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 48 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.1417200615982289707.1	x^18 - 3x^17 + 6x^16 - 9x^15 + 12x^14 - 15x^13 + 21x^12 - 29x^11 + 36x^10 - 38x^9 + 36x^8 - 32x^7 + 31x^6 - 32x^5 + 30x^4 - 23x^3 + 13x^2 - 5x + 1	\( -\,23^{6}\cdot 43^{3}\cdot 347^{2} \)	18T556	Trivial
18.0.11436479389438477403.1	x^18 - 4x^17 + 7x^16 - 9x^15 + 15x^14 - 24x^13 + 28x^12 - 30x^11 + 36x^10 - 39x^9 + 36x^8 - 30x^7 + 28x^6 - 24x^5 + 15x^4 - 9x^3 + 7x^2 - 4x + 1	\( -\,23^{6}\cdot 43^{2}\cdot 347^{3} \)	18T556	Trivial
18.2.29952577460023808000.1	x^18 - 5x^17 + 14x^16 - 25x^15 + 23x^14 + 21x^13 - 137x^12 + 330x^11 - 559x^10 + 747x^9 - 826x^8 + 768x^7 - 606x^6 + 405x^5 - 226x^4 + 102x^3 - 35x^2 + 8x - 1	\( 2^{12}\cdot 5^{3}\cdot 37^{6}\cdot 151^{2} \)	18T556	Trivial
18.2.85913224501051936768.1	x^18 - 8x^17 + 32x^16 - 83x^15 + 154x^14 - 216x^13 + 232x^12 - 192x^11 + 130x^10 - 101x^9 + 130x^8 - 192x^7 + 232x^6 - 216x^5 + 154x^4 - 83x^3 + 32x^2 - 8x + 1	\( 2^{12}\cdot 13^{3}\cdot 37^{6}\cdot 61^{2} \)	18T556	Trivial
18.0.271903514215160479744.2	x^18 - x^16 + 2x^12 - 5x^8 + 8x^6 - 6x^4 + x^2 + 1	\( -\,2^{18}\cdot 23^{6}\cdot 2647^{2} \)	18T556	Trivial
18.0.321654971180475744256.2	x^18 - 4x^16 + 7x^14 - 10x^12 + 9x^10 + 3x^8 - 8x^6 - x^4 + 3x^2 + 1	\( -\,2^{18}\cdot 23^{6}\cdot 2879^{2} \)	18T556	Trivial
18.2.403131284197243703296.1	x^18 - 6x^17 + 18x^16 - 42x^15 + 92x^14 - 173x^13 + 253x^12 - 282x^11 + 238x^10 - 136x^9 + 29x^8 + 26x^7 - 33x^6 + 34x^5 - 30x^4 + 15x^3 - 5x^2 + 3x - 1	\( 2^{12}\cdot 13^{2}\cdot 37^{6}\cdot 61^{3} \)	18T556	Trivial
18.6.826088697125499392000.1	x^18 - 3x^17 + 4x^16 - 3x^15 - x^14 + x^13 + 23x^12 - 23x^10 - 41x^9 + 8x^8 + 48x^7 + 32x^6 - 29x^5 - 38x^4 + 8x^3 + 13x^2 - 1	\( 2^{12}\cdot 5^{3}\cdot 13^{2}\cdot 37^{6}\cdot 61^{2} \)	18T556	Trivial
18.4.981486058210060140544.1	x^18 - 5x^16 + 5x^14 + 8x^12 - 8x^10 - 17x^8 + 19x^6 - x^4 - 2x^2 + 1	\( -\,2^{24}\cdot 37^{6}\cdot 151^{2} \)	18T556	Trivial
18.4.1971322991175295565824.1	x^18 - 3x^16 + 4x^14 - 16x^12 + 14x^10 + 26x^8 - 12x^6 - 8x^4 + 9x^2 + 1	\( -\,2^{26}\cdot 37^{6}\cdot 107^{2} \)	18T556	Trivial
18.6.2606233441079984661125.1	x^18 - 9x^17 + 41x^16 - 124x^15 + 276x^14 - 476x^13 + 654x^12 - 726x^11 + 647x^10 - 441x^9 + 194x^8 - 6x^7 - 78x^6 + 82x^5 - 57x^4 + 32x^3 - 7x^2 - 3x + 1	\( 5^{3}\cdot 257^{6}\cdot 269^{2} \)	18T556	Trivial
18.8.6921799028386293612544.1	x^18 - 5x^16 + x^14 + 36x^12 - 88x^10 + 99x^8 - 69x^6 + 35x^4 - 10x^2 + 1	\( -\,2^{24}\cdot 37^{6}\cdot 401^{2} \)	18T556	Trivial
18.6.17243079894656518865069.1	x^18 - 4x^17 + 5x^16 + 6x^15 - 34x^14 + 87x^13 - 179x^12 + 257x^11 - 366x^10 + 476x^9 - 429x^8 + 419x^7 - 330x^6 + 198x^5 - 113x^4 - 10x^3 + 6x^2 - 28x + 1	\( 23^{9}\cdot 43^{3}\cdot 347^{2} \)	18T556	Trivial
18.6.23305262663824855660477.1	x^18 - x^17 - 7x^16 - 4x^15 + 14x^14 + 37x^13 - 8x^12 - 75x^11 - 37x^10 + 79x^9 + 165x^8 - 99x^7 - 200x^6 + 20x^5 + 422x^4 - 165x^3 - 232x^2 + 94x + 19	\( 23^{9}\cdot 59^{3}\cdot 251^{2} \)	18T556	Trivial
18.8.26935372233110278582272.1	x^18 - x^17 - 5x^16 - 7x^15 + 22x^14 + 38x^13 - 23x^12 - 74x^11 - 83x^10 + 128x^9 + 108x^8 + 8x^7 - 143x^6 - 83x^5 + 114x^4 + 24x^3 - 16x^2 - 6x - 1	\( -\,2^{12}\cdot 3^{3}\cdot 101^{6}\cdot 479^{2} \)	18T556	Trivial
18.8.27069274427408364077056.1	x^18 - x^16 + x^14 - 8x^12 + 4x^10 + 3x^8 + 11x^6 - 9x^4 - 2x^2 + 1	\( -\,2^{24}\cdot 13^{2}\cdot 37^{6}\cdot 61^{2} \)	18T556	Trivial
18.0.96412994581196722733056.1	x^18 + 10x^16 + 38x^14 + 66x^12 + 46x^10 + 7x^8 + 23x^6 + 44x^4 + 24x^2 + 4	\( -\,2^{16}\cdot 101^{2}\cdot 229^{6} \)	18T556	$[2]$
18.0.119087320609277524873216.1	x^18 + 9x^16 + 37x^14 + 93x^12 + 158x^10 + 187x^8 + 149x^6 + 69x^4 + 15x^2 + 1	\( -\,2^{12}\cdot 229^{6}\cdot 449^{2} \)	18T556	$[2]$
18.10.140215359130103174768525.1	x^18 - x^17 - 9x^16 + 15x^15 + 17x^14 - 71x^13 + 30x^12 + 89x^11 - 142x^10 + 61x^9 + 128x^8 - 265x^7 + 227x^6 - 66x^5 - 73x^4 + 95x^3 - 47x^2 + 11x - 1	\( 5^{2}\cdot 257^{6}\cdot 269^{3} \)	18T556	Trivial (GRH)
18.0.146106987309222598930432.1	x^18 - x^17 - 2x^16 + 3x^14 + x^13 - x^11 - x^9 - x^7 + x^5 + 3x^4 - 2x^2 - x + 1	\( -\,2^{12}\cdot 7^{3}\cdot 101^{6}\cdot 313^{2} \)	18T556	Trivial
18.2.148204394789719081222144.1	x^18 + 6x^16 + 15x^14 + 15x^12 - 5x^10 - 24x^8 - 160x^6 - 287x^4 - 141x^2 - 151	\( 2^{24}\cdot 37^{6}\cdot 151^{3} \)	18T556	Trivial
18.6.351641395308603027968000.1	x^18 - 5x^17 + 6x^16 + 17x^15 - 51x^14 + 3x^13 + 95x^12 + 36x^11 - 271x^10 + 21x^9 + 386x^8 - 134x^7 - 284x^6 + 169x^5 + 60x^4 - 64x^3 + 15x^2 + 2x - 1	\( 2^{12}\cdot 5^{3}\cdot 37^{6}\cdot 16361^{2} \)	18T556	Trivial (GRH)
18.4.442995137816722791202816.1	x^18 - x^16 - 9x^14 + 20x^12 - 20x^10 - 3x^8 + 39x^6 - 29x^4 + 1	\( -\,2^{30}\cdot 37^{6}\cdot 401^{2} \)	18T556	Trivial
18.2.514687157793406972592128.2	x^18 - 3x^16 + 6x^14 - 22x^12 + 82x^10 - 285x^8 + 524x^6 - 381x^4 + 202x^2 - 1303	\( 2^{18}\cdot 31^{6}\cdot 1303^{3} \)	18T556	Trivial (GRH)
18.10.655088336820521017856000.1	x^18 - 7x^17 + 12x^16 + 13x^15 - 22x^14 - 136x^13 + 316x^12 - 145x^11 - 39x^10 - 229x^9 + 332x^8 + 77x^7 - 618x^6 + 931x^5 - 367x^4 - 349x^3 + 245x^2 - 15x - 1	\( 2^{12}\cdot 5^{3}\cdot 13^{3}\cdot 37^{6}\cdot 61^{3} \)	18T556	Trivial (GRH)
18.2.719728602127529789882368.1	x^18 - 4x^16 + 14x^14 - 44x^12 + 211x^10 - 353x^8 + 700x^6 - 2652x^4 + 1685x^2 - 2647	\( 2^{18}\cdot 23^{6}\cdot 2647^{3} \)	18T556	Trivial (GRH)
18.12.1327814090454436325666816.1	x^18 - 13x^16 - 5x^15 + 71x^14 + 33x^13 - 193x^12 - 65x^11 + 247x^10 + 50x^9 - 114x^8 - 53x^7 - x^6 + 69x^5 + 7x^4 - 34x^3 + 3x^2 + 5x - 1	\( -\,2^{12}\cdot 11^{3}\cdot 101^{6}\cdot 479^{2} \)	18T556	Trivial (GRH)
18.12.4086195728400729669369856.1	x^18 - 9x^16 + 33x^14 - 44x^12 - 48x^10 + 211x^8 - 229x^6 + 103x^4 - 18x^2 + 1	\( -\,2^{24}\cdot 101^{6}\cdot 479^{2} \)	18T556	Trivial (GRH)
18.2.6533069575398096209317888.1	x^18 - 3x^17 + 2x^16 + 6x^15 - 17x^14 + 27x^13 - 34x^12 + 35x^11 - 30x^10 + 27x^9 - 30x^8 + 35x^7 - 34x^6 + 27x^5 - 17x^4 + 6x^3 + 2x^2 - 3x + 1	\( 2^{12}\cdot 7^{2}\cdot 101^{6}\cdot 313^{3} \)	18T556	Trivial (GRH)
18.4.9737712452700868996038656.1	x^18 + 2x^16 + 6x^14 + 41x^12 - 29x^10 - 290x^8 - 219x^6 + 206x^4 + 305x^2 + 101	\( -\,2^{16}\cdot 101^{3}\cdot 229^{6} \)	18T556	Trivial
18.12.11522585241472304020455424.1	x^18 - 13x^16 + 53x^14 - 48x^12 - 144x^10 + 279x^8 - 33x^6 - 129x^4 + 14x^2 + 1	\( -\,2^{24}\cdot 37^{6}\cdot 16361^{2} \)	18T556	Trivial (GRH)
18.6.12902043299659823440908288.1	x^18 - 7x^17 + 23x^16 - 64x^15 + 148x^14 - 202x^13 + 106x^12 + 40x^11 - 19x^10 + 27x^9 - 373x^8 + 184x^7 + 316x^6 + 402x^5 + 156x^4 - 24x^3 - 47x^2 + 5x + 1	\( 2^{12}\cdot 3^{3}\cdot 101^{6}\cdot 479^{3} \)	18T556	$[2]$
18.6.13996497268824222166417408.1	x^18 - 2x^17 - 2x^16 + 6x^15 - 54x^14 + 160x^13 - 64x^12 + 140x^11 + 304x^10 - 1052x^9 + 972x^8 - 1052x^7 + 508x^6 + 176x^5 - 48x^4 + 120x^3 - 40x^2 - 64x - 8	\( 2^{18}\cdot 37^{6}\cdot 97^{3}\cdot 151^{2} \)	18T556	Trivial (GRH)
18.0.25060147842334579130105856.1	x^18 + 15x^16 + 105x^14 + 437x^12 + 1129x^10 + 1753x^8 + 1488x^6 + 554x^4 + 45x^2 + 1	\( -\,2^{30}\cdot 3^{4}\cdot 257^{6} \)	18T556	$[4]$
18.8.25060147842334579130105856.1	x^18 + x^16 - 32x^14 - 27x^12 + 235x^10 + 221x^8 - 453x^6 - 490x^4 + 396x^2 + 81	\( -\,2^{30}\cdot 3^{4}\cdot 257^{6} \)	18T556	Trivial (GRH)
18.6.50531755915693886704734208.1	x^18 - 5x^17 + 4x^16 + 25x^15 - 41x^14 - 55x^13 + 93x^12 + 174x^11 - 87x^10 - 561x^9 - 180x^8 + 1612x^7 - 298x^6 - 2299x^5 + 1572x^4 + 1076x^3 - 657x^2 - 234x - 27	\( 2^{12}\cdot 37^{3}\cdot 101^{6}\cdot 479^{2} \)	18T556	Trivial
18.14.200481182738676633040846848.2	x^18 - 12x^16 + 69x^14 - 256x^12 + 634x^10 - 980x^8 + 873x^6 - 418x^4 + 96x^2 - 8	\( 2^{33}\cdot 3^{4}\cdot 257^{6} \)	18T556	Trivial (GRH)
18.12.223663619334408807557214208.1	x^18 - 5x^17 - 3x^16 + 31x^15 + 26x^14 - 100x^13 - 45x^12 + 32x^11 - 289x^10 + 252x^9 + 1368x^8 + 456x^7 - 2083x^6 - 2273x^5 + 1016x^4 + 2424x^3 + 298x^2 - 816x - 289	\( -\,2^{12}\cdot 37^{6}\cdot 43^{3}\cdot 16361^{2} \)	18T556	Trivial (GRH)
18.14.598454220018575765219049472.1	x^18 - 13x^16 + 65x^14 - 156x^12 + 184x^10 - 109x^8 + 67x^6 - 69x^4 + 38x^2 - 7	\( 2^{24}\cdot 7^{3}\cdot 101^{6}\cdot 313^{2} \)	18T556	Trivial (GRH)
18.2.910488406744794714241404928.1	x^18 - 3x^17 + 11x^16 - 22x^15 + 56x^14 - 11x^13 - 148x^12 + 649x^11 - 2357x^10 + 7145x^9 - 15018x^8 + 26166x^7 - 46510x^6 + 86497x^5 - 135268x^4 + 156103x^3 - 121270x^2 + 56220x - 10457	\( 2^{12}\cdot 97^{3}\cdot 101^{6}\cdot 479^{2} \)	18T556	Trivial
18.0.1231906670745385481992474624.1	x^18 - 6x^16 + 15x^14 - 14x^12 - 9x^10 + 30x^8 - 15x^6 - 10x^4 + 8x^2 + 1	\( -\,2^{12}\cdot 229^{6}\cdot 45667^{2} \)	18T556	$[2]$ (GRH)
18.6.1983170262474484544188583936.1	x^18 - x^17 - 5x^16 - 30x^15 - 54x^14 - 79x^13 - 131x^12 - 153x^11 - 344x^10 - 81x^9 - 308x^8 - 60x^7 + 12x^6 - 284x^5 + 440x^4 - 372x^3 + 168x^2 - 8x - 8	\( 2^{12}\cdot 37^{6}\cdot 89^{3}\cdot 16361^{2} \)	18T556	Trivial
18.0.2113471087592457547129028608.1	x^18 - 6x^17 + 47x^16 - 202x^15 + 877x^14 - 2958x^13 + 9066x^12 - 24326x^11 + 57798x^10 - 123076x^9 + 232033x^8 - 388190x^7 + 571195x^6 - 719314x^5 + 766999x^4 - 649374x^3 + 420800x^2 - 179966x + 38543	\( -\,2^{18}\cdot 37^{6}\cdot 97^{3}\cdot 151^{3} \)	18T556	$[2, 12]$ (GRH)
18.6.8934376149939999921431117824.1	x^18 - 8x^17 + 22x^16 + 2x^15 - 200x^14 + 576x^13 - 416x^12 - 1256x^11 + 2008x^10 + 4038x^9 - 14024x^8 + 13764x^7 + 34268x^6 - 35896x^5 + 36788x^4 - 103512x^3 - 96814x^2 - 64800x - 86822	\( 2^{26}\cdot 37^{6}\cdot 139^{5} \)	18T556	$[3]$ (GRH)
18.0.141204899984457152700528984064.1	x^18 + 24x^16 + 220x^14 + 1010x^12 + 2543x^10 + 3581x^8 + 2690x^6 + 905x^4 + 66x^2 + 1	\( -\,2^{18}\cdot 257^{6}\cdot 43237^{2} \)	18T556	$[2, 68]$ (GRH)
18.0.143831668082131915073650688000.1	x^18 + 20x^16 + 167x^14 + 757x^12 + 2025x^10 + 3248x^8 + 3022x^6 + 1477x^4 + 293x^2 + 5	\( -\,2^{30}\cdot 5^{3}\cdot 37^{6}\cdot 107^{2}\cdot 191^{2} \)	18T556	$[2, 60]$ (GRH)
18.18.143831668082131915073650688000.1	x^18 - 20x^16 + 167x^14 - 757x^12 + 2025x^10 - 3248x^8 + 3022x^6 - 1477x^4 + 293x^2 - 5	\( 2^{30}\cdot 5^{3}\cdot 37^{6}\cdot 107^{2}\cdot 191^{2} \)	18T556	Trivial (GRH)
18.18.164318006876410189488454893568.1	x^18 - 38x^16 - 6x^15 + 498x^14 - 36x^13 - 3084x^12 + 1208x^11 + 9284x^10 - 6272x^9 - 12044x^8 + 10260x^7 + 6260x^6 - 6288x^5 - 1104x^4 + 1408x^3 + 40x^2 - 80x - 8	\( 2^{18}\cdot 37^{6}\cdot 97^{3}\cdot 16361^{2} \)	18T556	Trivial (GRH)