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 60)

Label	Polynomial	Discriminant	Galois group	Class group
18.2.297720850308809660352.1	x^18 - 3x^17 + 2x^16 + 10x^14 - 23x^13 + 6x^12 + 20x^11 - 11x^10 + 7x^9 - 65x^8 + 106x^7 - 43x^6 - 60x^5 + 101x^4 - 69x^3 + 28x^2 - 7x + 1	\( 2^{6}\cdot 3^{6}\cdot 23^{7}\cdot 37^{4} \)	18T835	Trivial
18.2.297720850308809660352.2	x^18 - 4x^17 + 10x^16 - 27x^15 + 57x^14 - 83x^13 + 97x^12 - 102x^11 + 82x^10 - 36x^9 + 13x^8 - 34x^7 + 37x^6 - 5x^5 - 2x^4 - 15x^3 + 16x^2 - 7x + 1	\( 2^{6}\cdot 3^{6}\cdot 23^{7}\cdot 37^{4} \)	18T835	Trivial (GRH)
18.0.828440626946252967936.2	x^18 + 7x^16 + 23x^14 + 43x^12 + 53x^10 + 48x^8 + 47x^6 + 15x^4 + 15x^2 + 1	\( -\,2^{12}\cdot 3^{6}\cdot 23^{6}\cdot 37^{4} \)	18T835	Trivial
18.0.6847579557102622188096.1	x^18 - 5x^17 + 6x^16 + 14x^15 - 44x^14 + 16x^13 + 76x^12 - 89x^11 - 36x^10 + 104x^9 - x^8 - 77x^7 + 28x^6 + 25x^5 - 14x^4 - 4x^3 + 7x^2 + 1	\( -\,2^{6}\cdot 3^{6}\cdot 23^{8}\cdot 37^{4} \)	18T835	Trivial (GRH)
18.4.15269546948445306880000.1	x^18 - 7x^17 + 18x^16 - 17x^15 - 18x^14 + 82x^13 - 117x^12 + 56x^11 + 65x^10 - 114x^9 + 93x^8 - 178x^7 + 313x^6 - 260x^5 + 88x^4 - 19x^3 + 25x^2 - 5x - 5	\( -\,2^{18}\cdot 5^{4}\cdot 11^{4}\cdot 23^{6}\cdot 43 \)	18T835	Trivial (GRH)
18.2.31604411125851914240000.1	x^18 - 2x^17 - x^16 + 12x^15 - 11x^14 - 34x^13 + 40x^12 + 40x^11 - 78x^10 - 2x^9 + 163x^8 + 84x^7 - 18x^6 + 76x^5 + 156x^4 + 112x^3 + 44x^2 + 10x + 1	\( 2^{18}\cdot 5^{4}\cdot 11^{4}\cdot 23^{6}\cdot 89 \)	18T835	Trivial (GRH)
18.2.48649486789232721920000.1	x^18 - x^17 - x^16 - x^15 - x^14 + 7x^13 - 9x^12 + 2x^11 + 3x^10 - 5x^9 + 9x^8 - 19x^7 + 10x^6 - 8x^5 + 10x^4 - 7x^3 + x^2 - 3x + 1	\( 2^{18}\cdot 5^{4}\cdot 11^{4}\cdot 23^{6}\cdot 137 \)	18T835	Trivial (GRH)
18.4.52183948285615365881856.1	x^18 - 7x^17 + 13x^16 + 12x^15 - 56x^14 + 20x^13 + 64x^12 - 50x^11 + x^10 + 17x^9 - 33x^8 + 26x^7 + 8x^6 - 24x^5 - 14x^4 - 18x^3 - 7x^2 + x - 1	\( -\,2^{16}\cdot 3^{12}\cdot 47^{6}\cdot 139 \)	18T835	Trivial
18.2.61569550495258417299456.1	x^18 - 2x^17 - 6x^16 + 16x^15 + 6x^14 - 52x^13 + 30x^12 + 86x^11 - 96x^10 - 48x^9 + 130x^8 - 114x^7 + 58x^6 - 4x^5 + 28x^4 - 28x^3 + 6x - 2	\( 2^{18}\cdot 3^{12}\cdot 41\cdot 47^{6} \)	18T835	Trivial
18.4.113633837755872051200000.1	x^18 - 2x^17 - x^16 - 2x^15 + 7x^14 + 12x^13 + 2x^12 + 8x^11 - 21x^10 - 16x^9 - 21x^8 + 8x^7 + 2x^6 + 12x^5 + 7x^4 - 2x^3 - x^2 - 2x + 1	\( -\,2^{24}\cdot 5^{5}\cdot 11^{4}\cdot 23^{6} \)	18T835	Trivial (GRH)
18.2.156551844856846097645568.1	x^18 - 6x^17 + 11x^16 - 26x^14 + 36x^13 + 40x^12 - 240x^11 + 298x^10 + 48x^9 - 456x^8 + 456x^7 + 10x^6 - 456x^5 + 420x^4 - 132x^3 - 15x^2 + 18x - 3	\( 2^{16}\cdot 3^{13}\cdot 47^{6}\cdot 139 \)	18T835	Trivial
18.4.184708651485775251898368.1	x^18 - 2x^17 + 3x^16 + 12x^15 - 52x^14 + 134x^13 - 214x^12 + 236x^11 - 134x^10 - 62x^9 + 252x^8 - 336x^7 + 292x^6 - 198x^5 + 114x^4 - 60x^3 + 21x^2 - 3	\( -\,2^{18}\cdot 3^{13}\cdot 41\cdot 47^{6} \)	18T835	Trivial
18.0.1454513123275162255360000.1	x^18 + 4x^16 + 2x^14 + 7x^12 + 62x^10 + 95x^8 + 10x^6 - 35x^4 + 5x^2 + 1	\( -\,2^{30}\cdot 5^{4}\cdot 11^{4}\cdot 23^{6} \)	18T835	Trivial (GRH)
18.0.2749938873692103639040000.1	x^18 - 8x^17 + 33x^16 - 80x^15 + 117x^14 - 76x^13 - 45x^12 + 136x^11 - 87x^10 - 36x^9 + 117x^8 - 166x^7 + 115x^6 - 16x^5 - 62x^4 + 152x^3 + 88x^2 + 88	\( -\,2^{24}\cdot 5^{4}\cdot 11^{6}\cdot 23^{6} \)	18T835	Trivial (GRH)
18.0.6005178718012435119004224.1	x^18 - 6x^17 + 19x^16 - 39x^15 + 67x^14 - 70x^13 + 55x^12 + 37x^11 - 61x^10 + 108x^9 - 137x^8 + 61x^7 - 42x^6 - 129x^5 + 122x^4 + 4x^3 + 17x^2 + 71x + 23	\( -\,2^{6}\cdot 3^{12}\cdot 7^{6}\cdot 107^{6} \)	18T835	Trivial (GRH)
18.6.7272565616375811276800000.1	x^18 - 15x^16 + 71x^14 - 106x^12 - 54x^10 + 81x^8 - 17x^6 - 45x^4 + 30x^2 - 5	\( 2^{30}\cdot 5^{5}\cdot 11^{4}\cdot 23^{6} \)	18T835	Trivial (GRH)
18.6.13749694368460518195200000.1	x^18 - 7x^17 + 14x^16 + 5x^15 - 53x^14 + 88x^13 - 121x^12 + 168x^11 - 103x^10 - 285x^9 + 932x^8 - 1539x^7 + 1428x^6 + 25x^5 - 885x^4 + 565x^3 + 385x^2 - 330x + 55	\( 2^{24}\cdot 5^{5}\cdot 11^{6}\cdot 23^{6} \)	18T835	Trivial (GRH)
18.6.18015536154037305357012672.1	x^18 - 6x^17 + 10x^16 + 16x^15 - 89x^14 + 150x^13 - 102x^12 - 235x^11 + 1044x^10 - 1586x^9 + 502x^8 + 1546x^7 - 2702x^6 + 3408x^5 - 4101x^4 + 3105x^3 - 1008x^2 + 27x + 27	\( 2^{6}\cdot 3^{13}\cdot 7^{6}\cdot 107^{6} \)	18T835	Trivial (GRH)
18.6.18068410525828031145050112.2	x^18 - 7x^16 + 12x^14 + 16x^12 - 50x^10 - 38x^8 + 88x^6 + 68x^4 - 47x^2 - 47	\( 2^{26}\cdot 3^{12}\cdot 47^{7} \)	18T835	Trivial (GRH)
18.0.54205231577484093435150336.1	x^18 - 2x^17 + 8x^16 - 20x^15 + 36x^14 - 84x^13 + 124x^12 - 242x^11 + 322x^10 - 466x^9 + 684x^8 - 648x^7 + 1050x^6 - 548x^5 + 1232x^4 - 228x^3 + 864x^2 + 112x + 394	\( -\,2^{26}\cdot 3^{13}\cdot 47^{7} \)	18T835	$[2]$ (GRH)
18.12.59664311399347335360555859375.1	x^18 - 9x^17 + 38x^16 - 100x^15 + 109x^14 + 273x^13 - 1272x^12 + 2185x^11 - 1281x^10 - 2494x^9 + 6364x^8 - 5801x^7 + 1021x^6 + 3096x^5 - 3160x^4 + 1106x^3 - 49x^2 - 27x - 1	\( -\,5^{8}\cdot 7\cdot 139^{4}\cdot 197^{6} \)	18T835	Trivial (GRH)
18.4.59664311399347335360555859375.1	x^18 + 29x^16 + 217x^14 + 629x^12 + 643x^10 - 136x^8 - 470x^6 - 121x^4 + 22x^2 + 7	\( -\,5^{8}\cdot 7\cdot 139^{4}\cdot 197^{6} \)	18T835	Trivial (GRH)
18.10.144899041969843528732778515625.1	x^18 - 9x^17 + 42x^16 - 132x^15 + 218x^14 + 70x^13 - 1142x^12 + 2588x^11 - 2927x^10 + 1017x^9 + 2018x^8 - 3620x^7 + 2767x^6 - 891x^5 - 148x^4 + 179x^3 - 25x^2 - 6x + 1	\( 5^{8}\cdot 17\cdot 139^{4}\cdot 197^{6} \)	18T835	Trivial (GRH)
18.10.144899041969843528732778515625.2	x^18 - 6x^17 + 23x^16 - 95x^15 + 247x^14 - 70x^13 - 1350x^12 + 3384x^11 - 2552x^10 - 1786x^9 + 3468x^8 + 924x^7 - 5733x^6 + 5181x^5 - 1049x^4 - 1380x^3 + 1050x^2 - 275x + 25	\( 5^{8}\cdot 17\cdot 139^{4}\cdot 197^{6} \)	18T835	Trivial (GRH)
18.4.230133772540339722105001171875.1	x^18 - 5x^17 - 13x^16 + 82x^15 + 104x^14 - 526x^13 - 792x^12 + 1601x^11 + 3617x^10 - 731x^9 - 7461x^8 - 6575x^7 + 848x^6 + 5349x^5 + 4121x^4 + 877x^3 - 783x^2 - 260x + 85	\( -\,3^{3}\cdot 5^{8}\cdot 139^{4}\cdot 197^{6} \)	18T835	Trivial (GRH)
18.12.298321556996736676802779296875.1	x^18 - 4x^17 - 19x^16 + 69x^15 + 193x^14 - 487x^13 - 1550x^12 + 2387x^11 + 7731x^10 - 7169x^9 - 19768x^8 + 2727x^7 + 22718x^6 + 15339x^5 + 3469x^4 - 123x^3 - 165x^2 - 23x - 1	\( -\,5^{9}\cdot 7\cdot 139^{4}\cdot 197^{6} \)	18T835	Trivial (GRH)
18.12.366509341453133631500557421875.1	x^18 - 6x^17 + 12x^16 - 13x^15 - 22x^14 + 144x^13 + 9x^12 - 353x^11 - 1049x^10 + 1776x^9 + 4809x^8 - 5823x^7 - 10456x^6 + 6504x^5 + 11777x^4 + 337x^3 - 3432x^2 - 976x - 64	\( -\,5^{8}\cdot 43\cdot 139^{4}\cdot 197^{6} \)	18T835	Trivial (GRH)
18.8.366509341453133631500557421875.1	x^18 - 8x^17 + 7x^16 + 76x^15 - 115x^14 - 321x^13 + 313x^12 + 1292x^11 + 244x^10 - 6092x^9 - 728x^8 + 18476x^7 - 4685x^6 - 27214x^5 + 7681x^4 + 21831x^3 - 862x^2 - 8488x - 2504	\( -\,5^{8}\cdot 43\cdot 139^{4}\cdot 197^{6} \)	18T835	Trivial (GRH)
18.8.545502275651175637582225000000.1	x^18 - 177x^14 + 131x^12 + 2128x^10 + 1065x^8 - 2865x^6 - 687x^4 - 22x^2 + 1	\( -\,2^{6}\cdot 5^{8}\cdot 139^{4}\cdot 197^{6} \)	18T835	Trivial (GRH)
18.8.545502275651175637582225000000.2	x^18 + 4x^16 - 91x^14 - 447x^12 + 17x^10 + 1322x^8 + 736x^6 - 396x^4 - 91x^2 + 25	\( -\,2^{6}\cdot 5^{8}\cdot 139^{4}\cdot 197^{6} \)	18T835	Trivial (GRH)
18.8.707448263735118404989448046875.1	x^18 - 7x^17 + 18x^16 - 16x^15 - 39x^14 + 251x^13 - 698x^12 + 760x^11 + 616x^10 - 1445x^9 - 2104x^8 + 4601x^7 + 434x^6 - 1425x^5 - 804x^4 - 5477x^3 + 4840x^2 + 266x - 503	\( -\,5^{8}\cdot 83\cdot 139^{4}\cdot 197^{6} \)	18T835	Trivial (GRH)
18.10.724495209849217643663892578125.1	x^18 - 9x^17 + 19x^16 + 52x^15 - 324x^14 + 644x^13 - 137x^12 - 2532x^11 + 6932x^10 - 9591x^9 + 5603x^8 + 5384x^7 - 16653x^6 + 20386x^5 - 14946x^4 + 6628x^3 - 1226x^2 - 231x + 85	\( 5^{9}\cdot 17\cdot 139^{4}\cdot 197^{6} \)	18T835	Trivial (GRH)
18.14.724495209849217643663892578125.1	x^18 - 2x^17 - 29x^16 + 18x^15 + 248x^14 - 133x^13 - 1003x^12 + 999x^11 + 2197x^10 - 5250x^9 - 4356x^8 + 14206x^7 + 11231x^6 - 16088x^5 - 16894x^4 + 3612x^3 + 8488x^2 + 2743x + 227	\( 5^{9}\cdot 17\cdot 139^{4}\cdot 197^{6} \)	18T835	Trivial (GRH)
18.6.724495209849217643663892578125.1	x^18 + 28x^16 + 196x^14 + 306x^12 - 788x^10 - 1724x^8 + 445x^6 + 2039x^4 + 670x^2 - 85	\( 5^{9}\cdot 17\cdot 139^{4}\cdot 197^{6} \)	18T835	Trivial (GRH)
18.14.724495209849217643663892578125.2	x^18 - 2x^17 - 17x^16 + 7x^15 + 132x^14 + 255x^13 - 631x^12 - 2141x^11 + 1160x^10 + 4991x^9 + 3452x^8 + 2060x^7 - 16956x^6 - 19823x^5 + 20531x^4 + 19891x^3 - 7863x^2 - 4657x + 995	\( 5^{9}\cdot 17\cdot 139^{4}\cdot 197^{6} \)	18T835	Trivial (GRH)
18.8.980199401560706223780560546875.1	x^18 - 9x^17 + 45x^16 - 156x^15 + 366x^14 - 546x^13 + 301x^12 + 846x^11 - 2395x^10 + 2504x^9 - 46x^8 - 3428x^7 + 3761x^6 - 104x^5 - 2135x^4 + 1093x^3 + 102x^2 - 200x + 40	\( -\,5^{9}\cdot 23\cdot 139^{4}\cdot 197^{6} \)	18T835	Trivial (GRH)
18.12.1014293293788904701129449609375.1	x^18 - 3x^17 - 24x^16 + 96x^15 + 108x^14 - 882x^13 + 987x^12 + 1413x^11 - 6993x^10 + 12395x^9 - 882x^8 - 32055x^7 + 38740x^6 + 3233x^5 - 27650x^4 + 8633x^3 + 4538x^2 - 2280x + 200	\( -\,5^{8}\cdot 7\cdot 17\cdot 139^{4}\cdot 197^{6} \)	18T835	Trivial (GRH)
18.6.1474560838869584145339451953125.1	x^18 - 4x^17 - 5x^16 + 40x^15 + 9x^14 - 298x^13 + 255x^12 + 1197x^11 - 2144x^10 - 1625x^9 + 6495x^8 - 1372x^7 - 8561x^6 + 5974x^5 + 4929x^4 - 6180x^3 - 512x^2 + 2449x - 683	\( 5^{8}\cdot 139^{4}\cdot 173\cdot 197^{6} \)	18T835	Trivial (GRH)
18.6.1576842515554179577386119140625.1	x^18 - 4x^17 - x^16 + 47x^15 - 142x^14 + 10x^13 + 513x^12 - 1210x^11 + 2132x^10 - 1078x^9 - 4654x^8 + 14964x^7 - 18245x^6 + 4800x^5 + 14840x^4 - 21560x^3 + 5600x^2 + 11200x - 8000	\( 5^{9}\cdot 37\cdot 139^{4}\cdot 197^{6} \)	18T835	Trivial (GRH)
18.8.2727511378255878187911125000000.1	x^18 + 2x^16 - 174x^14 - 265x^12 + 1110x^10 + 2052x^8 + 94x^6 - 638x^4 + 100x^2 + 5	\( -\,2^{6}\cdot 5^{9}\cdot 139^{4}\cdot 197^{6} \)	18T835	Trivial (GRH)
18.10.3622476049246088218319462890625.1	x^18 - 9x^17 + 16x^16 + 76x^15 - 375x^14 + 581x^13 + 370x^12 - 3663x^11 + 7505x^10 - 6450x^9 - 3302x^8 + 17439x^7 - 23691x^6 + 16778x^5 - 5340x^4 - 880x^3 + 1456x^2 - 512x + 64	\( 5^{10}\cdot 17\cdot 139^{4}\cdot 197^{6} \)	18T835	$[2]$ (GRH)
18.6.7884212577770897886930595703125.1	x^18 - 6x^17 + 5x^16 + 31x^15 - 95x^14 - 162x^13 + 204x^12 + 1092x^11 - 3291x^10 - 3018x^9 + 9321x^8 + 11782x^7 - 17855x^6 - 7532x^5 + 20815x^4 - 5669x^3 - 19316x^2 + 9444x - 1096	\( 5^{10}\cdot 37\cdot 139^{4}\cdot 197^{6} \)	18T835	$[2]$ (GRH)
18.0.74575522193513939612532736000000.1	x^18 + 47x^16 + 844x^14 + 7443x^12 + 34748x^10 + 88667x^8 + 124179x^6 + 91012x^4 + 30384x^2 + 3364	\( -\,2^{22}\cdot 5^{6}\cdot 53^{4}\cdot 229^{6} \)	18T835	$[2, 2, 4, 8]$ (GRH)
18.12.74575522193513939612532736000000.1	x^18 - 35x^16 + 292x^14 - 103x^12 - 5420x^10 + 7757x^8 + 22131x^6 - 35528x^4 + 3120x^2 + 784	\( -\,2^{22}\cdot 5^{6}\cdot 53^{4}\cdot 229^{6} \)	18T835	Trivial (GRH)
18.16.75824816315513413623929275000000.1	x^18 - 8x^16 - 233x^14 + 4233x^12 - 29497x^10 + 108494x^8 - 226196x^6 + 266185x^4 - 163325x^2 + 40171	\( -\,2^{6}\cdot 5^{8}\cdot 139^{5}\cdot 197^{6} \)	18T835	Trivial (GRH)
18.16.174560728208376204026312000000000.1	x^18 - 26x^16 + 163x^14 + 565x^12 - 8221x^10 + 27766x^8 - 38974x^6 + 21878x^4 - 4485x^2 + 245	\( -\,2^{12}\cdot 5^{9}\cdot 139^{4}\cdot 197^{6} \)	18T835	Trivial (GRH)
18.12.298302088774055758450130944000000.1	x^18 - 3x^17 - 23x^16 + 68x^15 + 28x^14 - 256x^13 + 980x^12 - 884x^11 - 3545x^10 + 5383x^9 - 2809x^8 - 4572x^7 + 20028x^6 - 4076x^5 - 10010x^4 + 3522x^3 + 691x^2 - 375x + 29	\( -\,2^{24}\cdot 5^{6}\cdot 53^{4}\cdot 229^{6} \)	18T835	Trivial (GRH)
18.0.298302088774055758450130944000000.2	x^18 + 38x^16 + 594x^14 + 4945x^12 + 23820x^10 + 68144x^8 + 115757x^6 + 112852x^4 + 57264x^2 + 11449	\( -\,2^{24}\cdot 5^{6}\cdot 53^{4}\cdot 229^{6} \)	18T835	$[2, 2, 160]$ (GRH)
18.4.1895620407887835340598231875000000.1	x^18 - 3x^17 - 3x^16 - 77x^15 + 563x^14 - 1044x^13 - 2749x^12 + 14333x^11 - 19637x^10 + 15400x^9 - 63011x^8 + 142297x^7 - 117079x^6 + 73366x^5 - 181136x^4 + 236452x^3 - 110700x^2 + 21728x - 1592	\( -\,2^{6}\cdot 5^{10}\cdot 139^{5}\cdot 197^{6} \)	18T835	$[2]$ (GRH)
18.10.1895620407887835340598231875000000.1	x^18 - 4x^17 - 15x^16 + 112x^15 - 237x^14 - 218x^13 + 3951x^12 - 9260x^11 + 1065x^10 + 34040x^9 - 117752x^8 + 111778x^7 + 296175x^6 - 522324x^5 - 685871x^4 + 19856x^3 + 139813x^2 + 430x - 415	\( 2^{6}\cdot 5^{10}\cdot 139^{5}\cdot 197^{6} \)	18T835	Trivial (GRH)