$[2]$ (GRH)
20.8.791440955544624095439021483753472.1	x^20 - 6x^19 + 9x^18 + 24x^17 - 177x^16 + 530x^15 - 515x^14 - 1744x^13 + 7593x^12 - 14064x^11 + 8841x^10 + 28612x^9 - 91520x^8 + 116060x^7 - 64174x^6 + 6790x^5 - 6254x^4 + 14100x^3 + 711x^2 - 4382x - 449	\( 2^{34}\cdot 7^{11}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.10.989211243530600674561802500000000.1	x^20 - 6x^18 - 102x^16 + 806x^14 - 848x^12 - 2064x^10 - 18x^8 + 590x^6 + 50x^4 - 24x^2 - 1	\( -\,2^{8}\cdot 5^{10}\cdot 13^{12}\cdot 19^{8} \)	20T633	Trivial (GRH)
20.10.989211243530600674561802500000000.2	x^20 + 3x^18 - 23x^16 - 50x^14 + 182x^12 + 188x^10 - 543x^8 + 19x^6 + 146x^4 + 23x^2 - 1	\( -\,2^{8}\cdot 5^{10}\cdot 13^{12}\cdot 19^{8} \)	20T633	Trivial (GRH)
20.12.2729663703817172900595808790904832.1	x^20 - 6x^19 - 23x^18 + 198x^17 + 82x^16 - 2588x^15 + 2075x^14 + 17320x^13 - 27089x^12 - 63410x^11 + 145925x^10 + 127220x^9 - 413721x^8 - 152650x^7 + 603232x^6 + 171608x^5 - 351031x^4 - 119520x^3 + 68688x^2 + 25872x + 968	\( 2^{34}\cdot 7^{9}\cdot 13^{14} \)	20T633	Trivial (GRH)
20.8.2729663703817172900595808790904832.1	x^20 - 8x^19 + 24x^18 - 42x^17 + 57x^16 + 24x^15 - 481x^14 + 2142x^13 - 6799x^12 + 14196x^11 - 20613x^10 + 21264x^9 - 14282x^8 + 11226x^7 - 12985x^6 + 3642x^5 + 10733x^4 - 5848x^3 - 808x^2 - 312x - 4	\( 2^{34}\cdot 7^{9}\cdot 13^{14} \)	20T633	Trivial (GRH)
20.12.2729663703817172900595808790904832.2	x^20 - 2x^19 - 9x^18 + 6x^17 - 94x^16 - 38x^15 + 1267x^14 + 1824x^13 - 4020x^12 - 13146x^11 - 3933x^10 + 31066x^9 + 44530x^8 - 6310x^7 - 68428x^6 - 50132x^5 + 12185x^4 + 24696x^3 + 4744x^2 - 2384x - 712	\( 2^{34}\cdot 7^{9}\cdot 13^{14} \)	20T633	$[2]$ (GRH)
20.8.2729663703817172900595808790904832.2	x^20 - 6x^19 + 9x^18 + 30x^17 - 42x^16 - 330x^15 + 323x^14 + 1958x^13 - 2029x^12 - 7898x^11 + 6324x^10 + 31926x^9 + 5410x^8 - 68044x^7 - 59876x^6 + 33940x^5 + 63383x^4 + 14828x^3 - 13836x^2 - 8216x - 1262	\( 2^{34}\cdot 7^{9}\cdot 13^{14} \)	20T633	$[2]$ (GRH)
20.12.4134875196314770784334479588589568.3	x^20 - 6x^18 - 71x^16 + 76x^14 + 438x^12 - 570x^10 - 568x^8 + 1196x^6 - 503x^4 - 20x^2 + 28	\( 2^{42}\cdot 7^{9}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.16.4134875196314770784334479588589568.3	x^20 - 24x^18 + 208x^16 - 820x^14 + 1381x^12 - 146x^10 - 2374x^8 + 2418x^6 - 495x^4 - 62x^2 + 7	\( 2^{42}\cdot 7^{9}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.4.4134875196314770784334479588589568.3	x^20 + 20x^18 + 46x^16 - 608x^14 - 4082x^12 - 10390x^10 - 12530x^8 - 6508x^6 - 642x^4 + 332x^2 + 7	\( 2^{42}\cdot 7^{9}\cdot 13^{12} \)	20T633	$[2]$ (GRH)