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 matches 1-50 of 68)

Label	Polynomial	Discriminant	Galois group	Class group
18.2.9190341683468403200000.1	x^18 - 4x^17 + 2x^16 + 19x^15 - 38x^14 + 78x^12 - 72x^11 - 42x^10 + 117x^9 - 42x^8 - 72x^7 + 78x^6 - 38x^4 + 19x^3 + 2x^2 - 4x + 1	\( 2^{12}\cdot 5^{5}\cdot 23^{4}\cdot 37^{6} \)	18T882	Trivial
18.2.28768603724533934663125.1	x^18 - 3x^17 + 5x^16 - 5x^15 + 2x^14 + 9x^13 - 20x^12 + 30x^11 - 47x^10 + 53x^9 - 26x^8 - 2x^7 - 17x^6 + 70x^5 - 98x^4 + 76x^3 - 35x^2 + 9x - 1	\( 5^{4}\cdot 23^{6}\cdot 43^{4}\cdot 103\cdot 883 \)	18T882	Trivial
18.4.82920283397994741760000.1	x^18 - 11x^14 - 11x^12 + 12x^10 - 2x^8 - 35x^6 - 21x^4 - x^2 + 1	\( -\,2^{18}\cdot 5^{4}\cdot 23^{6}\cdot 43^{4} \)	18T882	Trivial
18.4.82920283397994741760000.2	x^18 - 4x^14 + 5x^10 - 11x^8 + 14x^6 - 12x^4 + 5x^2 + 1	\( -\,2^{18}\cdot 5^{4}\cdot 23^{6}\cdot 43^{4} \)	18T882	Trivial
18.0.82920283397994741760000.3	x^18 - x^16 - 6x^14 + 15x^12 - 9x^10 - 26x^8 + 65x^6 - 10x^4 - 5x^2 + 1	\( -\,2^{18}\cdot 5^{4}\cdot 23^{6}\cdot 43^{4} \)	18T882	Trivial
18.0.82920283397994741760000.4	x^18 + 7x^16 + 21x^14 + 41x^12 + 57x^10 + 44x^8 + 5x^6 - 10x^4 + 1	\( -\,2^{18}\cdot 5^{4}\cdot 23^{6}\cdot 43^{4} \)	18T882	Trivial
18.2.414601416989973708800000.1	x^18 - 2x^16 - 4x^14 + 13x^12 - 14x^10 + 9x^8 - 9x^6 + 15x^4 - 5x^2 - 5	\( 2^{18}\cdot 5^{5}\cdot 23^{6}\cdot 43^{4} \)	18T882	Trivial
18.6.414601416989973708800000.3	x^18 - 6x^14 - 4x^12 + 33x^10 - 24x^8 - 29x^6 + 25x^4 + 10x^2 - 5	\( 2^{18}\cdot 5^{5}\cdot 23^{6}\cdot 43^{4} \)	18T882	Trivial (GRH)
18.6.414601416989973708800000.4	x^18 - 9x^16 + 33x^14 - 68x^12 + 101x^10 - 129x^8 + 127x^6 - 80x^4 + 30x^2 - 5	\( 2^{18}\cdot 5^{5}\cdot 23^{6}\cdot 43^{4} \)	18T882	Trivial (GRH)
18.2.588181867741977804800000.1	x^18 - 4x^17 + 5x^16 - 8x^14 + 12x^12 - 16x^11 - 2x^10 + 16x^9 - 2x^8 - 16x^7 + 12x^6 - 8x^4 + 5x^2 - 4x + 1	\( 2^{18}\cdot 5^{5}\cdot 23^{4}\cdot 37^{6} \)	18T882	Trivial
18.6.588181867741977804800000.1	x^18 - 2x^17 - 6x^16 + 12x^15 + 27x^14 - 90x^13 + 45x^12 + 168x^11 - 353x^10 + 180x^9 + 264x^8 - 450x^7 + 268x^6 - 80x^5 - 63x^4 + 152x^3 - 115x^2 + 48x - 5	\( 2^{18}\cdot 5^{5}\cdot 23^{4}\cdot 37^{6} \)	18T882	Trivial
18.6.588181867741977804800000.2	x^18 + x^16 - 11x^14 - 52x^12 + 84x^10 + 241x^8 - 61x^6 - 131x^4 + 58x^2 - 5	\( 2^{18}\cdot 5^{5}\cdot 23^{4}\cdot 37^{6} \)	18T882	Trivial
18.4.797540172515229271921875.1	x^18 - x^17 - x^16 + x^15 - 22x^14 + 23x^13 - 65x^12 + 77x^11 - 94x^10 + 113x^9 - 94x^8 + 77x^7 - 65x^6 + 23x^5 - 22x^4 + x^3 - x^2 - x + 1	\( -\,3^{11}\cdot 5^{6}\cdot 257^{6} \)	18T882	Trivial
18.4.797540172515229271921875.2	x^18 - 7x^16 - x^15 + 10x^14 + 2x^13 - 3x^12 + 6x^11 + 102x^10 + 116x^9 - 23x^8 - 28x^7 + 35x^6 + 9x^5 - 22x^4 + 27x^3 + 31x^2 + 9x + 1	\( -\,3^{11}\cdot 5^{6}\cdot 257^{6} \)	18T882	Trivial
18.4.910968108161839657261875.1	x^18 - 8x^17 + 22x^16 - 17x^15 - 17x^14 - 41x^13 + 315x^12 - 524x^11 + 227x^10 + 219x^9 - 49x^8 - 471x^7 + 557x^6 - 265x^5 + 96x^4 - 111x^3 + 89x^2 - 13x - 1	\( -\,3^{9}\cdot 5^{4}\cdot 257^{7} \)	18T882	$[2]$
18.8.910968108161839657261875.1	x^18 - 2x^17 - 3x^16 + 6x^15 - 19x^14 + 30x^13 + 33x^12 - 102x^11 + 131x^10 + 95x^9 - 291x^8 - 17x^7 + 374x^6 - 228x^5 - 529x^4 + 472x^3 + 335x^2 - 240x - 45	\( -\,3^{9}\cdot 5^{4}\cdot 257^{7} \)	18T882	Trivial
18.8.4554840540809198286309375.1	x^18 - 2x^17 - 6x^16 + 16x^15 + 11x^14 - 26x^13 - 15x^12 - 10x^11 + x^10 + 99x^9 - 38x^8 - 84x^7 + 100x^6 - 48x^5 - 18x^4 + 30x^3 - 15x^2 + 3	\( -\,3^{9}\cdot 5^{5}\cdot 257^{7} \)	18T882	Trivial (GRH)
18.0.4696625460367461267984375.1	x^18 - x^17 + 7x^16 - 8x^15 + 5x^14 - 23x^13 - 17x^12 + 5x^11 + 50x^10 + 155x^9 + 154x^8 + 71x^7 - 152x^6 - 399x^5 - 450x^4 - 122x^3 + 418x^2 + 486x + 157	\( -\,3^{9}\cdot 5^{6}\cdot 53\cdot 257^{6} \)	18T882	$[2]$
18.2.14704546693549445120000000.1	x^18 - 2x^17 - 3x^16 + 2x^15 + 36x^14 - 4x^13 - 36x^12 - 82x^11 + 42x^10 + 52x^9 + 42x^8 - 82x^7 - 36x^6 - 4x^5 + 36x^4 + 2x^3 - 3x^2 - 2x + 1	\( 2^{18}\cdot 5^{7}\cdot 23^{4}\cdot 37^{6} \)	18T882	Trivial
18.4.22774202704045991431546875.1	x^18 - x^17 + 6x^16 + 6x^15 + 6x^14 + 64x^13 + 105x^12 + 244x^11 - 290x^10 - 90x^9 - 5x^8 + 213x^7 - 97x^6 - 123x^5 + 179x^4 - 94x^3 + 32x^2 - 10x + 1	\( -\,3^{9}\cdot 5^{6}\cdot 257^{7} \)	18T882	Trivial (GRH)
18.4.37643639535486579507200000.1	x^18 + 7x^16 - x^14 + 74x^10 - 45x^8 - 109x^6 + 99x^4 - 36x^2 + 5	\( -\,2^{24}\cdot 5^{5}\cdot 23^{4}\cdot 37^{6} \)	18T882	Trivial
18.8.37643639535486579507200000.1	x^18 + 3x^16 - 13x^14 - 4x^12 - 6x^10 + 51x^8 - 113x^6 + 119x^4 - 48x^2 + 5	\( -\,2^{24}\cdot 5^{5}\cdot 23^{4}\cdot 37^{6} \)	18T882	Trivial
18.4.37643639535486579507200000.2	x^18 + 7x^16 + 15x^14 - 40x^12 - 246x^10 - 185x^8 + 215x^6 + 399x^4 + 196x^2 + 5	\( -\,2^{24}\cdot 5^{5}\cdot 23^{4}\cdot 37^{6} \)	18T882	Trivial
18.8.37643639535486579507200000.2	x^18 - 13x^16 + 75x^14 - 248x^12 + 510x^10 - 645x^8 + 387x^6 + 127x^4 - 320x^2 + 125	\( -\,2^{24}\cdot 5^{5}\cdot 23^{4}\cdot 37^{6} \)	18T882	Trivial
18.2.37643639535486579507200000.1	x^18 + 13x^16 + 75x^14 + 248x^12 + 510x^10 + 645x^8 + 387x^6 - 127x^4 - 320x^2 - 125	\( 2^{24}\cdot 5^{5}\cdot 23^{4}\cdot 37^{6} \)	18T882	Trivial
18.6.37643639535486579507200000.1	x^18 - 12x^16 + 55x^14 - 115x^12 + 115x^10 - 82x^8 + 48x^6 + 17x^4 - 21x^2 - 5	\( 2^{24}\cdot 5^{5}\cdot 23^{4}\cdot 37^{6} \)	18T882	Trivial
18.6.37643639535486579507200000.2	x^18 - 7x^16 - x^14 + 74x^10 + 45x^8 - 109x^6 - 99x^4 - 36x^2 - 5	\( 2^{24}\cdot 5^{5}\cdot 23^{4}\cdot 37^{6} \)	18T882	Trivial
18.10.112720192589815389289805625.1	x^18 - 9x^17 + 26x^16 - 4x^15 - 118x^14 + 182x^13 + 91x^12 - 442x^11 + 244x^10 + 353x^9 - 513x^8 + 38x^7 + 352x^6 - 223x^5 - 61x^4 + 137x^3 - 27x^2 - 27x + 9	\( 3^{8}\cdot 5^{4}\cdot 257^{6}\cdot 95401 \)	18T882	Trivial (GRH)
18.10.121542268763869632320000000.1	x^18 - 4x^17 - 7x^16 + 47x^15 - 7x^14 - 177x^13 + 235x^12 + 193x^11 - 923x^10 + 416x^9 + 1538x^8 - 1585x^7 - 1205x^6 + 2045x^5 + 421x^4 - 1128x^3 - 15x^2 + 205x - 25	\( 2^{12}\cdot 5^{7}\cdot 23^{6}\cdot 37^{6} \)	18T882	Trivial (GRH)
18.6.121542268763869632320000000.1	x^18 - 7x^17 + 9x^16 + 37x^15 - 83x^14 - 113x^13 + 352x^12 + 209x^11 - 920x^10 - 219x^9 + 1601x^8 + 133x^7 - 2168x^6 + 506x^5 + 1564x^4 - 835x^3 - 276x^2 + 227x - 17	\( 2^{12}\cdot 5^{7}\cdot 23^{6}\cdot 37^{6} \)	18T882	$[2]$
18.6.121542268763869632320000000.2	x^18 - 5x^17 + 5x^16 + 29x^15 - 97x^14 + 7x^13 + 398x^12 - 405x^11 - 682x^10 + 1273x^9 - 45x^8 - 1209x^7 + 1524x^6 - 1056x^5 - 1618x^4 + 4105x^3 - 1650x^2 - 977x + 151	\( 2^{12}\cdot 5^{7}\cdot 23^{6}\cdot 37^{6} \)	18T882	Trivial
18.0.234118803797592791916301875.1	x^18 - x^17 - 6x^16 - 15x^15 + 42x^14 + 5x^13 + 56x^12 + 82x^11 + 605x^10 - 1159x^9 - 492x^8 + 478x^7 + 4745x^6 - 6145x^5 + 2857x^4 - 357x^3 + 95x^2 + 105x + 45	\( -\,3^{9}\cdot 5^{4}\cdot 257^{8} \)	18T882	$[2, 2]$
18.8.13113603874315113519521529856.1	x^18 + 6x^16 + 5x^14 - 28x^12 - 46x^10 + 29x^8 + 72x^6 - 3x^4 - 26x^2 + 4	\( -\,2^{16}\cdot 193^{4}\cdot 229^{6} \)	18T882	Trivial (GRH)
18.8.19629261226638283944334162176.1	x^18 - 3x^17 - 12x^16 + 48x^15 + 42x^14 - 363x^13 + 384x^12 + 594x^11 - 2184x^10 + 2885x^9 - 654x^8 - 4608x^7 + 8631x^6 - 7926x^5 + 4356x^4 - 1212x^3 - 96x^2 + 120x - 4	\( -\,2^{8}\cdot 3^{22}\cdot 367^{6} \)	18T882	Trivial (GRH)
18.12.19629261226638283944334162176.2	x^18 - 24x^16 + 195x^14 - 582x^12 + 168x^10 + 1461x^8 - 1041x^6 - 240x^4 - 3x^2 + 1	\( -\,2^{8}\cdot 3^{22}\cdot 367^{6} \)	18T882	Trivial (GRH)
18.12.58887783679914851833002486528.1	x^18 - 9x^17 + 24x^16 - 5x^15 - 117x^14 + 447x^13 - 403x^12 - 1596x^11 + 2442x^10 + 1969x^9 - 3426x^8 - 1242x^7 + 2075x^6 + 390x^5 - 504x^4 - 83x^3 + 33x^2 + 12x + 1	\( -\,2^{8}\cdot 3^{23}\cdot 367^{6} \)	18T882	Trivial (GRH)
18.10.58887783679914851833002486528.1	x^18 - 9x^17 + 12x^16 + 82x^15 - 231x^14 + 539x^12 - 543x^11 - 297x^10 + 844x^9 - 297x^8 - 543x^7 + 539x^6 - 231x^4 + 82x^3 + 12x^2 - 9x + 1	\( 2^{8}\cdot 3^{23}\cdot 367^{6} \)	18T882	Trivial (GRH)
18.10.58887783679914851833002486528.2	x^18 - 9x^17 + 18x^16 + 55x^15 - 276x^14 + 435x^13 - 391x^12 + 366x^11 - 426x^10 + 490x^9 - 426x^8 + 366x^7 - 391x^6 + 435x^5 - 276x^4 + 55x^3 + 18x^2 - 9x + 1	\( 2^{8}\cdot 3^{23}\cdot 367^{6} \)	18T882	Trivial (GRH)
18.6.58887783679914851833002486528.3	x^18 + 12x^16 - 54x^14 - 635x^12 - 825x^10 + 1953x^8 + 2041x^6 - 1476x^4 - 288x^2 - 12	\( 2^{8}\cdot 3^{23}\cdot 367^{6} \)	18T882	Trivial (GRH)
18.6.58887783679914851833002486528.4	x^18 - 12x^16 - 13x^15 + 12x^14 + 6x^13 - 17x^12 - 3x^11 + 12x^10 + 4x^9 + 12x^8 - 3x^7 - 17x^6 + 6x^5 + 12x^4 - 13x^3 - 12x^2 + 1	\( 2^{8}\cdot 3^{23}\cdot 367^{6} \)	18T882	Trivial (GRH)
18.16.78517044906553135777336648704.1	x^18 - 27x^16 + 186x^14 - 399x^12 - 333x^10 + 2511x^8 - 3717x^6 + 2430x^4 - 729x^2 + 81	\( -\,2^{10}\cdot 3^{22}\cdot 367^{6} \)	18T882	Trivial (GRH)
18.4.78517044906553135777336648704.1	x^18 + 21x^16 + 57x^14 - 128x^12 - 486x^10 + 9x^8 + 924x^6 + 675x^4 + 144x^2 + 9	\( -\,2^{10}\cdot 3^{22}\cdot 367^{6} \)	18T882	Trivial (GRH)
18.14.235551134719659407332009946112.1	x^18 - 33x^16 - 49x^15 + 327x^14 + 921x^13 - 327x^12 - 3264x^11 - 1599x^10 + 4676x^9 + 3198x^8 - 5607x^7 - 5501x^6 + 2070x^5 + 3402x^4 + 276x^3 - 540x^2 - 72x + 24	\( 2^{10}\cdot 3^{23}\cdot 367^{6} \)	18T882	Trivial (GRH)
18.2.235551134719659407332009946112.1	x^18 + 27x^16 + 291x^14 + 1591x^12 + 4578x^10 + 6318x^8 + 2827x^6 - 333x^4 - 81x^2 - 3	\( 2^{10}\cdot 3^{23}\cdot 367^{6} \)	18T882	$[2]$ (GRH)
18.14.235551134719659407332009946112.2	x^18 - 3x^17 - 12x^16 + 47x^15 + 33x^14 - 294x^13 - 19x^12 + 1614x^11 - 585x^10 - 6105x^9 + 3633x^8 + 11373x^7 - 6912x^6 - 8976x^5 + 4554x^4 + 2190x^3 - 1011x^2 - 18x + 12	\( 2^{10}\cdot 3^{23}\cdot 367^{6} \)	18T882	Trivial (GRH)
18.2.235551134719659407332009946112.2	x^18 + 3x^16 - 123x^14 - 1259x^12 - 5340x^10 - 11832x^8 - 13821x^6 - 7428x^4 - 1104x^2 - 48	\( 2^{10}\cdot 3^{23}\cdot 367^{6} \)	18T882	$[2]$ (GRH)
18.8.314068179626212543109346594816.1	x^18 + 9x^16 - 3x^14 - 102x^12 - 24x^10 + 177x^8 - 12x^6 - 69x^4 + 18x^2 + 1	\( -\,2^{12}\cdot 3^{22}\cdot 367^{6} \)	18T882	Trivial (GRH)
18.16.706653404158978221996029838336.1	x^18 - 36x^16 + 363x^14 - 1710x^12 + 4317x^10 - 5898x^8 + 3858x^6 - 585x^4 - 315x^2 + 9	\( -\,2^{10}\cdot 3^{24}\cdot 367^{6} \)	18T882	$[2]$ (GRH)
18.4.706653404158978221996029838336.1	x^18 + 12x^16 - 45x^14 - 1011x^12 - 4887x^10 - 10848x^8 - 11847x^6 - 5778x^4 - 936x^2 + 36	\( -\,2^{10}\cdot 3^{24}\cdot 367^{6} \)	18T882	$[2]$ (GRH)
18.8.942204538878637629328039784448.1	x^18 - 12x^16 - 45x^14 + 495x^12 + 1647x^10 - 1674x^8 - 6345x^6 + 1944x^4 + 4860x^2 + 972	\( -\,2^{12}\cdot 3^{23}\cdot 367^{6} \)	18T882	Trivial (GRH)