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 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.2.5907704981594290903125.1	x^18 - x^17 + x^16 - x^15 - 2x^14 - 5x^13 + x^12 - 11x^11 - 11x^9 - 11x^7 + x^6 - 5x^5 - 2x^4 - x^3 + x^2 - x + 1	\( 3^{8}\cdot 5^{5}\cdot 257^{6} \)	18T487	Trivial
18.2.5907704981594290903125.2	x^18 - x^17 + 5x^16 - 9x^15 - x^14 + 21x^13 - 47x^12 + 69x^11 - 59x^10 + 43x^9 - 59x^8 + 69x^7 - 47x^6 + 21x^5 - x^4 - 9x^3 + 5x^2 - x + 1	\( 3^{8}\cdot 5^{5}\cdot 257^{6} \)	18T487	Trivial
18.0.19243070375507393321875.1	x^18 - 6x^17 + 23x^16 - 49x^15 + 67x^14 - 23x^13 - 47x^12 + 81x^11 + 31x^10 - 66x^9 - 14x^8 + 85x^7 + 73x^6 - 115x^5 + 60x^4 - 5x^3 + 20x^2 + 5	\( -\,5^{5}\cdot 23^{9}\cdot 43^{4} \)	18T487	Trivial
18.0.82920283397994741760000.2	x^18 + 3x^16 + 7x^12 + 52x^10 + 100x^8 + 93x^6 + 45x^4 + 11x^2 + 1	\( -\,2^{18}\cdot 5^{4}\cdot 23^{6}\cdot 43^{4} \)	18T487	Trivial
18.6.229758542086710080000000.1	x^18 - 3x^17 - 8x^16 + 25x^15 + 29x^14 - 77x^13 - 77x^12 + 94x^11 + 129x^10 - 7x^9 - 52x^8 - 26x^7 - 90x^6 - 63x^5 + 96x^4 + 120x^3 - x^2 - 60x - 25	\( 2^{12}\cdot 5^{7}\cdot 23^{4}\cdot 37^{6} \)	18T487	Trivial (GRH)
18.6.414601416989973708800000.1	x^18 - 7x^16 + 12x^14 + 6x^12 - 151x^8 + 248x^6 - 150x^4 + 45x^2 - 5	\( 2^{18}\cdot 5^{5}\cdot 23^{6}\cdot 43^{4} \)	18T487	Trivial (GRH)
18.6.414601416989973708800000.2	x^18 - 6x^16 + 14x^14 - 46x^12 + 143x^10 - 130x^8 - 86x^6 + 70x^4 + 20x^2 - 5	\( 2^{18}\cdot 5^{5}\cdot 23^{6}\cdot 43^{4} \)	18T487	Trivial (GRH)
18.8.2584030158949342841026875.1	x^18 - 10x^16 - 19x^15 - 4x^14 + 72x^13 + 225x^12 + 375x^11 + 437x^10 + 347x^9 + 132x^8 - 71x^7 - 184x^6 - 163x^5 - 86x^4 - 24x^3 + 12x^2 + 10x + 1	\( -\,3^{15}\cdot 5^{4}\cdot 257^{6} \)	18T487	Trivial (GRH)
18.8.7528727907097315901440000.1	x^18 - x^16 - 7x^14 - 16x^12 + 36x^10 + 179x^8 - 433x^6 + 359x^4 - 142x^2 + 25	\( -\,2^{24}\cdot 5^{4}\cdot 23^{4}\cdot 37^{6} \)	18T487	Trivial
18.0.22363777452552012346880000.1	x^18 - 6x^17 + 13x^16 + 5x^15 - 91x^14 + 222x^13 - 186x^12 - 231x^11 + 889x^10 - 1263x^9 + 1216x^8 - 886x^7 + 1074x^6 - 500x^5 + 524x^4 - 48x^3 + 112x^2 - 8x + 8	\( -\,2^{12}\cdot 5^{4}\cdot 23^{7}\cdot 37^{6} \)	18T487	Trivial
18.4.188218197677432897536000000.1	x^18 - 6x^17 + 13x^16 - 6x^15 + 5x^14 - 88x^13 + 140x^12 + 300x^11 - 954x^10 + 342x^9 + 1055x^8 + 1046x^7 - 6245x^6 + 4728x^5 + 6241x^4 - 13732x^3 + 8646x^2 - 942x - 1103	\( -\,2^{24}\cdot 5^{6}\cdot 23^{4}\cdot 37^{6} \)	18T487	Trivial
18.0.309733882939010758901760000.1	x^18 + 8x^16 + 35x^14 + 139x^12 + 433x^10 + 823x^8 + 857x^6 + 450x^4 + 108x^2 + 9	\( -\,2^{18}\cdot 3^{8}\cdot 5^{4}\cdot 257^{6} \)	18T487	$[12]$
18.4.481838586054228217692160000.1	x^18 + x^16 - 23x^14 - 10x^12 + 64x^10 - 59x^8 - 31x^6 + 103x^4 - 76x^2 + 25	\( -\,2^{30}\cdot 5^{4}\cdot 23^{4}\cdot 37^{6} \)	18T487	Trivial (GRH)
18.6.929201648817032276705280000.1	x^18 - 10x^14 + 39x^12 - 153x^10 + 21x^8 + 211x^6 + 21x^4 - 18x^2 - 3	\( 2^{18}\cdot 3^{9}\cdot 5^{4}\cdot 257^{6} \)	18T487	Trivial (GRH)
18.10.3038556719096740808000000000.1	x^18 - 6x^17 - 4x^16 + 52x^15 + 2x^14 - 155x^13 + 9x^12 + 316x^11 + 320x^10 - 582x^9 - 1861x^8 - 718x^7 + 1371x^6 + 2748x^5 + 2970x^4 + 441x^3 - 109x^2 - 23x - 1	\( 2^{12}\cdot 5^{9}\cdot 23^{6}\cdot 37^{6} \)	18T487	$[2]$ (GRH)
18.10.10486279463550222213103747072.1	x^18 - 17x^16 + 125x^14 - 529x^12 + 1434x^10 - 2584x^8 + 3051x^6 - 2220x^4 + 888x^2 - 148	\( 2^{20}\cdot 37^{5}\cdot 229^{6} \)	18T487	Trivial (GRH)
18.12.19629261226638283944334162176.1	x^18 - 21x^16 - 8x^15 + 147x^14 + 120x^13 - 451x^12 - 606x^11 + 810x^10 + 1448x^9 - 1206x^8 - 1326x^7 + 1099x^6 - 540x^5 + 450x^4 + 978x^3 - 1134x^2 + 324x - 18	\( -\,2^{8}\cdot 3^{22}\cdot 367^{6} \)	18T487	Trivial (GRH)
18.6.58887783679914851833002486528.1	x^18 - 8x^15 + 3x^14 + 72x^13 + 39x^12 - 264x^11 - 981x^10 - 1346x^9 + 426x^8 + 3240x^7 + 3337x^6 - 1656x^5 - 6876x^4 - 2874x^3 + 4158x^2 + 3348x + 414	\( 2^{8}\cdot 3^{23}\cdot 367^{6} \)	18T487	Trivial (GRH)
18.6.58887783679914851833002486528.2	x^18 - 17x^15 - 18x^14 + 66x^13 + 43x^12 + 504x^11 - 1206x^10 + 519x^9 - 2340x^8 + 4374x^7 + 699x^6 - 3726x^5 - 378x^4 + 2016x^3 - 378x^2 - 216x + 54	\( 2^{8}\cdot 3^{23}\cdot 367^{6} \)	18T487	Trivial (GRH)
18.12.176663351039744555499007459584.1	x^18 - 3x^17 - 21x^16 + 53x^15 + 240x^14 - 615x^13 - 1151x^12 + 3330x^11 + 3693x^10 - 13002x^9 - 3324x^8 + 28392x^7 - 9030x^6 - 27888x^5 + 18930x^4 + 8196x^3 - 9480x^2 + 1584x + 96	\( -\,2^{8}\cdot 3^{24}\cdot 367^{6} \)	18T487	$[2]$ (GRH)
18.18.658491794966495684087373619003392.1	x^18 - 61x^16 + 1484x^14 - 18248x^12 + 117886x^10 - 371682x^8 + 451164x^6 - 168432x^4 + 14553x^2 - 297	\( 2^{28}\cdot 3^{15}\cdot 11^{5}\cdot 101^{6} \)	18T487	Trivial (GRH)
18.18.1170652079940436771710886433783808.1	x^18 - 2x^17 - 49x^16 + 92x^15 + 937x^14 - 1618x^13 - 8977x^12 + 13936x^11 + 45926x^10 - 63080x^9 - 122098x^8 + 147480x^7 + 148208x^6 - 150744x^5 - 54156x^4 + 30912x^3 + 3000x^2 - 432x - 24	\( 2^{32}\cdot 3^{13}\cdot 11^{5}\cdot 101^{6} \)	18T487	Trivial (GRH)
18.0.4682608319761747086843545735135232.1	x^18 - 4x^17 + 24x^16 - 72x^15 + 286x^14 - 148x^13 + 152x^12 + 2480x^11 + 11008x^10 - 22504x^9 + 85248x^8 + 267320x^7 - 606644x^6 + 1081216x^5 + 4450248x^4 - 3234976x^3 - 1479936x^2 + 23748256x + 21791344	\( -\,2^{34}\cdot 3^{13}\cdot 11^{5}\cdot 101^{6} \)	18T487	$[2, 2, 116]$ (GRH)
18.0.10535868719463930945397977904054272.1	x^18 + 61x^16 + 1484x^14 + 18248x^12 + 117886x^10 + 371682x^8 + 451164x^6 + 168432x^4 + 14553x^2 + 297	\( -\,2^{32}\cdot 3^{15}\cdot 11^{5}\cdot 101^{6} \)	18T487	$[2, 2, 2, 58]$ (GRH)