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 50 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.12912557303290376372337.1	x^20 - 5x^19 + 6x^18 + 11x^17 - 38x^16 + 35x^15 + 11x^14 - 60x^13 + 79x^12 - 69x^11 + 39x^10 + 5x^9 - 49x^8 + 68x^7 - 41x^6 - 7x^5 + 32x^4 - 27x^3 + 14x^2 - 5x + 1	\( 3^{10}\cdot 31^{8}\cdot 256393 \)	20T647	Trivial
20.0.93156735146378005577728.1	x^20 - 2x^17 + x^16 - 10x^15 + 3x^14 - 4x^13 + 9x^12 - 2x^11 + 46x^10 - 22x^9 + 67x^8 - 26x^7 + 41x^6 - 16x^5 + 15x^4 - 8x^3 + 5x^2 - 2x + 1	\( 2^{30}\cdot 11^{8}\cdot 337\cdot 1201 \)	20T647	Trivial
20.10.8095471366604708725498046875.1	x^20 - 10x^19 + 50x^18 - 165x^17 + 356x^16 - 400x^15 - 195x^14 + 1735x^13 - 3456x^12 + 3407x^11 - 282x^10 - 4525x^9 + 7220x^8 - 5379x^7 + 649x^6 + 3055x^5 - 3530x^4 + 2000x^3 - 559x^2 + 28x + 1	\( -\,5^{10}\cdot 211^{9} \)	20T647	Trivial (GRH)
20.10.2906949957743139152698231750656.1	x^20 - 10x^19 + 38x^18 - 42x^17 - 185x^16 + 892x^15 - 1788x^14 + 2006x^13 - 1504x^12 + 1280x^11 - 740x^10 - 1364x^9 + 1747x^8 + 408x^7 + 296x^6 - 910x^5 - 177x^4 + 142x^3 + 32x^2 - 14x + 1	\( -\,2^{30}\cdot 3^{10}\cdot 71^{9} \)	20T647	Trivial (GRH)
20.10.2906949957743139152698231750656.2	x^20 - 6x^19 + 6x^18 + 40x^17 - 124x^16 + 64x^15 + 312x^14 - 592x^13 - 148x^12 + 800x^11 + 1168x^10 - 2112x^9 - 1936x^8 + 2736x^7 + 2192x^6 - 1504x^5 - 2880x^4 + 1792x^3 + 608x^2 - 384x - 32	\( -\,2^{30}\cdot 3^{10}\cdot 71^{9} \)	20T647	Trivial (GRH)
20.10.2906949957743139152698231750656.3	x^20 - 8x^19 + 18x^18 + 12x^17 - 102x^16 + 40x^15 + 296x^14 + 120x^13 - 1518x^12 + 1910x^11 - 1404x^10 - 352x^9 + 3091x^8 - 1944x^7 - 1440x^6 + 1630x^5 - 118x^4 - 348x^3 + 150x^2 - 22x + 1	\( -\,2^{30}\cdot 3^{10}\cdot 71^{9} \)	20T647	Trivial (GRH)
20.8.6654746033489194899189150390625.1	x^20 - 10x^19 + 51x^18 - 174x^17 + 428x^16 - 772x^15 + 980x^14 - 694x^13 - 258x^12 + 1522x^11 - 2293x^10 + 1955x^9 - 713x^8 - 554x^7 + 1094x^6 - 887x^5 + 423x^4 - 108x^3 + 3x^2 + 6x - 1	\( 5^{10}\cdot 29\cdot 211^{8}\cdot 5981 \)	20T647	Trivial (GRH)
20.12.14289092045807824849178632126464.1	x^20 - 14x^18 + 41x^16 + 232x^14 - 1438x^12 + 1052x^10 + 6426x^8 - 11704x^6 + 1789x^4 + 4290x^2 + 349	\( 2^{30}\cdot 3^{10}\cdot 71^{8}\cdot 349 \)	20T647	Trivial (GRH)
20.8.14289092045807824849178632126464.1	x^20 + 14x^18 + 41x^16 - 232x^14 - 1438x^12 - 1052x^10 + 6426x^8 + 11704x^6 + 1789x^4 - 4290x^2 + 349	\( 2^{30}\cdot 3^{10}\cdot 71^{8}\cdot 349 \)	20T647	Trivial (GRH)
20.4.18789018913575782539820446777344.1	x^20 - 10x^19 + 57x^18 - 228x^17 + 695x^16 - 1684x^15 + 3296x^14 - 5230x^13 + 6620x^12 - 6362x^11 + 3928x^10 - 66x^9 - 3382x^8 + 4788x^7 - 3903x^6 + 1950x^5 - 363x^4 - 264x^3 + 245x^2 - 88x + 13	\( 2^{20}\cdot 3^{10}\cdot 71^{8}\cdot 311\cdot 1511 \)	20T647	Trivial (GRH)
20.12.38854866336594916280431294808064.1	x^20 - 6x^18 - 31x^16 + 168x^14 + 354x^12 - 1492x^10 - 1462x^8 + 4808x^6 + 1213x^4 - 3478x^2 + 949	\( 2^{30}\cdot 3^{10}\cdot 13\cdot 71^{8}\cdot 73 \)	20T647	Trivial (GRH)
20.8.38854866336594916280431294808064.1	x^20 + 6x^18 - 31x^16 - 168x^14 + 354x^12 + 1492x^10 - 1462x^8 - 4808x^6 + 1213x^4 + 3478x^2 + 949	\( 2^{30}\cdot 3^{10}\cdot 13\cdot 71^{8}\cdot 73 \)	20T647	Trivial (GRH)
20.10.40230886178715161405440000000000.1	x^20 - 4x^18 - 67x^16 + 166x^14 + 128x^12 - 390x^10 - 109x^8 + 286x^6 + 63x^4 - 44x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 211^{8} \)	20T647	Trivial (GRH)
20.14.40230886178715161405440000000000.1	x^20 - 10x^18 + 8x^16 + 218x^14 - 889x^12 + 1161x^10 - 134x^8 - 514x^6 + 36x^4 + 15x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 211^{8} \)	20T647	Trivial (GRH)
20.18.40230886178715161405440000000000.1	x^20 - 15x^18 + 67x^16 + 17x^14 - 954x^12 + 2868x^10 - 3604x^8 + 2016x^6 - 464x^4 + 40x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 211^{8} \)	20T647	Trivial (GRH)
20.2.40230886178715161405440000000000.1	x^20 + 15x^18 + 67x^16 - 17x^14 - 954x^12 - 2868x^10 - 3604x^8 - 2016x^6 - 464x^4 - 40x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 211^{8} \)	20T647	Trivial (GRH)
20.6.40230886178715161405440000000000.1	x^20 + 7x^18 - 12x^16 - 176x^14 - 288x^12 + 342x^10 + 991x^8 + 530x^6 - 40x^4 - 53x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 211^{8} \)	20T647	Trivial (GRH)
20.10.40230886178715161405440000000000.2	x^20 - 9x^18 + 3x^16 + 121x^14 - 168x^12 - 420x^10 + 578x^8 + 580x^6 - 438x^4 - 218x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 211^{8} \)	20T647	Trivial (GRH)
20.14.40230886178715161405440000000000.2	x^20 - 8x^18 + 15x^16 + 22x^14 - 87x^12 + 38x^10 + 89x^8 - 94x^6 + 23x^4 + 3x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 211^{8} \)	20T647	Trivial (GRH)
20.18.40230886178715161405440000000000.2	x^20 - 14x^18 + 74x^16 - 170x^14 + 75x^12 + 429x^10 - 918x^8 + 770x^6 - 275x^4 + 30x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 211^{8} \)	20T647	Trivial (GRH)
20.2.40230886178715161405440000000000.2	x^20 + 14x^18 + 74x^16 + 170x^14 + 75x^12 - 429x^10 - 918x^8 - 770x^6 - 275x^4 - 30x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 211^{8} \)	20T647	Trivial (GRH)
20.6.40230886178715161405440000000000.2	x^20 + 17x^18 + 104x^16 + 235x^14 - 152x^12 - 1483x^10 - 1615x^8 + 1206x^6 + 2399x^4 - 50x^2 - 841	\( -\,2^{20}\cdot 5^{10}\cdot 211^{8} \)	20T647	Trivial (GRH)
20.14.40230886178715161405440000000000.3	x^20 - x^18 - 31x^16 + 70x^14 + 115x^12 - 384x^10 + 117x^8 + 330x^6 - 255x^4 + 40x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 211^{8} \)	20T647	Trivial (GRH)
20.6.40230886178715161405440000000000.3	x^20 + 14x^18 + 28x^16 - 142x^14 - 418x^12 + 202x^10 + 1128x^8 + 537x^6 - 104x^4 - 56x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 211^{8} \)	20T647	Trivial (GRH)
20.14.40230886178715161405440000000000.4	x^20 - 33x^16 + 19x^14 + 288x^12 - 315x^10 - 639x^8 + 1085x^6 - 472x^4 + 66x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 211^{8} \)	20T647	Trivial (GRH)
20.6.40230886178715161405440000000000.4	x^20 + 14x^18 + 43x^16 - 14x^14 - 211x^12 - 225x^10 + 36x^8 + 148x^6 + 58x^4 + 2x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 211^{8} \)	20T647	Trivial (GRH)
20.20.269662190855447784427693097877504.1	x^20 - 10x^19 + 27x^18 + 42x^17 - 304x^16 + 188x^15 + 1160x^14 - 1618x^13 - 2074x^12 + 4462x^11 + 1690x^10 - 6300x^9 - 250x^8 + 4896x^7 - 471x^6 - 2004x^5 + 252x^4 + 354x^3 - 31x^2 - 10x + 1	\( 2^{20}\cdot 3^{10}\cdot 13\cdot 71^{9}\cdot 7307 \)	20T647	Trivial (GRH)
20.16.545032645598262935221392409362432.1	x^20 - 12x^18 + 53x^16 - 90x^14 - 33x^12 + 320x^10 - 370x^8 + 50x^6 + 157x^4 - 88x^2 + 13	\( 2^{40}\cdot 3^{10}\cdot 13\cdot 71^{8} \)	20T647	Trivial (GRH)
20.4.545032645598262935221392409362432.1	x^20 + 22x^18 + 149x^16 + 336x^14 - 492x^12 - 4106x^10 - 8833x^8 - 9122x^6 - 4535x^4 - 840x^2 + 13	\( 2^{40}\cdot 3^{10}\cdot 13\cdot 71^{8} \)	20T647	Trivial (GRH)
20.16.545032645598262935221392409362432.2	x^20 - 22x^18 + 149x^16 - 336x^14 - 492x^12 + 4106x^10 - 8833x^8 + 9122x^6 - 4535x^4 + 840x^2 + 13	\( 2^{40}\cdot 3^{10}\cdot 13\cdot 71^{8} \)	20T647	Trivial (GRH)
20.12.706388839731582814105670315409408.1	x^20 - 8x^19 + 18x^18 + 64x^17 - 456x^16 + 742x^15 + 1512x^14 - 8476x^13 + 11518x^12 + 12156x^11 - 66624x^10 + 87666x^9 + 23639x^8 - 200536x^7 + 233064x^6 - 106766x^5 - 10204x^4 + 37256x^3 - 18846x^2 + 4208x - 359	\( 2^{30}\cdot 3^{15}\cdot 71^{9} \)	20T647	Trivial (GRH)
20.8.706388839731582814105670315409408.1	x^20 - 8x^19 + 18x^18 - 32x^17 + 114x^16 - 68x^15 + 60x^14 - 580x^13 - 257x^12 + 306x^11 + 3570x^10 - 4440x^9 - 13642x^8 - 12022x^7 + 7998x^6 + 27772x^5 - 14092x^4 - 2680x^3 + 1380x^2 + 278x + 13	\( 2^{30}\cdot 3^{15}\cdot 71^{9} \)	20T647	Trivial (GRH)
20.12.706388839731582814105670315409408.2	x^20 - 8x^19 + 18x^18 + 88x^17 - 828x^16 + 2794x^15 - 4056x^14 - 2026x^13 + 19048x^12 - 33756x^11 + 23208x^10 + 16374x^9 - 53929x^8 + 57422x^7 - 36024x^6 + 11338x^5 + 3974x^4 - 3442x^3 - 264x^2 + 128x + 13	\( 2^{30}\cdot 3^{15}\cdot 71^{9} \)	20T647	Trivial (GRH)
20.8.706388839731582814105670315409408.2	x^20 - 8x^19 + 18x^18 - 56x^17 + 324x^16 - 356x^15 - 1572x^14 + 2528x^13 + 2818x^12 - 1914x^11 - 7776x^10 + 2496x^9 + 4883x^8 - 4924x^7 - 4056x^6 + 5314x^5 + 2774x^4 - 2944x^3 + 612x^2 + 962x - 347	\( 2^{30}\cdot 3^{15}\cdot 71^{9} \)	20T647	Trivial (GRH)
20.12.1166695699182739680757760000000000.1	x^20 - 2x^18 - 54x^16 + 181x^14 + 477x^12 - 2489x^10 + 2170x^8 + 1429x^6 - 1647x^4 + 146x^2 + 29	\( 2^{20}\cdot 5^{10}\cdot 29\cdot 211^{8} \)	20T647	Trivial (GRH)
20.12.3684293267187500000000000000000000.1	x^20 - 5x^18 - 60x^16 + 545x^14 - 1505x^12 + 1307x^10 + 605x^8 - 1045x^6 + 55x^4 + 110x^2 + 11	\( 2^{20}\cdot 5^{26}\cdot 11^{9} \)	20T647	Trivial (GRH)
20.16.3684293267187500000000000000000000.1	x^20 - 5x^18 - 70x^16 + 435x^14 - 595x^12 - 882x^10 + 3190x^8 - 3245x^6 + 1375x^4 - 220x^2 + 11	\( 2^{20}\cdot 5^{26}\cdot 11^{9} \)	20T647	Trivial (GRH)
20.4.3684293267187500000000000000000000.1	x^20 + 5x^18 - 70x^16 - 435x^14 - 595x^12 + 882x^10 + 3190x^8 + 3245x^6 + 1375x^4 + 220x^2 + 11	\( 2^{20}\cdot 5^{26}\cdot 11^{9} \)	20T647	Trivial (GRH)
20.8.3684293267187500000000000000000000.1	x^20 + 5x^18 - 60x^16 - 545x^14 - 1505x^12 - 1307x^10 + 605x^8 + 1045x^6 + 55x^4 - 110x^2 + 11	\( 2^{20}\cdot 5^{26}\cdot 11^{9} \)	20T647	Trivial (GRH)
20.12.3684293267187500000000000000000000.2	x^20 - 20x^18 + 105x^16 - 95x^14 - 460x^12 + 592x^10 + 770x^8 - 660x^6 - 605x^4 + 11	\( 2^{20}\cdot 5^{26}\cdot 11^{9} \)	20T647	Trivial (GRH)
20.16.3684293267187500000000000000000000.2	x^20 - 20x^18 + 135x^16 - 285x^14 - 505x^12 + 2517x^10 - 1155x^8 - 4180x^6 + 3905x^4 - 495x^2 + 11	\( 2^{20}\cdot 5^{26}\cdot 11^{9} \)	20T647	Trivial (GRH)
20.4.3684293267187500000000000000000000.2	x^20 + 20x^18 + 135x^16 + 285x^14 - 505x^12 - 2517x^10 - 1155x^8 + 4180x^6 + 3905x^4 + 495x^2 + 11	\( 2^{20}\cdot 5^{26}\cdot 11^{9} \)	20T647	Trivial (GRH)
20.8.3684293267187500000000000000000000.2	x^20 + 15x^18 + 35x^16 - 230x^14 - 375x^12 + 1058x^10 + 825x^8 - 1045x^6 - 880x^4 - 110x^2 + 11	\( 2^{20}\cdot 5^{26}\cdot 11^{9} \)	20T647	Trivial (GRH)
20.12.3684293267187500000000000000000000.3	x^20 - 10x^18 - 10x^16 + 435x^14 - 1600x^12 + 493x^10 + 7370x^8 - 12705x^6 + 4125x^4 + 2585x^2 + 11	\( 2^{20}\cdot 5^{26}\cdot 11^{9} \)	20T647	Trivial (GRH)
20.8.3684293267187500000000000000000000.3	x^20 + 10x^18 - 10x^16 - 435x^14 - 1600x^12 - 493x^10 + 7370x^8 + 12705x^6 + 4125x^4 - 2585x^2 + 11	\( 2^{20}\cdot 5^{26}\cdot 11^{9} \)	20T647	$[2]$ (GRH)
20.0.6853400654600934079309919922683904.1	x^20 + 46x^18 + 905x^16 + 9976x^14 + 67778x^12 + 294020x^10 + 815802x^8 + 1411160x^6 + 1437469x^4 + 773118x^2 + 167389	\( 2^{30}\cdot 3^{10}\cdot 71^{8}\cdot 73\cdot 2293 \)	20T647	$[2, 310]$ (GRH)
20.20.6853400654600934079309919922683904.1	x^20 - 46x^18 + 905x^16 - 9976x^14 + 67778x^12 - 294020x^10 + 815802x^8 - 1411160x^6 + 1437469x^4 - 773118x^2 + 167389	\( 2^{30}\cdot 3^{10}\cdot 71^{8}\cdot 73\cdot 2293 \)	20T647	Trivial (GRH)
20.10.8488716983708899056547840000000000.1	x^20 + 11x^18 - 60x^16 - 809x^14 - 1496x^12 + 2471x^10 + 4651x^8 - 3654x^6 - 1245x^4 + 1282x^2 - 211	\( -\,2^{20}\cdot 5^{10}\cdot 211^{9} \)	20T647	Trivial (GRH)
20.10.8488716983708899056547840000000000.2	x^20 - 11x^18 - 60x^16 + 809x^14 - 1496x^12 - 2471x^10 + 4651x^8 + 3654x^6 - 1245x^4 - 1282x^2 - 211	\( -\,2^{20}\cdot 5^{10}\cdot 211^{9} \)	20T647	Trivial (GRH)
20.0.8488716983708899056547840000000000.1	x^20 + 31x^18 + 400x^16 + 2803x^14 + 11673x^12 + 29690x^10 + 45591x^8 + 40229x^6 + 18429x^4 + 3581x^2 + 211	\( 2^{20}\cdot 5^{10}\cdot 211^{9} \)	20T647	$[806]$ (GRH)