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 119)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.923324627983045303.1	x^18 - 4x^17 + 10x^16 - 17x^15 + 24x^14 - 28x^13 + 28x^12 - 22x^11 + 14x^10 - 8x^9 + 5x^8 - 3x^7 + 2x^6 - 3x^5 + 2x^4 + x^3 - 2x^2 + 1	\( -\,31^{6}\cdot 463\cdot 1499^{2} \)	18T912	Trivial
18.2.4837319251866194741.1	x^18 - 3x^17 + 2x^16 - 5x^15 + 15x^14 - 6x^13 + 2x^12 - 29x^11 + 17x^10 + 11x^9 + 17x^8 - 29x^7 + 2x^6 - 6x^5 + 15x^4 - 5x^3 + 2x^2 - 3x + 1	\( 23^{6}\cdot 59^{2}\cdot 149\cdot 251^{2} \)	18T912	Trivial
18.2.18454992633836467177.1	x^18 - 2x^17 + 4x^15 - 5x^14 - 6x^13 + 18x^12 - x^11 - 18x^10 + 9x^9 + 13x^8 - 25x^7 - 6x^6 + 23x^5 + 10x^4 - 11x^3 - 5x^2 + x + 1	\( 7^{4}\cdot 23^{6}\cdot 83^{2}\cdot 7537 \)	18T912	Trivial
18.4.42892090922754093056.1	x^18 - x^17 - 5x^16 + 9x^15 + 3x^14 - 13x^13 + 2x^12 - 3x^11 + 10x^10 + 13x^9 - 23x^8 - 5x^7 + 8x^6 - 4x^5 + 8x^4 + 9x^3 - 6x^2 - 5x + 1	\( -\,2^{12}\cdot 37^{6}\cdot 151^{2}\cdot 179 \)	18T912	Trivial
18.2.44055316944848498413.1	x^18 - 5x^17 + 14x^16 - 27x^15 + 44x^14 - 68x^13 + 98x^12 - 117x^11 + 102x^10 - 50x^9 - 18x^8 + 74x^7 - 101x^6 + 95x^5 - 69x^4 + 39x^3 - 17x^2 + 5x - 1	\( 23^{7}\cdot 59^{3}\cdot 251^{2} \)	18T912	Trivial
18.0.271903514215160479744.3	x^18 + 3x^16 + 8x^14 + 12x^12 + 11x^10 + 5x^8 - 2x^6 - 2x^4 + 1	\( -\,2^{18}\cdot 23^{6}\cdot 2647^{2} \)	18T912	Trivial
18.4.981486058210060140544.2	x^18 + 2x^16 - 3x^14 - 9x^12 - x^10 + 4x^8 - 10x^6 - 11x^4 + x^2 + 1	\( -\,2^{24}\cdot 37^{6}\cdot 151^{2} \)	18T912	Trivial
18.0.1013272289731515463499.1	x^18 - 7x^17 + 26x^16 - 62x^15 + 99x^14 - 113x^13 + 117x^12 - 170x^11 + 291x^10 - 402x^9 + 416x^8 - 328x^7 + 198x^6 - 78x^5 + 12x^4 + 1	\( -\,23^{8}\cdot 59^{3}\cdot 251^{2} \)	18T912	Trivial
18.8.1077219661051651207168.1	x^18 - 10x^16 + 38x^14 - 5x^13 - 69x^12 + 36x^11 + 60x^10 - 90x^9 - 21x^8 + 106x^7 - 9x^6 - 64x^5 + 16x^4 + 21x^3 - 7x^2 - 3x + 1	\( -\,2^{12}\cdot 13^{2}\cdot 37^{6}\cdot 61^{2}\cdot 163 \)	18T912	Trivial
18.2.1275480948361771061248.1	x^18 - 7x^17 + 20x^16 - 34x^15 + 45x^14 - 41x^13 + 8x^12 + 55x^11 - 122x^10 + 151x^9 - 122x^8 + 55x^7 + 8x^6 - 41x^5 + 45x^4 - 34x^3 + 20x^2 - 7x + 1	\( 2^{12}\cdot 13^{2}\cdot 37^{6}\cdot 61^{2}\cdot 193 \)	18T912	Trivial
18.4.1315133205823795032064.1	x^18 - 2x^17 - 2x^16 + 13x^15 - 16x^14 - 17x^13 + 62x^12 - 44x^11 - 62x^10 + 115x^9 - 51x^8 - 77x^7 + 114x^6 + 7x^5 - 62x^4 + 8x^3 + 7x^2 - 3x + 1	\( -\,2^{12}\cdot 13^{2}\cdot 37^{6}\cdot 61^{2}\cdot 199 \)	18T912	Trivial
18.2.1384063617346584909197.1	x^18 - 2x^17 + 3x^16 - 11x^15 + 16x^14 - 23x^13 + 63x^12 - 81x^11 + 49x^10 - 93x^9 + 172x^8 - 111x^7 + 6x^6 - 103x^5 + 218x^4 - 162x^3 + 63x^2 - 14x + 1	\( 31^{6}\cdot 463\cdot 1499^{3} \)	18T912	Trivial
18.4.1789858461677911793443.1	x^18 + 2x^16 - 7x^15 + 3x^14 - 12x^13 + 24x^12 - 16x^11 + 28x^10 - 44x^9 + 27x^8 - 28x^7 + 39x^6 - 19x^5 + 8x^4 - 12x^3 + 5x^2 + 3x - 1	\( -\,11\cdot 23^{6}\cdot 43^{2}\cdot 347^{2}\cdot 4937 \)	18T912	Trivial
18.4.5678874869175838572544.1	x^18 - 4x^16 + 7x^14 - 3x^12 - 14x^10 + 33x^8 - 38x^6 + 24x^4 - 8x^2 + 1	\( -\,2^{18}\cdot 23^{6}\cdot 12097^{2} \)	18T912	Trivial
18.0.5678874869175838572544.2	x^18 + x^16 - 4x^14 - 6x^12 - 7x^10 + 9x^8 + 33x^6 + 24x^4 + 7x^2 + 1	\( -\,2^{18}\cdot 23^{6}\cdot 12097^{2} \)	18T912	Trivial
18.2.6476705729335868051456.1	x^18 - 3x^17 + 3x^16 + x^15 + 7x^14 - 27x^13 + 10x^12 + 13x^11 + 36x^10 - 85x^9 + x^8 - 31x^7 + 80x^6 - 54x^5 + 30x^4 - 5x^3 + 6x^2 - x + 1	\( 2^{12}\cdot 37^{6}\cdot 151^{3}\cdot 179 \)	18T912	Trivial
18.4.6921799028386293612544.1	x^18 - 3x^16 - 9x^14 + 6x^12 + 2x^10 - 29x^8 - 33x^6 - 15x^4 + 1	\( -\,2^{24}\cdot 37^{6}\cdot 401^{2} \)	18T912	Trivial
18.4.10973670169044928311296.1	x^18 - 4x^17 + 8x^16 - 15x^15 + 24x^14 - 34x^13 + 44x^12 - 52x^11 + 58x^10 - 59x^9 + 58x^8 - 52x^7 + 44x^6 - 34x^5 + 24x^4 - 15x^3 + 8x^2 - 4x + 1	\( -\,2^{12}\cdot 11\cdot 101^{6}\cdot 479^{2} \)	18T912	Trivial
18.6.23305262663824855660477.2	x^18 - 4x^17 - 6x^16 + 40x^15 - 9x^14 - 140x^13 + 102x^12 + 245x^11 - 185x^10 - 380x^9 + 357x^8 + 209x^7 - 349x^6 + 105x^5 + 68x^4 - 85x^3 + 33x^2 - 2x - 1	\( 23^{9}\cdot 59^{3}\cdot 251^{2} \)	18T912	Trivial
18.6.36911436023151122501632.1	x^18 - 2x^17 - x^16 - 7x^15 + 25x^14 - 5x^13 - 3x^12 - 45x^11 - 35x^10 + 144x^9 - 16x^8 - 39x^7 + x^6 - 55x^5 - 9x^4 + 26x^3 + 15x^2 + 5x + 1	\( 2^{12}\cdot 37\cdot 101^{6}\cdot 479^{2} \)	18T912	Trivial
18.6.52873138087216472772608.1	x^18 - 9x^16 - 2x^15 + 30x^14 + 9x^13 - 42x^12 - 4x^11 + 8x^10 - 21x^9 + 47x^8 + 28x^7 - 63x^6 - 11x^5 + 33x^4 - 3x^3 - 2x^2 + 7x + 1	\( 2^{12}\cdot 53\cdot 101^{6}\cdot 479^{2} \)	18T912	Trivial
18.6.114572806177519174272989.1	x^18 - x^17 - 3x^16 + 3x^15 - 19x^14 + 42x^13 + 38x^12 - 215x^11 + 246x^10 + 159x^9 - 620x^8 + 466x^7 + 76x^6 - 454x^5 + 364x^4 - 161x^3 + 47x^2 - 7x + 1	\( 31^{6}\cdot 47\cdot 2083\cdot 36313^{2} \)	18T912	Trivial (GRH)
18.4.120964639986159441620992.1	x^18 - 4x^17 + 2x^16 + x^15 + 4x^14 - 2x^13 - 2x^12 - 6x^11 + 6x^10 + x^9 + 6x^8 - 6x^7 - 2x^6 - 2x^5 + 4x^4 + x^3 + 2x^2 - 4x + 1	\( -\,2^{12}\cdot 37^{6}\cdot 43\cdot 16361^{2} \)	18T912	Trivial
18.8.120964639986159441620992.1	x^18 - 3x^17 - x^16 + 10x^15 - 10x^14 + 4x^13 - 8x^11 + 21x^10 - 27x^9 + 21x^8 - 8x^7 + 4x^5 - 10x^4 + 10x^3 - x^2 - 3x + 1	\( -\,2^{12}\cdot 37^{6}\cdot 43\cdot 16361^{2} \)	18T912	Trivial (GRH)
18.8.126696010133518717775872.1	x^18 - 3x^17 - 4x^16 + 8x^15 + 27x^14 - 39x^13 - 18x^12 + 39x^11 - 56x^10 + 91x^9 - 109x^7 + 94x^6 - 13x^5 - 49x^4 + 34x^3 - 5x + 1	\( -\,2^{12}\cdot 101^{6}\cdot 127\cdot 479^{2} \)	18T912	Trivial
18.2.148204394789719081222144.2	x^18 - 6x^17 + 17x^16 - 30x^15 + 23x^14 + 32x^13 - 70x^12 - 76x^11 + 500x^10 - 1052x^9 + 1343x^8 - 1362x^7 + 1435x^6 - 1254x^5 + 613x^4 - 50x^3 - 84x^2 - 16x - 1	\( 2^{24}\cdot 37^{6}\cdot 151^{3} \)	18T912	Trivial
18.2.148643350471608574398464.1	x^18 - 4x^17 + 8x^16 - 11x^15 + 10x^14 - 6x^13 + 4x^12 - 8x^11 + 14x^10 - 17x^9 + 14x^8 - 8x^7 + 4x^6 - 6x^5 + 10x^4 - 11x^3 + 8x^2 - 4x + 1	\( 2^{12}\cdot 101^{6}\cdot 149\cdot 479^{2} \)	18T912	Trivial
18.8.162609839777665755885568.1	x^18 - 4x^17 - x^16 + 28x^15 - 53x^14 + 32x^13 + 22x^12 - 72x^11 + 174x^10 - 456x^9 + 817x^8 - 696x^7 - 177x^6 + 1028x^5 - 1053x^4 + 540x^3 - 148x^2 + 20x - 1	\( -\,2^{12}\cdot 101^{6}\cdot 163\cdot 479^{2} \)	18T912	Trivial
18.8.165974738585660629200896.1	x^18 - 8x^17 + 23x^16 - 17x^15 - 59x^14 + 169x^13 - 149x^12 - 99x^11 + 385x^10 - 386x^9 + 64x^8 + 275x^7 - 347x^6 + 189x^5 - 19x^4 - 44x^3 + 31x^2 - 9x + 1	\( -\,2^{12}\cdot 37^{6}\cdot 59\cdot 16361^{2} \)	18T912	Trivial
18.12.165974738585660629200896.1	x^18 - 4x^17 + x^16 + 20x^15 - 42x^14 + 7x^13 + 114x^12 - 130x^11 - 66x^10 + 203x^9 - 109x^8 - 134x^7 + 169x^6 + 49x^5 - 83x^4 - 11x^3 + 16x^2 + x - 1	\( -\,2^{12}\cdot 37^{6}\cdot 59\cdot 16361^{2} \)	18T912	Trivial
18.8.178571541841731106156544.1	x^18 - x^17 - 11x^16 + 13x^15 + 40x^14 - 68x^13 - 75x^12 + 176x^11 + 99x^10 - 296x^9 - 132x^8 + 398x^7 + 155x^6 - 413x^5 - 96x^4 + 312x^3 + 50x^2 - 140x - 49	\( -\,2^{12}\cdot 101^{6}\cdot 179\cdot 479^{2} \)	18T912	Trivial
18.4.178571541841731106156544.1	x^18 - 4x^17 + 25x^15 - 58x^14 + 62x^13 - 16x^12 - 58x^11 + 118x^10 - 139x^9 + 118x^8 - 58x^7 - 16x^6 + 62x^5 - 58x^4 + 25x^3 - 4x + 1	\( -\,2^{12}\cdot 101^{6}\cdot 179\cdot 479^{2} \)	18T912	Trivial
18.4.178571541841731106156544.2	x^18 - 4x^17 + 6x^16 - 12x^15 + 24x^14 - 33x^13 + 75x^12 - 158x^11 + 228x^10 - 280x^9 + 279x^8 - 144x^7 - 35x^6 + 78x^5 - 16x^4 - 19x^3 + 9x^2 + x - 1	\( -\,2^{12}\cdot 101^{6}\cdot 179\cdot 479^{2} \)	18T912	Trivial
18.8.178571541841731106156544.2	x^18 - 3x^17 - 3x^16 + 13x^15 - 7x^14 + 7x^13 + 20x^12 - 103x^11 + 42x^10 + 171x^9 - 53x^8 - 251x^7 - 138x^6 + 436x^5 + 30x^4 - 175x^3 + 68x^2 - 13x + 1	\( -\,2^{12}\cdot 101^{6}\cdot 179\cdot 479^{2} \)	18T912	Trivial
18.8.188479787885411222990848.1	x^18 - 2x^17 - 8x^16 + 27x^15 - 26x^14 - 18x^13 + 66x^12 - 52x^11 - 16x^10 + 57x^9 - 16x^8 - 52x^7 + 66x^6 - 18x^5 - 26x^4 + 27x^3 - 8x^2 - 2x + 1	\( -\,2^{12}\cdot 37^{6}\cdot 67\cdot 16361^{2} \)	18T912	Trivial
18.6.250368673459725355913216.1	x^18 - 9x^17 + 48x^16 - 180x^15 + 511x^14 - 1141x^13 + 2034x^12 - 2909x^11 + 3306x^10 - 2901x^9 + 1832x^8 - 653x^7 - 84x^6 + 257x^5 - 133x^4 + 10x^3 + 16x^2 - 5x - 1	\( 2^{12}\cdot 37^{6}\cdot 89\cdot 16361^{2} \)	18T912	Trivial
18.10.250368673459725355913216.1	x^18 - 8x^17 + 23x^16 - 36x^15 + 57x^14 - 80x^13 + 30x^12 + 44x^11 - 70x^10 + 136x^9 - 139x^8 + 18x^7 + 83x^6 - 106x^5 + 35x^4 + 24x^3 - 12x^2 - 2x + 1	\( 2^{12}\cdot 37^{6}\cdot 89\cdot 16361^{2} \)	18T912	Trivial
18.4.256106564050292863664128.1	x^18 - 3x^16 - 21x^14 + 14x^12 + 106x^10 + 71x^8 + 75x^6 + 121x^4 + 37	\( -\,2^{24}\cdot 37^{7}\cdot 401^{2} \)	18T912	Trivial
18.8.256106564050292863664128.1	x^18 + 3x^16 - 13x^14 - 48x^12 + 38x^10 + 163x^8 + 23x^6 - 161x^4 - 56x^2 + 37	\( -\,2^{24}\cdot 37^{7}\cdot 401^{2} \)	18T912	Trivial
18.8.256106564050292863664128.2	x^18 - 4x^16 + 21x^14 - 45x^12 + 55x^10 - 174x^8 + 274x^6 - 53x^4 - 111x^2 + 37	\( -\,2^{24}\cdot 37^{7}\cdot 401^{2} \)	18T912	Trivial
18.8.256106564050292863664128.3	x^18 - 3x^16 - 9x^14 + 46x^12 - 38x^10 - 209x^8 + 599x^6 - 343x^4 - 148x^2 + 37	\( -\,2^{24}\cdot 37^{7}\cdot 401^{2} \)	18T912	Trivial
18.10.272873722759475949703168.1	x^18 - 3x^17 - 2x^16 + 10x^15 + 3x^14 - 35x^13 + 24x^12 + 147x^11 - 120x^10 - 425x^9 + 194x^8 + 737x^7 - 254x^6 - 625x^5 + 287x^4 + 154x^3 - 114x^2 + 21x - 1	\( 2^{12}\cdot 37^{6}\cdot 97\cdot 16361^{2} \)	18T912	Trivial
18.12.301005034384164191940608.1	x^18 - 6x^17 + 8x^16 + 16x^15 - 65x^14 + 90x^13 + 17x^12 - 278x^11 + 321x^10 + 90x^9 - 394x^8 + 194x^7 + 108x^6 - 154x^5 + 31x^4 + 36x^3 - 15x^2 - 2x + 1	\( -\,2^{12}\cdot 37^{6}\cdot 107\cdot 16361^{2} \)	18T912	Trivial
18.6.306631296709101840388096.1	x^18 - 2x^17 - 7x^16 + 24x^15 - 9x^14 - 62x^13 + 60x^12 + 108x^11 - 90x^10 - 156x^9 + 25x^8 + 216x^7 + 67x^6 - 194x^5 + 17x^4 + 92x^3 - 1	\( 2^{12}\cdot 37^{6}\cdot 109\cdot 16361^{2} \)	18T912	Trivial
18.10.306631296709101840388096.1	x^18 - 2x^17 - 7x^16 + 23x^15 - 19x^14 - 17x^13 + 101x^12 - 207x^11 + 139x^10 + 202x^9 - 406x^8 + 149x^7 + 137x^6 - 109x^5 - 9x^4 + 32x^3 - 7x^2 - 3x + 1	\( 2^{12}\cdot 37^{6}\cdot 109\cdot 16361^{2} \)	18T912	Trivial
18.10.385398969258228918652928.1	x^18 - x^17 - 13x^16 + 4x^15 + 70x^14 + 21x^13 - 184x^12 - 139x^11 + 233x^10 + 255x^9 - 148x^8 - 188x^7 + 84x^6 + 61x^5 - 48x^4 - 5x^3 + 4x^2 + 1	\( 2^{12}\cdot 37^{6}\cdot 137\cdot 16361^{2} \)	18T912	Trivial
18.4.391025231583166567100416.1	x^18 - x^17 - 5x^16 + 13x^15 + 12x^14 - 42x^13 - 35x^12 + 54x^11 + 71x^10 + 186x^9 + 186x^8 - 28x^7 - 55x^6 + 85x^5 + 80x^4 - 78x^3 - 62x^2 - 14x - 1	\( -\,2^{12}\cdot 37^{6}\cdot 139\cdot 16361^{2} \)	18T912	Trivial
18.4.442995137816722791202816.2	x^18 - x^16 - x^14 + 6x^12 - 8x^10 - 7x^8 + 5x^6 + x^4 + 2x^2 + 1	\( -\,2^{30}\cdot 37^{6}\cdot 401^{2} \)	18T912	Trivial (GRH)
18.6.462417895033383361183744.1	x^18 - 8x^17 + 26x^16 - 44x^15 + 36x^14 + 34x^13 - 208x^12 + 398x^11 - 392x^10 + 306x^9 - 372x^8 + 160x^7 + 360x^6 - 312x^5 - 22x^4 - 124x^3 + 252x^2 - 64x - 26	\( 2^{26}\cdot 37^{6}\cdot 139^{3} \)	18T912	Trivial
18.6.462417895033383361183744.2	x^18 - 8x^17 + 29x^16 - 66x^15 + 106x^14 - 134x^13 + 126x^12 - 74x^11 + 114x^10 - 470x^9 + 1046x^8 - 1214x^7 + 646x^6 + 82x^5 - 354x^4 + 234x^3 - 71x^2 + 2x + 1	\( 2^{26}\cdot 37^{6}\cdot 139^{3} \)	18T912	Trivial