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 all 48 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.96734117658432135757824.1	x^20 - 2x^18 + 4x^12 + 8x^10 - 14x^8 - 8x^6 + 15x^4 + 8x^2 + 1	\( 2^{24}\cdot 3^{10}\cdot 13^{4}\cdot 43^{4} \)	20T1028	Trivial (GRH)
20.0.1141225493760614275743744.2	x^20 - 7x^16 - 2x^14 + 29x^12 - 54x^10 + 77x^8 - 44x^6 - 4x^4 + 16x^2 + 16	\( 2^{32}\cdot 3^{10}\cdot 7^{4}\cdot 37^{4} \)	20T1028	Trivial (GRH)
20.0.2631600323952640000000000.2	x^20 - x^18 + x^16 - x^12 + 5x^10 - x^8 + 10x^6 - 5x^4 + x^2 + 1	\( 2^{32}\cdot 5^{10}\cdot 89^{4} \)	20T1028	Trivial (GRH)
20.0.2631600323952640000000000.3	x^20 - 2x^19 - 3x^18 + 6x^16 + 18x^15 + 15x^14 - 10x^13 - 51x^12 - 86x^11 - 54x^10 + 14x^9 + 127x^8 + 186x^7 + 191x^6 + 118x^5 + 56x^4 + 4x^3 - 5x^2 - 2x + 1	\( 2^{32}\cdot 5^{10}\cdot 89^{4} \)	20T1028	Trivial
20.4.5089088419440640000000000.1	x^20 - x^19 + 2x^18 + x^17 - 6x^16 + 7x^15 - 29x^14 + 36x^13 - 58x^12 + 94x^11 - 99x^10 + 115x^9 - 115x^8 + 60x^7 - 13x^6 - 39x^5 + 85x^4 - 64x^3 + 27x^2 - 9x + 1	\( 2^{20}\cdot 5^{10}\cdot 89^{6} \)	20T1028	Trivial (GRH)
20.4.13699542148527028116127744.1	x^20 - 2x^16 - 42x^14 + 25x^12 + 88x^10 - 31x^8 - 62x^6 + 10x^4 + 16x^2 + 1	\( 2^{38}\cdot 2657^{4} \)	20T1028	Trivial (GRH)
20.8.13699542148527028116127744.1	x^20 - 4x^19 + 4x^18 + 6x^17 - 10x^16 + 4x^15 - 9x^14 - 14x^13 - 23x^12 + 88x^11 + 8x^10 - 80x^9 - 18x^8 + 52x^7 + 76x^6 - 148x^5 + 82x^4 - 28x^3 + 22x^2 - 12x + 2	\( 2^{38}\cdot 2657^{4} \)	20T1028	Trivial (GRH)
20.4.54798168594108112464510976.2	x^20 + 7x^16 - 4x^15 - 26x^14 - 44x^13 - 8x^12 + 48x^11 + 84x^10 + 48x^9 - 8x^8 - 44x^7 - 26x^6 - 4x^5 + 7x^4 + 1	\( 2^{40}\cdot 2657^{4} \)	20T1028	Trivial (GRH)
20.4.288585859854484970400390625.1	x^20 - 6x^19 + 14x^18 - 21x^17 + 40x^16 - 60x^15 + 3x^14 + 126x^13 - 230x^12 + 382x^11 - 570x^10 + 197x^9 + 981x^8 - 1528x^7 + 265x^6 + 1238x^5 - 1018x^4 - 168x^3 + 564x^2 - 220x + 11	\( 5^{10}\cdot 11^{8}\cdot 13^{10} \)	20T1028	Trivial (GRH)
20.4.1302806635376803840000000000.1	x^20 - 8x^19 + 28x^18 - 42x^17 - 50x^16 + 378x^15 - 792x^14 + 484x^13 + 1612x^12 - 4944x^11 + 6148x^10 - 1420x^9 - 8204x^8 + 16200x^7 - 17408x^6 + 13096x^5 - 7736x^4 + 3776x^3 - 1408x^2 + 304x - 16	\( 2^{28}\cdot 5^{10}\cdot 89^{6} \)	20T1028	Trivial (GRH)
20.4.24186411178020252160000000000.1	x^20 + 5x^18 + 4x^16 - 8x^14 - 7x^12 - 2x^10 - 6x^8 + 7x^6 + 3x^4 - 2x^2 + 4	\( 2^{18}\cdot 5^{10}\cdot 9859^{4} \)	20T1028	Trivial (GRH)
20.8.32224748018872701886161485824.1	x^20 - 8x^19 + 12x^18 + 74x^17 - 309x^16 + 220x^15 + 919x^14 - 1980x^13 + 326x^12 + 2840x^11 - 2753x^10 - 232x^9 + 1302x^8 - 192x^7 - 313x^6 + 60x^5 + 53x^4 - 16x^3 - 9x^2 + 2x + 1	\( 2^{36}\cdot 97^{2}\cdot 2657^{4} \)	20T1028	Trivial (GRH)
20.8.34918889042392681418447265625.1	x^20 - 2x^19 - 10x^18 + 22x^17 + 35x^16 - 114x^15 - 10x^14 + 393x^13 - 338x^12 - 774x^11 + 685x^10 + 1308x^9 - 262x^8 - 2186x^7 + 600x^6 + 1437x^5 - 864x^4 - 454x^3 + 340x^2 + 55x - 41	\( 5^{10}\cdot 11^{10}\cdot 13^{10} \)	20T1028	Trivial (GRH)
20.8.34918889042392681418447265625.2	x^20 - 5x^19 + 3x^18 + 41x^17 - 83x^16 - 83x^15 + 336x^14 + 305x^13 - 1641x^12 + 696x^11 + 3004x^10 - 4574x^9 + 1589x^8 + 1974x^7 - 2598x^6 + 1324x^5 - 264x^4 - 69x^3 + 57x^2 - 13x + 1	\( 5^{10}\cdot 11^{10}\cdot 13^{10} \)	20T1028	Trivial (GRH)
20.4.128898992075490807544645943296.1	x^20 - 2x^19 + 15x^18 - 8x^17 + 82x^16 - 108x^15 + 286x^14 - 388x^13 + 892x^12 - 1256x^11 + 1134x^10 - 1140x^9 + 775x^8 - 1234x^7 + 1825x^6 - 1848x^5 + 1520x^4 - 704x^3 + 192x^2 - 32	\( 2^{38}\cdot 97^{2}\cdot 2657^{4} \)	20T1028	Trivial (GRH)
20.8.128898992075490807544645943296.1	x^20 - 4x^19 - 8x^18 + 64x^17 - 33x^16 - 384x^15 + 612x^14 + 984x^13 - 2899x^12 - 496x^11 + 6780x^10 - 2420x^9 - 8624x^8 + 4252x^7 + 5858x^6 - 2236x^5 - 1718x^4 + 436x^3 + 188x^2 - 40x - 2	\( 2^{38}\cdot 97^{2}\cdot 2657^{4} \)	20T1028	Trivial (GRH)
20.0.1244962716142623139840000000000.1	x^20 + 5x^18 + 17x^16 + 137x^14 + 530x^12 + 954x^10 + 905x^8 + 476x^6 + 136x^4 + 19x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 71^{4}\cdot 263^{4} \)	20T1028	Trivial (GRH)
20.4.1244962716142623139840000000000.1	x^20 - 5x^18 - 5x^16 - 7x^14 - 45x^12 - 27x^10 + 21x^8 + 15x^6 + 12x^4 + 10x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 71^{4}\cdot 263^{4} \)	20T1028	Trivial (GRH)
20.0.1244962716142623139840000000000.2	x^20 + 9x^18 + 21x^16 + 46x^14 + 216x^12 + 637x^10 + 983x^8 + 809x^6 + 332x^4 + 54x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 71^{4}\cdot 263^{4} \)	20T1028	Trivial (GRH)
20.4.1244962716142623139840000000000.2	x^20 - x^18 - 7x^16 - 23x^14 + 74x^12 + 104x^10 - 728x^8 + 248x^6 + 555x^4 + 47x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 71^{4}\cdot 263^{4} \)	20T1028	Trivial (GRH)
20.4.2062383873207852920714335092736.1	x^20 - 2x^18 - 32x^17 + x^16 - 48x^15 + 312x^14 + 48x^13 + 766x^12 + 32x^11 + 948x^10 + 32x^9 + 766x^8 + 48x^7 + 312x^6 - 48x^5 + x^4 - 32x^3 - 2x^2 + 1	\( 2^{42}\cdot 97^{2}\cdot 2657^{4} \)	20T1028	Trivial (GRH)
20.8.2062383873207852920714335092736.1	x^20 - 8x^19 + 32x^18 - 52x^17 - 52x^16 + 540x^15 - 1222x^14 + 380x^13 + 2637x^12 - 4908x^11 + 3506x^10 + 1972x^9 - 7775x^8 + 8188x^7 - 3210x^6 - 2324x^5 + 4742x^4 - 3604x^3 + 1294x^2 - 120x - 25	\( 2^{42}\cdot 97^{2}\cdot 2657^{4} \)	20T1028	Trivial (GRH)
20.12.183584292633496284375040000000000.1	x^20 - 4x^19 - 3x^18 + 20x^17 + 41x^16 - 56x^15 - 476x^14 + 784x^13 - 359x^12 + 1094x^11 + 5323x^10 - 17792x^9 - 3263x^8 + 36726x^7 - 11280x^6 - 22304x^5 + 14027x^4 - 1102x^3 - 5739x^2 + 1236x + 821	\( 2^{20}\cdot 5^{10}\cdot 13^{4}\cdot 29^{4}\cdot 31^{6} \)	20T1028	Trivial (GRH)
20.8.183584292633496284375040000000000.1	x^20 - x^19 - 18x^18 + 32x^17 + 35x^16 - 44x^15 + 434x^14 - 2188x^13 + 1469x^12 + 4651x^11 - 6138x^10 + 6844x^9 - 18777x^8 + 18640x^7 - 21146x^6 + 49786x^5 - 40151x^4 + 14515x^3 - 33350x^2 + 33350x - 7975	\( 2^{20}\cdot 5^{10}\cdot 13^{4}\cdot 29^{4}\cdot 31^{6} \)	20T1028	Trivial (GRH)
20.12.183584292633496284375040000000000.2	x^20 - 29x^18 - 24x^17 + 286x^16 + 384x^15 - 1302x^14 - 2726x^13 + 1607x^12 + 9590x^11 + 6731x^10 - 18784x^9 - 18224x^8 + 24668x^7 + 9238x^6 - 15284x^5 + 277x^4 + 3730x^3 - 731x^2 - 280x + 76	\( 2^{20}\cdot 5^{10}\cdot 13^{4}\cdot 29^{4}\cdot 31^{6} \)	20T1028	Trivial (GRH)
20.8.183584292633496284375040000000000.2	x^20 - 3x^19 - 7x^18 + 11x^17 + 9x^16 + 226x^15 - 962x^14 + 2140x^13 - 4019x^12 + 5171x^11 + 1351x^10 - 16779x^9 + 33795x^8 - 15670x^7 - 17818x^6 + 17486x^5 - 5419x^4 + 35x^3 + 279x^2 - 27x + 1	\( 2^{20}\cdot 5^{10}\cdot 13^{4}\cdot 29^{4}\cdot 31^{6} \)	20T1028	Trivial (GRH)
20.12.216657449683526321367040000000000.1	x^20 - 4x^18 - 93x^16 - 30x^14 + 2302x^12 + 4680x^10 - 11948x^8 - 24533x^6 + 24387x^4 - 4752x^2 + 121	\( 2^{20}\cdot 5^{10}\cdot 11^{10}\cdot 13^{8} \)	20T1028	Trivial (GRH)
20.8.216657449683526321367040000000000.1	x^20 - 23x^18 + 204x^16 - 833x^14 + 1250x^12 + 239x^10 + 372x^8 + 1702x^6 - 13519x^4 + 935x^2 + 14641	\( 2^{20}\cdot 5^{10}\cdot 11^{10}\cdot 13^{8} \)	20T1028	Trivial (GRH)
20.12.216657449683526321367040000000000.2	x^20 - 5x^18 - 4x^16 + 8x^14 + 292x^12 - 979x^10 + 825x^8 + 418x^6 - 506x^4 - 242x^2 + 121	\( 2^{20}\cdot 5^{10}\cdot 11^{10}\cdot 13^{8} \)	20T1028	Trivial (GRH)
20.8.216657449683526321367040000000000.2	x^20 + 4x^18 - 66x^16 - 142x^14 + 937x^12 - 271x^10 - 2300x^8 + 1374x^6 + 1892x^4 - 1309x^2 + 121	\( 2^{20}\cdot 5^{10}\cdot 11^{10}\cdot 13^{8} \)	20T1028	Trivial (GRH)
20.0.386855836117226742051972447207424.1	x^20 - 4x^19 - 6x^18 + 12x^17 + 119x^16 - 212x^15 + 80x^14 - 488x^13 + 947x^12 - 4508x^11 + 14200x^10 - 28960x^9 + 68544x^8 - 113416x^7 + 191478x^6 - 217264x^5 + 219800x^4 - 150188x^3 + 88070x^2 - 30108x + 8462	\( 2^{40}\cdot 2657^{6} \)	20T1028	$[2, 4]$ (GRH)
20.16.31025745455060872059381760000000000.1	x^20 - 4x^19 - 38x^18 + 109x^17 + 529x^16 - 1202x^15 - 3642x^14 + 7042x^13 + 13616x^12 - 24492x^11 - 25750x^10 + 49200x^9 + 17388x^8 - 49768x^7 + 7896x^6 + 16948x^5 - 9800x^4 + 1744x^3 + 132x^2 - 60x - 4	\( 2^{20}\cdot 5^{10}\cdot 13^{6}\cdot 29^{4}\cdot 31^{6} \)	20T1028	Trivial (GRH)
20.12.50078585648402965630812160000000000.1	x^20 - 2x^18 - 52x^16 + 112x^14 + 864x^12 - 1984x^10 - 4608x^8 + 11008x^6 + 2304x^4 - 6656x^2 + 1024	\( 2^{38}\cdot 5^{10}\cdot 13^{4}\cdot 29^{4}\cdot 31^{4} \)	20T1028	Trivial (GRH)
20.12.50078585648402965630812160000000000.2	x^20 - 9x^18 + 23x^16 + 6x^14 - 86x^12 + 46x^10 + 92x^8 - 56x^6 - 36x^4 + 16x^2 + 4	\( 2^{38}\cdot 5^{10}\cdot 13^{4}\cdot 29^{4}\cdot 31^{4} \)	20T1028	Trivial (GRH)
20.8.80536614178062737656473290627088384.1	x^20 + 2x^18 - 15x^16 - 18x^14 + 66x^12 + 52x^10 - 95x^8 - 44x^6 + 32x^4 + 16x^2 + 1	\( 2^{40}\cdot 3^{10}\cdot 23^{4}\cdot 1451^{4} \)	20T1028	Trivial (GRH)
20.16.154394390104770375159408640000000000.1	x^20 - 54x^18 + 1162x^16 - 38x^15 - 12768x^14 + 964x^13 + 75572x^12 - 6726x^11 - 228826x^10 - 12424x^9 + 272542x^8 + 314242x^7 + 108136x^6 - 1152224x^5 - 477021x^4 + 1420982x^3 + 469316x^2 - 474920x - 172880	\( 2^{20}\cdot 5^{10}\cdot 13^{4}\cdot 29^{6}\cdot 31^{6} \)	20T1028	Trivial (GRH)
20.8.305379083898498109827057671208960000.1	x^20 + 14x^18 + 66x^16 + 88x^14 - 164x^12 - 376x^10 + 220x^8 + 408x^6 - 300x^4 + 40x^2 + 4	\( 2^{46}\cdot 3^{10}\cdot 5^{4}\cdot 37^{4}\cdot 89^{4} \)	20T1028	Trivial (GRH)
20.4.496411927280973952950108160000000000.1	x^20 - 9x^19 + 44x^18 - 141x^17 + 381x^16 - 814x^15 + 438x^14 + 5506x^13 - 23992x^12 + 41448x^11 + 330x^10 - 139922x^9 + 157422x^8 + 448344x^7 - 1983912x^6 + 3755096x^5 - 4591244x^4 + 3841380x^3 - 2411536x^2 + 602780x + 345220	\( 2^{24}\cdot 5^{10}\cdot 13^{6}\cdot 29^{4}\cdot 31^{6} \)	20T1028	$[2]$ (GRH)
20.8.496411927280973952950108160000000000.1	x^20 - 3x^19 - 10x^18 + 74x^17 - 185x^16 - 182x^15 + 1950x^14 - 5168x^13 + 4181x^12 + 18679x^11 - 30482x^10 + 6736x^9 - 145851x^8 + 846882x^7 - 1187858x^6 - 1565642x^5 + 5591073x^4 - 4295009x^3 - 3561028x^2 + 5884406x - 2848669	\( 2^{24}\cdot 5^{10}\cdot 13^{6}\cdot 29^{4}\cdot 31^{6} \)	20T1028	$[2]$ (GRH)
20.4.496411927280973952950108160000000000.2	x^20 - 4x^19 - 6x^18 + 3x^17 - 83x^16 + 502x^15 + 262x^14 - 106x^13 - 1741x^12 - 15830x^11 + 11468x^10 + 25565x^9 - 8639x^8 + 195260x^7 - 204976x^6 - 348632x^5 + 139931x^4 + 738530x^3 - 118358x^2 - 497699x + 371831	\( 2^{24}\cdot 5^{10}\cdot 13^{6}\cdot 29^{4}\cdot 31^{6} \)	20T1028	$[2, 2]$ (GRH)
20.8.496411927280973952950108160000000000.2	x^20 - 4x^19 + 2x^18 + 43x^17 - 157x^16 - 14x^15 + 830x^14 - 2506x^13 - 4470x^12 + 11768x^11 + 33414x^10 + 23316x^9 - 29686x^8 - 49590x^7 - 78822x^6 - 210482x^5 - 207507x^4 - 182320x^3 - 303400x^2 - 250111x - 53861	\( 2^{24}\cdot 5^{10}\cdot 13^{6}\cdot 29^{4}\cdot 31^{6} \)	20T1028	Trivial (GRH)
20.0.909981640506746603991752188943663104.1	x^20 - 6x^19 + 69x^18 - 292x^17 + 1606x^16 - 5778x^15 + 19584x^14 - 70552x^13 + 179453x^12 - 528056x^11 + 1294936x^10 - 2773796x^9 + 6856148x^8 - 10134664x^7 + 26644588x^6 - 27420408x^5 + 71119940x^4 - 46490160x^3 + 131507456x^2 - 30312416x + 102461764	\( 2^{38}\cdot 97^{2}\cdot 2657^{6} \)	20T1028	$[2]$ (GRH)
20.12.3639926562026986415967008755774652416.1	x^20 - 8x^19 + 30x^18 - 176x^17 + 564x^16 + 1068x^15 - 12182x^14 + 45076x^13 - 69687x^12 - 139296x^11 + 732390x^10 - 1578764x^9 + 1455417x^8 + 4954512x^7 - 9709878x^6 + 2865480x^5 - 11267540x^4 - 13729296x^3 + 49234722x^2 + 15782492x - 22172191	\( 2^{40}\cdot 97^{2}\cdot 2657^{6} \)	20T1028	Trivial (GRH)
20.4.3712221088506796755731344625454022656.1	x^20 + 10x^18 + 31x^16 + 4x^14 - 152x^12 - 240x^10 + 36x^8 + 360x^6 + 297x^4 + 90x^2 + 9	\( 2^{58}\cdot 3^{18}\cdot 7^{4}\cdot 61^{4} \)	20T1028	Trivial (GRH)
20.12.113631861215080224467348285440000000000.1	x^20 - x^19 - 21x^18 + 61x^17 - 177x^16 - 676x^15 + 3960x^14 - 4704x^13 + 85642x^12 + 80254x^11 - 2192766x^10 - 233250x^9 + 17793574x^8 + 3352516x^7 - 60534112x^6 - 40761296x^5 + 44334749x^4 + 121164707x^3 + 136837803x^2 + 5360629x - 56509	\( 2^{20}\cdot 5^{10}\cdot 13^{4}\cdot 29^{10}\cdot 31^{4} \)	20T1028	$[2]$ (GRH)
20.16.1818109779441283591477572567040000000000.1	x^20 - 9x^19 - 12x^18 + 128x^17 + 525x^16 + 4236x^15 - 39076x^14 - 66298x^13 + 785766x^12 - 405306x^11 - 6177196x^10 + 10947276x^9 + 17250050x^8 - 57718272x^7 + 2051604x^6 + 94957418x^5 - 25985931x^4 - 67041885x^3 + 9187632x^2 + 16815772x + 1862501	\( 2^{24}\cdot 5^{10}\cdot 13^{4}\cdot 29^{10}\cdot 31^{4} \)	20T1028	$[2]$ (GRH)
20.16.1818109779441283591477572567040000000000.2	x^20 - 6x^19 - 85x^18 + 458x^17 + 2899x^16 - 12350x^15 - 52856x^14 + 140894x^13 + 529618x^12 - 530826x^11 - 2216342x^10 - 1532790x^9 - 3948130x^8 + 13834086x^7 + 61562848x^6 - 19969942x^5 - 150272139x^4 - 5953928x^3 + 73196147x^2 - 11874188x - 2533049	\( 2^{24}\cdot 5^{10}\cdot 13^{4}\cdot 29^{10}\cdot 31^{4} \)	20T1028	$[2]$ (GRH)
20.20.1389549804808197507073369468751841433841827840000000000.1	x^20 - 2278x^18 + 2225780x^16 - 1226506384x^14 + 421312835904x^12 - 93996224024960x^10 + 13732302535071360x^8 - 1288401536737102336x^6 + 73545110298746947584x^4 - 2273477282314176759808x^2 + 28413322415166317694976	\( 2^{40}\cdot 5^{10}\cdot 13^{4}\cdot 29^{4}\cdot 31^{4}\cdot 1381^{6} \)	20T1028	Trivial (GRH)