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 matches 1-50 of 62)

Label	Polynomial	Discriminant	Galois group	Class group
18.2.62526016613841031168.1	x^18 + 2x^16 - x^15 + 2x^14 - 2x^13 + 2x^12 - 4x^11 + 2x^10 - 5x^9 + 2x^8 - 4x^7 + 2x^6 - 2x^5 + 2x^4 - x^3 + 2x^2 + 1	\( 2^{12}\cdot 37^{7}\cdot 401^{2} \)	18T884	Trivial
18.2.480818966845638049792.1	x^18 + 7x^16 + 20x^14 - 6x^13 + 32x^12 - 28x^11 + 22x^10 - 54x^9 - 6x^8 - 60x^7 - 20x^6 - 38x^5 - 8x^4 - 16x^3 + x^2 + 2x - 1	\( 2^{18}\cdot 37^{7}\cdot 139^{2} \)	18T884	Trivial
18.2.567421627402691018752.1	x^18 - 4x^17 + 6x^16 - 4x^15 + 3x^14 + 2x^13 - 17x^12 - 2x^11 + 97x^10 - 202x^9 + 232x^8 - 192x^7 + 106x^6 - 49x^4 + 22x^3 + 7x^2 - 4x - 1	\( 2^{18}\cdot 37^{7}\cdot 151^{2} \)	18T884	Trivial
18.4.2599263699746061406367.1	x^18 - 8x^17 + 23x^16 - 23x^15 - 21x^14 + 81x^13 - 69x^12 - 90x^11 + 270x^10 - 157x^9 - 204x^8 + 298x^7 - 22x^6 - 170x^5 + 102x^4 + 5x^3 - 25x^2 + 9x - 1	\( -\,23^{7}\cdot 59^{4}\cdot 251^{2} \)	18T884	Trivial
18.6.4001665063285825994752.1	x^18 - 2x^17 - 3x^16 + 6x^15 + 7x^14 - 6x^13 - 24x^12 + 10x^11 + 34x^10 - 30x^9 - 35x^8 + 42x^7 + 35x^6 - 48x^5 - 63x^4 - 18x^3 + 8x^2 + 6x + 1	\( 2^{18}\cdot 37^{7}\cdot 401^{2} \)	18T884	Trivial
18.6.4001665063285825994752.2	x^18 - 8x^17 + 27x^16 - 48x^15 + 33x^14 + 42x^13 - 104x^12 + 44x^11 + 104x^10 - 160x^9 + 37x^8 + 108x^7 - 99x^6 - 4x^5 + 41x^4 - 10x^3 - 8x^2 + 2x + 1	\( 2^{18}\cdot 37^{7}\cdot 401^{2} \)	18T884	Trivial
18.0.6253780826948691034112.1	x^18 + 2x^16 - 2x^14 + 11x^10 - 2x^8 + 4x^6 + 8x^4 - 8x^2 + 23	\( -\,2^{18}\cdot 23^{7}\cdot 2647^{2} \)	18T884	Trivial
18.0.6253780826948691034112.2	x^18 - 8x^16 + 32x^14 - 77x^12 + 116x^10 - 95x^8 + 7x^6 + 71x^4 - 69x^2 + 23	\( -\,2^{18}\cdot 23^{7}\cdot 2647^{2} \)	18T884	Trivial
18.6.100758244279412523585536.1	x^18 - 2x^17 - 2x^16 + 13x^15 - 22x^14 + 10x^13 + 20x^12 - 38x^11 + 28x^10 - 17x^9 + 28x^8 - 38x^7 + 20x^6 + 10x^5 - 22x^4 + 13x^3 - 2x^2 - 2x + 1	\( 2^{12}\cdot 101^{7}\cdot 479^{2} \)	18T884	Trivial
18.0.130614121991044287168512.1	x^18 + 7x^16 + 21x^14 + 54x^12 + 94x^10 + 136x^8 + 153x^6 + 125x^4 + 77x^2 + 23	\( -\,2^{18}\cdot 23^{7}\cdot 12097^{2} \)	18T884	Trivial
18.4.130614121991044287168512.1	x^18 - 4x^16 + 3x^14 + 7x^12 - 4x^10 - 23x^8 + 13x^6 + 50x^4 - 67x^2 + 23	\( -\,2^{18}\cdot 23^{7}\cdot 12097^{2} \)	18T884	Trivial
18.0.130614121991044287168512.2	x^18 + x^16 - 6x^14 + 15x^12 + 31x^10 - 46x^8 + 49x^6 + 160x^4 - x^2 + 23	\( -\,2^{18}\cdot 23^{7}\cdot 12097^{2} \)	18T884	Trivial
18.2.256106564050292863664128.1	x^18 + 3x^16 - 9x^14 - 46x^12 - 38x^10 + 209x^8 + 599x^6 + 343x^4 - 148x^2 - 37	\( 2^{24}\cdot 37^{7}\cdot 401^{2} \)	18T884	Trivial
18.6.256106564050292863664128.1	x^18 + 3x^16 - 21x^14 - 14x^12 + 106x^10 - 71x^8 + 75x^6 - 121x^4 - 37	\( 2^{24}\cdot 37^{7}\cdot 401^{2} \)	18T884	Trivial
18.2.256106564050292863664128.2	x^18 - 3x^16 - 13x^14 + 48x^12 + 38x^10 - 163x^8 + 23x^6 + 161x^4 - 56x^2 - 37	\( 2^{24}\cdot 37^{7}\cdot 401^{2} \)	18T884	Trivial
18.2.256106564050292863664128.3	x^18 + 4x^16 + 21x^14 + 45x^12 + 55x^10 + 174x^8 + 274x^6 + 53x^4 - 111x^2 - 37	\( 2^{24}\cdot 37^{7}\cdot 401^{2} \)	18T884	Trivial
18.6.815505904551504375513088.1	x^18 - 7x^17 + 19x^16 - 26x^15 + 4x^14 + 18x^13 - 60x^12 + 138x^11 - 109x^10 + 205x^9 - 305x^8 + 426x^7 - 336x^6 + 128x^5 + 14x^4 - 18x^3 + 3x^2 - 7x + 1	\( 2^{16}\cdot 37^{7}\cdot 107^{4} \)	18T884	Trivial
18.6.815505904551504375513088.2	x^18 - x^17 + 3x^16 - 14x^15 + 16x^14 - 20x^13 + 60x^12 - 70x^11 + 31x^10 - 59x^9 + 73x^8 + 28x^7 - 60x^6 + 42x^5 - 104x^4 + 78x^3 + 37x^2 - 53x + 13	\( 2^{16}\cdot 37^{7}\cdot 107^{4} \)	18T884	Trivial
18.6.5478279471638295786815488.1	x^18 - 6x^17 + 15x^16 - 22x^15 + 30x^14 - 62x^13 + 84x^12 + 150x^11 - 592x^10 + 178x^9 + 1002x^8 - 270x^7 - 2210x^6 + 2058x^5 + 856x^4 - 2322x^3 + 1747x^2 - 808x + 179	\( 2^{18}\cdot 37^{9}\cdot 401^{2} \)	18T884	Trivial
18.6.6448527633882401509474304.1	x^18 - 2x^17 - 6x^16 + 4x^15 + 33x^14 - 14x^13 - 61x^12 + 6x^11 + 103x^10 + 24x^9 - 114x^8 - 128x^7 + 56x^6 + 86x^5 + 27x^4 + 2x^3 + 3x^2 + 6x + 1	\( 2^{18}\cdot 101^{7}\cdot 479^{2} \)	18T884	Trivial
18.6.6448527633882401509474304.2	x^18 - 10x^16 - 14x^15 + 31x^14 + 68x^13 + 7x^12 - 40x^11 - 23x^10 - 86x^9 - 160x^8 - 94x^7 + 6x^6 + 40x^5 + 39x^4 + 30x^3 + 15x^2 + 2x - 1	\( 2^{18}\cdot 101^{7}\cdot 479^{2} \)	18T884	$[2]$
18.6.6448527633882401509474304.3	x^18 - 4x^17 - x^16 + 52x^15 - 185x^14 + 338x^13 - 358x^12 + 194x^11 + 20x^10 - 154x^9 + 179x^8 - 140x^7 + 103x^6 - 54x^5 - 9x^4 + 36x^3 - 28x^2 + 10x - 1	\( 2^{18}\cdot 101^{7}\cdot 479^{2} \)	18T884	Trivial
18.6.6448527633882401509474304.4	x^18 + 10x^16 + 11x^14 - 199x^12 - 937x^10 - 1576x^8 - 692x^6 + 559x^4 + 303x^2 - 101	\( 2^{18}\cdot 101^{7}\cdot 479^{2} \)	18T884	Trivial
18.6.6448527633882401509474304.5	x^18 - 2x^17 - 5x^16 + 32x^15 - 17x^14 - 162x^13 + 270x^12 + 268x^11 - 1006x^10 + 392x^9 + 1317x^8 - 1638x^7 + 61x^6 + 1100x^5 - 831x^4 + 270x^3 - 86x^2 + 46x - 11	\( 2^{18}\cdot 101^{7}\cdot 479^{2} \)	18T884	Trivial
18.10.6661494592726175761825792.1	x^18 - 4x^17 - 3x^16 + 36x^15 - 40x^14 - 50x^13 + 14x^12 + 340x^11 - 326x^10 - 598x^9 + 1120x^8 - 340x^7 - 180x^6 - 134x^5 + 238x^4 - 52x^3 - 23x^2 + 10x - 1	\( 2^{18}\cdot 37^{7}\cdot 16361^{2} \)	18T884	Trivial
18.14.6661494592726175761825792.1	x^18 - 13x^16 - 6x^15 + 65x^14 + 40x^13 - 140x^12 - 98x^11 + 82x^10 + 120x^9 + 123x^8 - 78x^7 - 197x^6 + 24x^5 + 97x^4 - 2x^3 - 18x^2 + 1	\( 2^{18}\cdot 37^{7}\cdot 16361^{2} \)	18T884	Trivial (GRH)
18.2.6661494592726175761825792.1	x^18 - 6x^17 + 22x^16 - 60x^15 + 135x^14 - 282x^13 + 495x^12 - 638x^11 + 659x^10 - 822x^9 + 1126x^8 - 1170x^7 + 1078x^6 - 858x^5 + 585x^4 - 352x^3 + 143x^2 - 92x + 19	\( 2^{18}\cdot 37^{7}\cdot 16361^{2} \)	18T884	Trivial
18.6.6661494592726175761825792.1	x^18 - 2x^17 + x^16 - 20x^15 + 34x^14 - 36x^13 + 76x^12 - 100x^11 + 144x^10 - 116x^9 + 146x^8 - 492x^7 + 330x^6 + 324x^5 - 248x^4 - 60x^3 + 19x^2 + 6x + 1	\( 2^{18}\cdot 37^{7}\cdot 16361^{2} \)	18T884	Trivial
18.10.6661494592726175761825792.2	x^18 - 4x^17 - 5x^16 + 22x^15 + 32x^14 - 50x^13 - 130x^12 + 18x^11 + 274x^10 + 186x^9 - 280x^8 - 446x^7 + 52x^6 + 410x^5 + 86x^4 - 154x^3 - 23x^2 + 18x + 1	\( 2^{18}\cdot 37^{7}\cdot 16361^{2} \)	18T884	Trivial
18.14.6661494592726175761825792.2	x^18 - 2x^17 - 16x^16 + 34x^15 + 65x^14 - 104x^13 - 173x^12 + 22x^11 + 325x^10 + 354x^9 - 242x^8 - 556x^7 - 72x^6 + 254x^5 + 65x^4 - 64x^3 - 7x^2 + 8x - 1	\( 2^{18}\cdot 37^{7}\cdot 16361^{2} \)	18T884	Trivial (GRH)
18.6.6661494592726175761825792.2	x^18 - 6x^17 + 15x^16 - 20x^15 + 13x^14 - 6x^13 - 34x^12 + 192x^11 - 306x^10 + 228x^9 - 273x^8 + 422x^7 - 171x^6 - 110x^5 + 69x^4 + 46x^3 - 60x^2 + 20x - 1	\( 2^{18}\cdot 37^{7}\cdot 16361^{2} \)	18T884	Trivial
18.10.6661494592726175761825792.3	x^18 - 16x^16 - 10x^15 + 85x^14 + 100x^13 - 115x^12 - 214x^11 - 233x^10 - 510x^9 - 20x^8 + 1700x^7 + 2242x^6 + 218x^5 - 1967x^4 - 2128x^3 - 1067x^2 - 274x - 29	\( 2^{18}\cdot 37^{7}\cdot 16361^{2} \)	18T884	Trivial
18.10.16390820099218743274504192.1	x^18 - 14x^16 + 83x^14 - 295x^12 + 701x^10 - 1118x^8 + 1160x^6 - 741x^4 + 259x^2 - 37	\( 2^{30}\cdot 37^{7}\cdot 401^{2} \)	18T884	Trivial (GRH)
18.6.16390820099218743274504192.1	x^18 - 19x^14 + x^12 + 69x^10 + 116x^8 - 64x^6 - 225x^4 + 185x^2 - 37	\( 2^{30}\cdot 37^{7}\cdot 401^{2} \)	18T884	Trivial
18.10.16390820099218743274504192.2	x^18 - 11x^16 + 46x^14 - 106x^12 + 148x^10 - 84x^8 - 34x^6 - 26x^4 + 111x^2 - 37	\( 2^{30}\cdot 37^{7}\cdot 401^{2} \)	18T884	Trivial (GRH)
18.6.16390820099218743274504192.2	x^18 - 2x^16 - 15x^14 + 75x^12 - 161x^10 + 144x^8 - 32x^6 - 25x^4 + 111x^2 - 37	\( 2^{30}\cdot 37^{7}\cdot 401^{2} \)	18T884	Trivial
18.10.412705768568473696606355456.1	x^18 - 4x^16 - 39x^14 + 173x^12 + 103x^10 - 802x^8 + 674x^6 - 519x^4 + 425x^2 - 101	\( 2^{24}\cdot 101^{7}\cdot 479^{2} \)	18T884	Trivial (GRH)
18.2.412705768568473696606355456.1	x^18 + 8x^16 - 23x^14 - 291x^12 - 669x^10 - 342x^8 + 310x^6 + 145x^4 - 199x^2 - 101	\( 2^{24}\cdot 101^{7}\cdot 479^{2} \)	18T884	$[2]$
18.10.412705768568473696606355456.2	x^18 - 18x^16 + 89x^14 + 37x^12 - 957x^10 + 612x^8 + 838x^6 + 159x^4 + 101x^2 - 101	\( 2^{24}\cdot 101^{7}\cdot 479^{2} \)	18T884	Trivial (GRH)
18.2.412705768568473696606355456.2	x^18 + 15x^16 + 91x^14 + 258x^12 + 214x^10 - 627x^8 - 1841x^6 - 1889x^4 - 808x^2 - 101	\( 2^{24}\cdot 101^{7}\cdot 479^{2} \)	18T884	Trivial
18.10.412705768568473696606355456.3	x^18 - 8x^17 + 13x^16 + 60x^15 - 198x^14 - 164x^13 + 1078x^12 + 148x^11 - 3384x^10 - 80x^9 + 6548x^8 + 1372x^7 - 6870x^6 - 3916x^5 + 1982x^4 + 2596x^3 + 987x^2 + 168x + 11	\( 2^{24}\cdot 101^{7}\cdot 479^{2} \)	18T884	Trivial (GRH)
18.2.412705768568473696606355456.3	x^18 + 3x^16 - 7x^14 - 36x^13 - 28x^12 + 28x^11 + 370x^10 - 474x^9 + 441x^8 - 1246x^7 + 2557x^6 - 1544x^5 - 1881x^4 + 446x^3 + 2244x^2 + 1120x - 2107	\( 2^{24}\cdot 101^{7}\cdot 479^{2} \)	18T884	Trivial
18.10.412705768568473696606355456.4	x^18 - 12x^16 - 6x^15 + 61x^14 + 70x^13 - 253x^12 - 458x^11 + 1009x^10 + 1634x^9 - 2398x^8 - 3400x^7 + 2464x^6 + 5250x^5 - 1545x^4 - 5124x^3 + 2073x^2 + 1190x - 557	\( 2^{24}\cdot 101^{7}\cdot 479^{2} \)	18T884	Trivial (GRH)
18.10.426335653934475248756850688.1	x^18 + 3x^16 - 33x^14 - 114x^12 + 218x^10 + 905x^8 - 81x^6 - 1137x^4 + 444x^2 - 37	\( 2^{24}\cdot 37^{7}\cdot 16361^{2} \)	18T884	Trivial (GRH)
18.10.26413169188382316582806749184.1	x^18 - 8x^16 - 25x^14 + 293x^12 - 745x^10 + 468x^8 + 802x^6 - 1393x^4 + 707x^2 - 101	\( 2^{30}\cdot 101^{7}\cdot 479^{2} \)	18T884	Trivial (GRH)
18.14.26413169188382316582806749184.1	x^18 - 23x^16 + 186x^14 - 670x^12 + 1040x^10 - 336x^8 - 478x^6 - 238x^4 + 707x^2 - 101	\( 2^{30}\cdot 101^{7}\cdot 479^{2} \)	18T884	Trivial (GRH)
18.2.26413169188382316582806749184.1	x^18 + 7x^16 - 30x^14 - 104x^12 + 688x^10 + 1554x^8 - 510x^6 - 2108x^4 - 909x^2 - 101	\( 2^{30}\cdot 101^{7}\cdot 479^{2} \)	18T884	Trivial (GRH)
18.6.26413169188382316582806749184.1	x^18 + 5x^16 - 46x^14 - 282x^12 - 300x^10 + 372x^8 + 642x^6 + 222x^4 - 505x^2 - 101	\( 2^{30}\cdot 101^{7}\cdot 479^{2} \)	18T884	Trivial (GRH)
18.10.26413169188382316582806749184.2	x^18 - 9x^16 - 25x^14 + 210x^12 - 476x^10 + 1593x^8 - 2511x^6 - 97x^4 + 606x^2 - 101	\( 2^{30}\cdot 101^{7}\cdot 479^{2} \)	18T884	Trivial (GRH)
18.14.26413169188382316582806749184.2	x^18 - 21x^16 + 116x^14 - 160x^12 - 254x^10 + 574x^8 + 120x^6 - 772x^4 + 505x^2 - 101	\( 2^{30}\cdot 101^{7}\cdot 479^{2} \)	18T884	Trivial (GRH)