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 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.2.15335719659532189696.1	x^18 + 5x^16 + 5x^14 - 8x^12 - 8x^10 + 17x^8 + 19x^6 + x^4 - 2x^2 - 1	\( 2^{18}\cdot 37^{6}\cdot 151^{2} \)	18T483	Trivial
18.2.30801921737113993216.1	x^18 - 2x^17 + 3x^16 - 2x^15 + 6x^14 - 12x^13 + 14x^12 + 2x^11 - 24x^10 + 36x^9 - 24x^8 + 2x^7 + 14x^6 - 12x^5 + 6x^4 - 2x^3 + 3x^2 - 2x + 1	\( 2^{20}\cdot 37^{6}\cdot 107^{2} \)	18T483	Trivial
18.2.108153109818535837696.1	x^18 + 5x^16 + x^14 - 36x^12 - 88x^10 - 99x^8 - 69x^6 - 35x^4 - 10x^2 - 1	\( 2^{18}\cdot 37^{6}\cdot 401^{2} \)	18T483	Trivial
18.2.271903514215160479744.1	x^18 + x^16 - 2x^12 + 5x^8 + 8x^6 + 6x^4 + x^2 - 1	\( 2^{18}\cdot 23^{6}\cdot 2647^{2} \)	18T483	Trivial
18.2.321654971180475744256.1	x^18 + 4x^16 + 7x^14 + 10x^12 + 9x^10 - 3x^8 - 8x^6 + x^4 + 3x^2 - 1	\( 2^{18}\cdot 23^{6}\cdot 2879^{2} \)	18T483	Trivial
18.2.422957412928255688704.1	x^18 + x^16 + x^14 + 8x^12 + 4x^10 - 3x^8 + 11x^6 + 9x^4 - 2x^2 - 1	\( 2^{18}\cdot 13^{2}\cdot 37^{6}\cdot 61^{2} \)	18T483	Trivial
18.6.5678874869175838572544.1	x^18 - 2x^16 - 8x^14 + 8x^12 + 22x^10 - 13x^8 - 28x^6 + 8x^4 + 14x^2 - 1	\( 2^{18}\cdot 23^{6}\cdot 12097^{2} \)	18T483	Trivial
18.6.6118200156819965607936.1	x^18 - 4x^17 + 6x^16 - 10x^15 + 12x^14 + 2x^13 - 13x^12 + 54x^11 - 127x^10 + 202x^9 - 289x^8 + 296x^7 - 207x^6 + 44x^5 + 52x^4 - 110x^3 + 83x^2 - 38x - 1	\( 2^{18}\cdot 3^{4}\cdot 257^{6} \)	18T483	Trivial
18.6.8510565221216186269696.1	x^18 - 2x^16 + 6x^14 - 27x^12 + 38x^10 - 51x^8 + 53x^6 - 25x^4 + 7x^2 - 1	\( 2^{18}\cdot 23^{6}\cdot 59^{2}\cdot 251^{2} \)	18T483	Trivial
18.2.63846808256261401083904.1	x^18 + 9x^16 + 33x^14 + 44x^12 - 48x^10 - 211x^8 - 229x^6 - 103x^4 - 18x^2 - 1	\( 2^{18}\cdot 101^{6}\cdot 479^{2} \)	18T483	Trivial
18.6.103261087140687424000000.1	x^18 - x^17 + x^16 - 8x^15 + 10x^14 - 13x^13 + 57x^12 - 53x^11 + 50x^10 - 169x^9 + 144x^8 - 214x^7 + 360x^6 - 268x^5 + 64x^4 + 156x^3 - 112x^2 + 8	\( 2^{12}\cdot 5^{6}\cdot 13^{2}\cdot 37^{6}\cdot 61^{2} \)	18T483	Trivial
18.6.180040394398004750319616.1	x^18 - 4x^17 + 6x^15 + 27x^14 - 30x^13 - 47x^12 - 50x^11 + 119x^10 + 136x^9 + 14x^8 - 182x^7 - 252x^6 + 106x^5 + 135x^4 + 148x^3 - 123x^2 + 24x - 1	\( 2^{18}\cdot 37^{6}\cdot 16361^{2} \)	18T483	Trivial (GRH)
18.6.442995137816722791202816.1	x^18 + x^16 - 9x^14 - 20x^12 - 20x^10 + 3x^8 + 39x^6 + 29x^4 - 1	\( 2^{30}\cdot 37^{6}\cdot 401^{2} \)	18T483	Trivial
18.6.504437627001826538684416.1	x^18 - 2x^17 + x^16 + 8x^15 - 50x^14 + 100x^13 - 14x^12 - 158x^11 - 120x^10 + 458x^9 + 42x^8 - 400x^7 + 60x^6 + 104x^5 - 40x^4 + 8x^3 + 7x^2 - 6x - 1	\( 2^{20}\cdot 37^{6}\cdot 13693^{2} \)	18T483	Trivial (GRH)
18.6.727255050293977521721344.1	x^18 - 7x^17 + 11x^16 + 20x^15 - 66x^14 + 29x^13 + 78x^12 - 127x^11 + 67x^10 + 69x^9 - 124x^8 + 62x^7 - 18x^6 - 25x^5 + 36x^4 - 19x^3 + 8x^2 - 2x - 1	\( 2^{12}\cdot 3^{6}\cdot 101^{6}\cdot 479^{2} \)	18T483	Trivial
18.10.1542607913299147563728896.1	x^18 - 10x^16 + 38x^14 - 66x^12 + 46x^10 - 7x^8 + 23x^6 - 44x^4 + 24x^2 - 4	\( 2^{20}\cdot 101^{2}\cdot 229^{6} \)	18T483	Trivial (GRH)
18.10.3727452451221516351176704.1	x^18 - 6x^16 + 26x^14 - 90x^12 + 165x^10 - 156x^8 + 161x^6 - 199x^4 + 91x^2 - 1	\( 2^{20}\cdot 157^{2}\cdot 229^{6} \)	18T483	Trivial (GRH)
18.14.25060147842334579130105856.1	x^18 - 15x^16 + 105x^14 - 437x^12 + 1129x^10 - 1753x^8 + 1488x^6 - 554x^4 + 45x^2 - 1	\( 2^{30}\cdot 3^{4}\cdot 257^{6} \)	18T483	Trivial (GRH)
18.2.225541330581011212170952704.1	x^18 + 10x^16 + x^14 - 226x^12 - 554x^10 + 200x^8 + 1505x^6 + 532x^4 - 1056x^2 - 576	\( 2^{30}\cdot 3^{6}\cdot 257^{6} \)	18T483	$[2]$
18.14.2455620135706104220223770624.1	x^18 - 7x^17 - 4x^16 + 144x^15 - 329x^14 - 393x^13 + 2576x^12 - 3345x^11 - 284x^10 + 4235x^9 - 3176x^8 - 207x^7 + 1578x^6 - 1101x^5 + 207x^4 + 232x^3 - 154x^2 + 29x - 1	\( 2^{12}\cdot 7^{8}\cdot 101^{6}\cdot 313^{2} \)	18T483	Trivial (GRH)
18.6.19404348200650937329358209024.1	x^18 - 2x^17 + 5x^16 - 14x^15 + 20x^14 + 232x^13 - 808x^12 + 982x^11 - 3238x^10 - 4232x^9 + 39754x^8 - 38726x^7 - 109654x^6 + 174916x^5 + 90374x^4 - 250076x^3 + 29957x^2 + 121672x - 51797	\( 2^{20}\cdot 37^{6}\cdot 139^{6} \)	18T483	Trivial (GRH)
18.6.19404348200650937329358209024.2	x^18 - 16x^15 - 92x^14 - 356x^13 - 456x^12 + 892x^11 + 5828x^10 + 20588x^9 + 41930x^8 + 56326x^7 + 64320x^6 + 34672x^5 - 7632x^4 + 21242x^3 + 19598x^2 - 7100x - 278	\( 2^{20}\cdot 37^{6}\cdot 139^{6} \)	18T483	Trivial (GRH)
18.18.141204899984457152700528984064.1	x^18 - 24x^16 + 220x^14 - 1010x^12 + 2543x^10 - 3581x^8 + 2690x^6 - 905x^4 + 66x^2 - 1	\( 2^{18}\cdot 257^{6}\cdot 43237^{2} \)	18T483	Trivial (GRH)
18.18.771751925088859090612673314816.1	x^18 - 20x^16 + 163x^14 - 702x^12 + 1724x^10 - 2414x^8 + 1802x^6 - 601x^4 + 57x^2 - 1	\( 2^{18}\cdot 257^{6}\cdot 101081^{2} \)	18T483	Trivial (GRH)