Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 28 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.2.836462656905295624404992.1	x^18 - x^16 - 25x^14 + 91x^12 + 30x^10 - 974x^8 + 3243x^6 - 5865x^4 + 6072x^2 - 2783	\( 2^{18}\cdot 11^{6}\cdot 23^{9} \)	18T781	Trivial (GRH)
18.2.836462656905295624404992.2	x^18 - 3x^16 + 21x^14 - 67x^12 + 152x^10 - 476x^8 + 345x^6 - 1426x^4 - 253x^2 - 2783	\( 2^{18}\cdot 11^{6}\cdot 23^{9} \)	18T781	Trivial (GRH)
18.8.5450990450694506414080000.1	x^18 - 8x^17 + 23x^16 - 6x^15 - 144x^14 + 404x^13 - 376x^12 - 406x^11 + 1756x^10 - 2502x^9 + 1632x^8 + 318x^7 - 1872x^6 + 2140x^5 - 1454x^4 + 638x^3 - 167x^2 + 22x - 1	\( -\,2^{26}\cdot 5^{4}\cdot 37^{9} \)	18T781	Trivial (GRH)
18.8.5450990450694506414080000.2	x^18 - 6x^17 + 19x^16 - 28x^15 - 12x^14 + 158x^13 - 390x^12 + 504x^11 - 300x^10 - 208x^9 + 604x^8 - 592x^7 + 348x^6 - 58x^5 - 66x^4 + 52x^3 - 33x^2 + 10x - 1	\( -\,2^{26}\cdot 5^{4}\cdot 37^{9} \)	18T781	Trivial (GRH)
18.0.9201089225958251868454912.1	x^18 + 16x^16 + 117x^14 + 540x^12 + 1842x^10 + 5217x^8 + 13386x^6 + 29601x^4 + 44528x^2 + 30613	\( -\,2^{18}\cdot 11^{7}\cdot 23^{9} \)	18T781	Trivial (GRH)
18.0.9201089225958251868454912.2	x^18 + 2x^16 - 16x^14 + 75x^12 + 73x^10 + 1025x^8 - 3298x^6 + 8107x^4 + 13915x^2 + 30613	\( -\,2^{18}\cdot 11^{7}\cdot 23^{9} \)	18T781	$[2]$ (GRH)
18.4.21803961802778025656320000.1	x^18 - 5x^16 - 26x^14 + 46x^12 + 276x^10 + 576x^8 + 814x^6 + 666x^4 + 259x^2 + 37	\( -\,2^{28}\cdot 5^{4}\cdot 37^{9} \)	18T781	Trivial (GRH)
18.4.87215847211112102625280000.1	x^18 - x^16 - 18x^14 + 38x^12 + 216x^10 - 44x^8 - 934x^6 - 1230x^4 - 481x^2 + 37	\( -\,2^{30}\cdot 5^{4}\cdot 37^{9} \)	18T781	Trivial (GRH)
18.2.2790907110755587284008960000.1	x^18 + 6x^16 - 6x^14 - 6x^12 + 470x^10 + 724x^8 - 2804x^6 - 5934x^4 - 1480x^2 - 74	\( 2^{35}\cdot 5^{4}\cdot 37^{9} \)	18T781	$[2]$ (GRH)
18.2.4858370905865925051228160000.1	x^18 - x^17 + 9x^16 + 6x^15 - 4x^14 + 144x^13 - 144x^12 + 304x^11 + 543x^10 + 2013x^9 + 3911x^8 + 12416x^7 + 20216x^6 + 25660x^5 + 19866x^4 + 6872x^3 - 3915x^2 + 2605x - 1367	\( 2^{16}\cdot 5^{4}\cdot 37^{9}\cdot 97^{3} \)	18T781	$[2]$ (GRH)
18.6.61549879966948467200000000000.1	x^18 - 4x^17 - 8x^16 + 18x^15 + 116x^14 - 60x^13 - 730x^12 + 880x^11 - 1872x^10 + 8330x^9 - 13718x^8 + 16004x^7 - 20008x^6 + 10920x^5 + 1546x^4 + 188x^3 + 54x^2 - 370x + 74	\( 2^{18}\cdot 5^{11}\cdot 37^{10} \)	18T781	$[2]$ (GRH)
18.6.179759723517039226895441920000.1	x^18 - 4x^17 + 13x^16 + 14x^15 - 140x^14 + 634x^13 - 1896x^12 + 5286x^11 - 15542x^10 + 36774x^9 - 84582x^8 + 168594x^7 - 279724x^6 + 361166x^5 - 114456x^4 - 569318x^3 + 873613x^2 - 261706x - 141319	\( 2^{16}\cdot 5^{4}\cdot 37^{10}\cdot 97^{3} \)	18T781	$[2]$ (GRH)
18.12.856584131654454329582896998483.1	x^18 - 2x^17 - 25x^16 + 51x^15 + 220x^14 - 515x^13 - 720x^12 + 2789x^11 - 325x^10 - 9572x^9 + 7621x^8 + 22488x^7 - 17154x^6 - 32373x^5 + 12294x^4 + 22047x^3 - 168x^2 - 3627x - 177	\( -\,3^{10}\cdot 53^{4}\cdot 107^{9} \)	18T781	Trivial (GRH)
18.12.856584131654454329582896998483.2	x^18 - 20x^16 - 11x^15 + 131x^14 + 343x^13 - 568x^12 - 3136x^11 + 4334x^10 + 8488x^9 - 18397x^8 + 5215x^7 + 18775x^6 - 33828x^5 + 17890x^4 + 17034x^3 - 25176x^2 + 10155x - 1239	\( -\,3^{10}\cdot 53^{4}\cdot 107^{9} \)	18T781	$[2]$ (GRH)
18.8.7709257184890088966246072986347.1	x^18 - 6x^17 + 20x^16 - 36x^15 - 44x^14 + 371x^13 - 1145x^12 + 3359x^11 - 8240x^10 + 12474x^9 - 4226x^8 - 23894x^7 + 49168x^6 - 36087x^5 - 4434x^4 + 25695x^3 - 17019x^2 + 4293x - 243	\( -\,3^{12}\cdot 53^{4}\cdot 107^{9} \)	18T781	$[2]$ (GRH)
18.8.7709257184890088966246072986347.2	x^18 - 3x^17 + x^16 + 35x^15 - 55x^14 + 185x^13 - 115x^12 + 616x^11 - 1125x^10 - 1519x^9 + 1926x^8 - 16052x^7 + 27731x^6 + 836x^5 + 17078x^4 - 42562x^3 - 16892x^2 + 31848x - 1787	\( -\,3^{12}\cdot 53^{4}\cdot 107^{9} \)	18T781	Trivial (GRH)
18.4.20714324019129661632580349263872.1	x^18 - 6x^17 - 12x^16 + 100x^15 + 180x^14 - 522x^13 - 1675x^12 - 1938x^11 - 2286x^10 - 1222x^9 + 7878x^8 + 22050x^7 + 41011x^6 + 99078x^5 + 200976x^4 + 248676x^3 + 173286x^2 + 59580x + 6273	\( -\,2^{16}\cdot 3^{24}\cdot 47^{9} \)	18T781	Trivial (GRH)
18.10.20714324019129661632580349263872.1	x^18 - 30x^16 - 67x^15 + 165x^14 + 1026x^13 + 2349x^12 + 2886x^11 - 3207x^10 - 27955x^9 - 68199x^8 - 94641x^7 - 99927x^6 - 95874x^5 - 57522x^4 - 4336x^3 + 6150x^2 + 186x - 82	\( 2^{16}\cdot 3^{24}\cdot 47^{9} \)	18T781	Trivial (GRH)
18.6.20714324019129661632580349263872.1	x^18 - 6x^17 - 6x^16 + 82x^15 - 210x^14 - 60x^13 + 1534x^12 - 3024x^11 - 1260x^10 + 13472x^9 - 15720x^8 - 17160x^7 + 64672x^6 - 21216x^5 - 118608x^4 + 73888x^3 + 112320x^2 - 42336x - 28832	\( 2^{16}\cdot 3^{24}\cdot 47^{9} \)	18T781	Trivial (GRH)
18.4.30551500695675537755123326279227.1	x^18 - 2x^17 - 11x^16 + 55x^15 - 276x^14 + 1164x^13 - 4398x^12 + 13569x^11 - 30716x^10 + 61923x^9 - 121767x^8 + 246321x^7 - 445980x^6 + 600622x^5 - 557129x^4 + 306286x^3 - 106880x^2 + 17574x - 2853	\( -\,3^{9}\cdot 53^{4}\cdot 107^{10} \)	18T781	$[2]$ (GRH)
18.10.331429184306074586121285588221952.1	x^18 - 6x^16 - 246x^14 + 703x^12 + 6456x^10 - 11796x^8 - 39437x^6 + 23142x^4 - 846x^2 - 423	\( 2^{20}\cdot 3^{24}\cdot 47^{9} \)	18T781	Trivial (GRH)
18.14.331429184306074586121285588221952.1	x^18 - 6x^17 - 18x^16 + 166x^15 - 57x^14 - 1626x^13 + 3044x^12 + 6696x^11 - 23193x^10 - 7058x^9 + 72834x^8 - 21378x^7 - 97667x^6 + 42438x^5 + 52812x^4 - 12984x^3 - 11592x^2 - 864x + 144	\( 2^{20}\cdot 3^{24}\cdot 47^{9} \)	18T781	Trivial (GRH)
18.6.331429184306074586121285588221952.1	x^18 - 3x^17 - 39x^16 + 152x^15 + 414x^14 - 2364x^13 + 194x^12 + 10620x^11 - 10317x^10 + 59x^9 - 26643x^8 + 30792x^7 + 28732x^6 - 3456x^5 - 13308x^4 - 47898x^3 + 15237x^2 - 22131x + 2649	\( 2^{20}\cdot 3^{24}\cdot 47^{9} \)	18T781	Trivial (GRH)
18.14.1325716737224298344485142352887808.1	x^18 - 51x^16 + 351x^14 + 91x^12 - 6672x^10 + 14796x^8 + 17232x^6 - 88704x^4 + 81216x^2 - 6768	\( 2^{22}\cdot 3^{24}\cdot 47^{9} \)	18T781	Trivial (GRH)
18.0.74849463536141758591392983590109184.1	x^18 + 42x^16 + 681x^14 + 5380x^12 + 21692x^10 + 43787x^8 + 43977x^6 + 21186x^4 + 4494x^2 + 321	\( -\,2^{18}\cdot 3^{9}\cdot 53^{4}\cdot 107^{9} \)	18T781	$[2, 4538]$ (GRH)
18.0.74849463536141758591392983590109184.2	x^18 + 57x^16 + 1211x^14 + 12568x^12 + 72546x^10 + 245270x^8 + 483426x^6 + 518415x^4 + 248454x^2 + 26001	\( -\,2^{18}\cdot 3^{9}\cdot 53^{4}\cdot 107^{9} \)	18T781	$[2, 5006]$ (GRH)
18.18.224548390608425275774178950770327552.1	x^18 - 58x^16 + 1355x^14 - 16452x^12 + 111831x^10 - 426231x^8 + 866076x^6 - 853911x^4 + 326457x^2 - 8667	\( 2^{18}\cdot 3^{10}\cdot 53^{4}\cdot 107^{9} \)	18T781	Trivial (GRH)
18.18.224548390608425275774178950770327552.2	x^18 - 61x^16 + 1462x^14 - 17501x^12 + 110662x^10 - 364243x^8 + 576661x^6 - 358746x^4 + 53607x^2 - 963	\( 2^{18}\cdot 3^{10}\cdot 53^{4}\cdot 107^{9} \)	18T781	$[2]$ (GRH)