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 40 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.2825584168318748978373.1	x^20 - 7x^19 + 24x^18 - 52x^17 + 75x^16 - 58x^15 - 28x^14 + 140x^13 - 109x^12 - 274x^11 + 1033x^10 - 1874x^9 + 2367x^8 - 2282x^7 + 1739x^6 - 1057x^5 + 509x^4 - 190x^3 + 53x^2 - 10x + 1	\( 3^{10}\cdot 37^{5}\cdot 109^{2}\cdot 241^{2} \)	20T781	Trivial (GRH)
20.0.72240803899347741904989.1	x^20 - 7x^19 + 26x^18 - 73x^17 + 170x^16 - 346x^15 + 622x^14 - 944x^13 + 1183x^12 - 1208x^11 + 995x^10 - 691x^9 + 396x^8 - 166x^7 + 19x^6 + 42x^5 + 19x^4 - 19x^3 - 2x^2 + x + 1	\( 3^{10}\cdot 37^{2}\cdot 109^{5}\cdot 241^{2} \)	20T781	Trivial (GRH)
20.2.802821734410240000000000.1	x^20 - x^18 - 4x^16 + 3x^14 + 4x^12 + 3x^10 - 8x^8 + 4x^6 - 7x^4 + 5x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 280001^{2} \)	20T781	Trivial (GRH)
20.2.802821734410240000000000.2	x^20 + x^18 - 4x^16 - 3x^14 + 4x^12 - 3x^10 - 8x^8 - 4x^6 - 7x^4 - 5x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 280001^{2} \)	20T781	Trivial (GRH)
20.0.2654273542869531455078125.1	x^20 - 10x^19 + 56x^18 - 215x^17 + 624x^16 - 1431x^15 + 2656x^14 - 4025x^13 + 4975x^12 - 4954x^11 + 3877x^10 - 2297x^9 + 1026x^8 - 482x^7 + 441x^6 - 437x^5 + 280x^4 - 95x^3 + 8x^2 + 2x + 1	\( 5^{10}\cdot 61^{5}\cdot 17939^{2} \)	20T781	Trivial
20.2.12164157316311040000000000.1	x^20 + 7x^18 + 23x^16 + 58x^14 + 110x^12 + 125x^10 + 63x^8 - 5x^6 - 16x^4 - 6x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 1039^{2}\cdot 1049^{2} \)	20T781	Trivial (GRH)
20.6.12164157316311040000000000.1	x^20 - 7x^18 + 23x^16 - 58x^14 + 110x^12 - 125x^10 + 63x^8 + 5x^6 - 16x^4 + 6x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 1039^{2}\cdot 1049^{2} \)	20T781	Trivial (GRH)
20.2.57538948540426240000000000.1	x^20 - 6x^16 - x^14 + 13x^12 + 12x^10 - 3x^8 - 19x^6 - 18x^4 - 7x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 2370451^{2} \)	20T781	Trivial (GRH)
20.6.57538948540426240000000000.1	x^20 - 6x^16 + x^14 + 13x^12 - 12x^10 - 3x^8 + 19x^6 - 18x^4 + 7x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 2370451^{2} \)	20T781	Trivial (GRH)
20.6.276787479753533440000000000.1	x^20 - 4x^18 - x^16 + 12x^14 - 8x^12 - 16x^10 + 29x^8 + 36x^6 - 5x^4 - 12x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 31^{2}\cdot 167711^{2} \)	20T781	Trivial (GRH)
20.6.276787479753533440000000000.2	x^20 + 4x^18 - x^16 - 12x^14 - 8x^12 + 16x^10 + 29x^8 - 36x^6 - 5x^4 + 12x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 31^{2}\cdot 167711^{2} \)	20T781	Trivial (GRH)
20.10.7753892385981245440000000000.1	x^20 - 23x^16 + 10x^14 + 115x^12 - 171x^10 + 44x^8 + 64x^6 - 51x^4 + 13x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 27517559^{2} \)	20T781	Trivial (GRH)
20.6.7753892385981245440000000000.1	x^20 - 23x^16 - 10x^14 + 115x^12 + 171x^10 + 44x^8 - 64x^6 - 51x^4 - 13x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 27517559^{2} \)	20T781	Trivial (GRH)
20.10.8239247507322480640000000000.1	x^20 - 10x^18 + 34x^16 - 24x^14 - 126x^12 + 316x^10 - 176x^8 - 227x^6 + 312x^4 - 100x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3169^{2}\cdot 8951^{2} \)	20T781	Trivial (GRH)
20.6.8239247507322480640000000000.1	x^20 + 10x^18 + 34x^16 + 24x^14 - 126x^12 - 316x^10 - 176x^8 + 227x^6 + 312x^4 + 100x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3169^{2}\cdot 8951^{2} \)	20T781	Trivial (GRH)
20.0.9876551853017526544345703125.1	x^20 + 9x^18 + 33x^16 - 32x^15 + 58x^14 - 249x^13 + 99x^12 - 749x^11 + 746x^10 - 620x^9 + 3755x^8 + 1950x^7 + 10325x^6 + 2625x^5 + 18375x^4 - 4375x^3 + 15000x^2 - 3125x + 3125	\( 5^{10}\cdot 61^{7}\cdot 17939^{2} \)	20T781	Trivial (GRH)
20.8.13390863387968309382119140625.1	x^20 - 2x^19 - 7x^18 - x^17 - 7x^16 + 96x^15 + 146x^14 + 69x^13 - 364x^12 - 1030x^11 + 67x^10 + 690x^9 + 1251x^8 - 213x^7 - 578x^6 - 757x^5 - 1088x^4 - 543x^3 - 920x^2 - 158x + 89	\( 5^{10}\cdot 1039^{2}\cdot 1049^{5} \)	20T781	Trivial (GRH)
20.10.37682138330093578240000000000.1	x^20 - x^18 - 13x^16 - 3x^14 + 193x^12 - 437x^10 + 222x^8 + 376x^6 - 543x^4 + 220x^2 - 16	\( -\,2^{20}\cdot 5^{10}\cdot 60662149^{2} \)	20T781	Trivial (GRH)
20.2.37682138330093578240000000000.1	x^20 + x^18 - 13x^16 + 3x^14 + 193x^12 + 437x^10 + 222x^8 - 376x^6 - 543x^4 - 220x^2 - 16	\( -\,2^{20}\cdot 5^{10}\cdot 60662149^{2} \)	20T781	Trivial (GRH)
20.0.856720461657154802252744140625.1	x^20 - x^19 + 13x^18 - 8x^17 + 72x^16 + 67x^15 + 209x^14 + 302x^13 + 1705x^12 - 816x^11 + 7499x^10 - 2850x^9 + 14636x^8 - 2752x^7 + 17136x^6 - 1344x^5 + 12672x^4 + 256x^3 + 5888x^2 + 512x + 1024	\( 5^{10}\cdot 41^{5}\cdot 27517559^{2} \)	20T781	$[3]$ (GRH)
20.0.856720461657154802252744140625.2	x^20 - x^19 + 3x^18 + 2x^17 + 17x^16 - 28x^15 - 146x^14 - 518x^13 - 55x^12 - 11x^11 + 3309x^10 + 330x^9 + 7876x^8 - 1232x^7 + 11616x^6 - 4384x^5 + 11072x^4 - 4864x^3 + 5888x^2 - 2048x + 1024	\( 5^{10}\cdot 41^{5}\cdot 27517559^{2} \)	20T781	$[7]$ (GRH)
20.10.870283298342363146240000000000.1	x^20 - 6x^18 - 27x^16 + 157x^14 + 174x^12 - 757x^10 - 880x^8 + 126x^6 + 358x^4 + 86x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 419^{2}\cdot 695771^{2} \)	20T781	Trivial (GRH)
20.10.870283298342363146240000000000.2	x^20 + 6x^18 - 27x^16 - 157x^14 + 174x^12 + 757x^10 - 880x^8 - 126x^6 + 358x^4 - 86x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 419^{2}\cdot 695771^{2} \)	20T781	Trivial (GRH)
20.0.1307963560411124698019840000000000.1	x^20 + 37x^18 + 545x^16 + 4213x^14 + 19106x^12 + 53478x^10 + 93622x^8 + 100350x^6 + 61380x^4 + 17908x^2 + 1331	\( 2^{20}\cdot 5^{10}\cdot 11^{5}\cdot 28162171^{2} \)	20T781	$[2, 450]$ (GRH)
20.20.1307963560411124698019840000000000.1	x^20 - 37x^18 + 545x^16 - 4213x^14 + 19106x^12 - 53478x^10 + 93622x^8 - 100350x^6 + 61380x^4 - 17908x^2 + 1331	\( 2^{20}\cdot 5^{10}\cdot 11^{5}\cdot 28162171^{2} \)	20T781	Trivial (GRH)
20.0.3021085858887094365354739931640625.1	x^20 - 3x^19 + 52x^18 - 135x^17 + 1247x^16 - 2692x^15 + 17378x^14 - 29493x^13 + 153043x^12 - 187172x^11 + 880244x^10 - 628003x^9 + 3345087x^8 - 451586x^7 + 8534495x^6 + 4248851x^5 + 16216658x^4 + 14203125x^3 + 27779804x^2 + 12803557x + 35645021	\( 5^{10}\cdot 31^{2}\cdot 409^{5}\cdot 167711^{2} \)	20T781	$[6]$ (GRH)
20.0.3021085858887094365354739931640625.2	x^20 - 5x^19 + 53x^18 - 202x^17 + 1266x^16 - 3900x^15 + 18822x^14 - 47783x^13 + 192547x^12 - 404725x^11 + 1398203x^10 - 2439278x^9 + 7236290x^8 - 10416274x^7 + 26190577x^6 - 30201330x^5 + 62910983x^4 - 53623372x^3 + 89094183x^2 - 43814976x + 53486371	\( 5^{10}\cdot 31^{2}\cdot 409^{5}\cdot 167711^{2} \)	20T781	$[6]$ (GRH)
20.16.12201047854910721083176960000000000.1	x^20 - 43x^18 + 667x^16 - 4561x^14 + 12699x^12 - 1660x^10 - 51614x^8 + 56690x^6 + 44802x^4 - 68951x^2 + 6859	\( 2^{20}\cdot 5^{10}\cdot 19^{5}\cdot 3821^{2}\cdot 5741^{2} \)	20T781	Trivial (GRH)
20.8.14735319462983715612393284462890625.1	x^20 - x^19 - 90x^18 + 71x^17 + 3581x^16 - 2132x^15 - 82643x^14 + 35541x^13 + 1217625x^12 - 370164x^11 - 11886078x^10 + 2677732x^9 + 77335700x^8 - 15382586x^7 - 328689387x^6 + 76009560x^5 + 865682349x^4 - 290470403x^3 - 1272386337x^2 + 587290123x + 860975209	\( 5^{10}\cdot 1039^{2}\cdot 1049^{7} \)	20T781	Trivial (GRH)
20.0.158263590809746088460400640000000000.1	x^20 - 2x^19 + 16x^18 - 22x^17 + 251x^16 - 312x^15 + 2463x^14 - 2000x^13 + 19766x^12 - 13838x^11 + 120498x^10 - 55698x^9 + 586287x^8 - 253640x^7 + 2275221x^6 - 618928x^5 + 6380134x^4 - 1342832x^3 + 12643885x^2 - 2415578x + 11745679	\( 2^{20}\cdot 5^{10}\cdot 11^{7}\cdot 28162171^{2} \)	20T781	$[2, 4128]$ (GRH)
20.20.158263590809746088460400640000000000.1	x^20 - 2x^19 - 54x^18 + 94x^17 + 1143x^16 - 1700x^15 - 12135x^14 + 14904x^13 + 68650x^12 - 65530x^11 - 204926x^10 + 137838x^9 + 308487x^8 - 134032x^7 - 202403x^6 + 65416x^5 + 42182x^4 - 16204x^3 - 169x^2 + 470x - 31	\( 2^{20}\cdot 5^{10}\cdot 11^{7}\cdot 28162171^{2} \)	20T781	Trivial (GRH)
20.12.663454504774367623174543360000000000.1	x^20 - 99x^18 - 38x^17 + 4222x^16 + 2612x^15 - 102439x^14 - 74430x^13 + 1581705x^12 + 1155418x^11 - 16443936x^10 - 10746878x^9 + 117660653x^8 + 62059998x^7 - 571168620x^6 - 227369546x^5 + 1754967268x^4 + 526391474x^3 - 2885229281x^2 - 508131864x + 1903025191	\( 2^{20}\cdot 5^{10}\cdot 79^{5}\cdot 4588681^{2} \)	20T781	Trivial (GRH)
20.12.663454504774367623174543360000000000.2	x^20 - 99x^18 - 22x^17 + 4312x^16 + 1948x^15 - 108829x^14 - 74370x^13 + 1749120x^12 + 1577342x^11 - 18422931x^10 - 20094922x^9 + 126327623x^8 + 156814362x^7 - 542617125x^6 - 722933074x^5 + 1355308903x^4 + 1756330666x^3 - 1769937551x^2 - 1655050866x + 1098795961	\( 2^{20}\cdot 5^{10}\cdot 79^{5}\cdot 4588681^{2} \)	20T781	Trivial (GRH)
20.16.898336514802612753926973440000000000.1	x^20 - 4x^19 - 63x^18 + 238x^17 + 1781x^16 - 6364x^15 - 29556x^14 + 101334x^13 + 313830x^12 - 1048588x^11 - 2182234x^10 + 7098988x^9 + 9888373x^8 - 30275176x^7 - 28527308x^6 + 75872184x^5 + 48979284x^4 - 98760184x^3 - 41887024x^2 + 50121528x + 11181241	\( 2^{20}\cdot 5^{10}\cdot 41^{5}\cdot 27517559^{2} \)	20T781	Trivial (GRH)
20.0.1389699584855939161315850240000000000.1	x^20 + 4x^18 + 10x^16 + 16x^14 + 19x^12 + 23x^10 + 24x^8 + 25x^6 + 15x^4 + 7x^2 + 11	\( 2^{20}\cdot 5^{10}\cdot 11^{5}\cdot 1871^{2}\cdot 490631^{2} \)	20T781	$[2]$ (GRH)
20.4.1389699584855939161315850240000000000.1	x^20 - 4x^18 + 10x^16 - 16x^14 + 19x^12 - 23x^10 + 24x^8 - 25x^6 + 15x^4 - 7x^2 + 11	\( 2^{20}\cdot 5^{10}\cdot 11^{5}\cdot 1871^{2}\cdot 490631^{2} \)	20T781	Trivial (GRH)
20.0.2175387789678847853864459764982874112.1	x^20 + 4x^18 + 10x^16 + 16x^14 + 19x^12 + 22x^10 + 22x^8 + 22x^6 + 13x^4 + 6x^2 + 7	\( 2^{50}\cdot 7^{5}\cdot 339057497^{2} \)	20T781	$[2]$ (GRH)
20.4.2175387789678847853864459764982874112.1	x^20 - 4x^18 + 10x^16 - 16x^14 + 19x^12 - 22x^10 + 22x^8 - 22x^6 + 13x^4 - 6x^2 + 7	\( 2^{50}\cdot 7^{5}\cdot 339057497^{2} \)	20T781	Trivial (GRH)
20.10.8411799526250997899915089732983470958069760000000000.1	x^20 - 1912x^18 + 1535084x^16 - 775539485x^14 + 265312180916x^12 - 58487400397679x^10 + 7046810726338171x^8 - 55091880668161990x^6 - 99376354587176198511x^4 + 9498393828889421896758x^2 - 223230418947143342493949	\( -\,2^{20}\cdot 5^{10}\cdot 60662149^{5} \)	20T781	$[10]$ (GRH)
20.2.8411799526250997899915089732983470958069760000000000.1	x^20 + 1912x^18 + 1535084x^16 + 775539485x^14 + 265312180916x^12 + 58487400397679x^10 + 7046810726338171x^8 + 55091880668161990x^6 - 99376354587176198511x^4 - 9498393828889421896758x^2 - 223230418947143342493949	\( -\,2^{20}\cdot 5^{10}\cdot 60662149^{5} \)	20T781	$[2, 2]$ (GRH)