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 62)

Label	Polynomial	Discriminant	Galois group	Class group
18.2.63147574802143803281.1	x^18 - x^17 + 2x^16 - 4x^15 + 6x^14 - 20x^13 + 22x^12 - 27x^11 + 19x^10 - 11x^9 + 16x^8 - 5x^7 + 2x^6 - 5x^5 - 9x^4 - 7x^3 - x^2 + 2x + 1	\( 23^{7}\cdot 2647^{3} \)	18T880	Trivial
18.0.7621550509827143696384.1	x^18 - x^17 + 6x^16 - 12x^15 + 22x^14 - 40x^13 + 66x^12 - 98x^11 + 119x^10 - 149x^9 + 186x^8 - 180x^7 + 168x^6 - 134x^5 + 52x^4 - 4x^3 + 4x^2 - 6x + 2	\( -\,2^{16}\cdot 37^{7}\cdot 107^{3} \)	18T880	Trivial
18.4.11057884553156973101663.1	x^18 - 2x^17 + 3x^16 + 5x^15 - 26x^14 + 38x^13 - 21x^12 - 66x^11 + 172x^10 - 180x^9 + 46x^8 + 149x^7 - 295x^6 + 190x^5 + 12x^4 - 99x^3 + 66x^2 - 17x + 1	\( -\,23^{7}\cdot 59^{3}\cdot 251^{3} \)	18T880	Trivial
18.4.11057884553156973101663.2	x^18 - 6x^17 + 25x^16 - 68x^15 + 132x^14 - 154x^13 + 42x^12 + 226x^11 - 448x^10 + 359x^9 + 23x^8 - 304x^7 + 213x^6 + 16x^5 - 109x^4 + 40x^3 + 6x^2 - 16x - 1	\( -\,23^{7}\cdot 59^{3}\cdot 251^{3} \)	18T880	Trivial
18.6.25072932662150253498368.1	x^18 - x^17 - 8x^16 + 3x^15 + 12x^14 + 6x^13 + 18x^12 - 23x^11 - 39x^10 + 21x^9 - 14x^8 - 7x^7 + 34x^6 + 15x^5 + 43x^4 + 65x^3 + 41x^2 + 11x + 1	\( 2^{12}\cdot 37^{7}\cdot 401^{3} \)	18T880	Trivial
18.4.66833836391543688921088.1	x^18 - 2x^17 - 2x^16 + 26x^14 - 42x^13 + 12x^12 + 6x^11 + 16x^10 - 28x^9 + 34x^8 + 28x^7 - 164x^6 + 124x^5 + 60x^4 - 88x^3 + 20x^2 + 2x - 2	\( -\,2^{18}\cdot 37^{7}\cdot 139^{3} \)	18T880	Trivial
18.0.85680665737806343831552.1	x^18 - 2x^17 + 5x^16 - 16x^15 + 25x^14 - 42x^13 + 64x^12 - 86x^11 + 92x^10 - 118x^9 + 153x^8 - 76x^7 + 161x^6 - 36x^5 + 115x^4 - 18x^3 + 60x^2 - 6x + 17	\( -\,2^{18}\cdot 37^{7}\cdot 151^{3} \)	18T880	Trivial
18.4.85680665737806343831552.1	x^18 - 4x^17 + 6x^16 - 8x^15 + 27x^14 - 52x^13 + 35x^12 - 76x^11 + 191x^10 - 76x^9 - 12x^8 - 232x^7 + 182x^6 + 138x^5 - 191x^4 + 140x^3 - 105x^2 + 54x - 17	\( -\,2^{18}\cdot 37^{7}\cdot 151^{3} \)	18T880	Trivial
18.6.1604667690377616223895552.1	x^18 - 2x^17 - 3x^16 + 8x^15 - 48x^14 + 70x^13 - 36x^12 - 16x^11 + 86x^10 - 362x^9 + 346x^8 + 584x^7 - 1432x^6 + 1114x^5 - 388x^4 + 280x^3 - 207x^2 + 12x + 1	\( 2^{18}\cdot 37^{7}\cdot 401^{3} \)	18T880	Trivial
18.6.1604667690377616223895552.2	x^18 - 2x^17 + 8x^16 - 22x^15 + 28x^14 - 60x^13 + 40x^12 + 84x^11 - 228x^10 + 708x^9 - 1132x^8 + 1260x^7 - 1324x^6 + 96x^5 + 1680x^4 - 2424x^3 + 2088x^2 - 1008x + 184	\( 2^{18}\cdot 37^{7}\cdot 401^{3} \)	18T880	Trivial
18.6.1604667690377616223895552.3	x^18 - 6x^17 + 10x^16 + 26x^15 - 177x^14 + 434x^13 - 601x^12 + 576x^11 - 635x^10 + 1114x^9 - 1780x^8 + 2132x^7 - 1968x^6 + 1200x^5 - 517x^4 + 364x^3 - 133x^2 - 42x + 1	\( 2^{18}\cdot 37^{7}\cdot 401^{3} \)	18T880	Trivial
18.2.15955301891595616150355968.1	x^18 - 17x^16 + 95x^14 - 63x^12 - 1369x^10 + 4766x^8 + 805x^6 - 33244x^4 + 65130x^2 - 40393	\( 2^{18}\cdot 31^{7}\cdot 1303^{3} \)	18T880	Trivial (GRH)
18.12.48263199009838598797471744.1	x^18 - 3x^17 - 3x^16 + 19x^15 - 49x^14 + 71x^13 + 104x^12 - 367x^11 + 376x^10 - 259x^9 - 321x^8 + 641x^7 - 78x^6 + 302x^5 - 138x^4 - 433x^3 + 18x^2 + 41x + 1	\( -\,2^{12}\cdot 101^{7}\cdot 479^{3} \)	18T880	Trivial (GRH)
18.8.48263199009838598797471744.1	x^18 - 2x^17 - 12x^16 + 39x^15 + 22x^14 - 104x^13 - 36x^12 + 56x^11 + 146x^10 - 85x^9 - 40x^8 + 118x^7 - 132x^6 + 54x^5 - 32x^4 + 17x^3 - 8x^2 + 6x - 1	\( -\,2^{12}\cdot 101^{7}\cdot 479^{3} \)	18T880	Trivial
18.8.48263199009838598797471744.2	x^18 - 5x^17 - x^16 + 43x^15 - 64x^14 - 68x^13 + 253x^12 - 144x^11 - 545x^10 + 1246x^9 - 760x^8 - 610x^7 + 1117x^6 - 621x^5 + 62x^4 + 234x^3 - 148x^2 + 20x + 1	\( -\,2^{12}\cdot 101^{7}\cdot 479^{3} \)	18T880	Trivial
18.10.102698732184167438329315328.1	x^18 - 12x^16 - x^14 + 465x^12 - 1517x^10 - 2470x^8 + 22528x^6 - 48351x^4 + 44511x^2 - 14837	\( 2^{24}\cdot 37^{7}\cdot 401^{3} \)	18T880	Trivial (GRH)
18.2.102698732184167438329315328.1	x^18 - 6x^17 + 10x^16 + 20x^15 - 113x^14 + 126x^13 + 337x^12 - 1246x^11 + 2115x^10 - 526x^9 - 3634x^8 + 10614x^7 - 15404x^6 + 17070x^5 - 13501x^4 + 8644x^3 - 3815x^2 + 1254x - 169	\( 2^{24}\cdot 37^{7}\cdot 401^{3} \)	18T880	Trivial
18.10.102698732184167438329315328.2	x^18 - 2x^17 + x^16 + 4x^15 - 61x^14 + 60x^13 + 24x^12 - 146x^11 + 760x^10 + 150x^9 - 725x^8 + 604x^7 - 231x^6 - 2298x^5 - 2747x^4 - 566x^3 + 406x^2 + 100x - 13	\( 2^{24}\cdot 37^{7}\cdot 401^{3} \)	18T880	Trivial (GRH)
18.2.102698732184167438329315328.2	x^18 + 7x^16 - 51x^14 - 174x^12 + 1312x^10 + 73x^8 - 8441x^6 + 7399x^4 + 12578x^2 - 14837	\( 2^{24}\cdot 37^{7}\cdot 401^{3} \)	18T880	Trivial
18.0.1361907441288065751736030903.1	x^18 + 23x^16 - 29x^15 + 70x^14 - 545x^13 - 896x^12 - 1908x^11 - 2443x^10 + 7651x^9 + 29066x^8 + 77548x^7 + 161183x^6 + 252612x^5 + 325599x^4 + 373699x^3 + 318952x^2 + 206479x + 132661	\( -\,23^{7}\cdot 43^{3}\cdot 347^{5} \)	18T880	$[2, 2]$ (GRH)
18.0.1580039033725662741877489664.1	x^18 - 5x^16 - 89x^14 + 774x^12 + 1005x^10 - 18725x^8 + 68533x^6 - 83974x^4 - 96776x^2 + 278231	\( -\,2^{18}\cdot 23^{7}\cdot 12097^{3} \)	18T880	Trivial (GRH)
18.0.3088844736629670323038191616.1	x^18 + 7x^16 - 16x^15 + x^14 - 26x^13 + 190x^12 + 380x^11 - 830x^10 + 1718x^9 + 1275x^8 - 2184x^7 + 4177x^6 - 1646x^5 + 3469x^4 - 3742x^3 + 5018x^2 - 364x + 1421	\( -\,2^{18}\cdot 101^{7}\cdot 479^{3} \)	18T880	$[2]$
18.12.3088844736629670323038191616.1	x^18 - 17x^16 - 6x^15 + 71x^14 + 106x^13 + 150x^12 - 650x^11 - 1570x^10 + 2104x^9 + 3109x^8 - 5022x^7 - 2521x^6 + 7246x^5 + 2121x^4 - 3728x^3 - 1320x^2 - 74x + 1	\( -\,2^{18}\cdot 101^{7}\cdot 479^{3} \)	18T880	Trivial (GRH)
18.4.3088844736629670323038191616.1	x^18 - 8x^17 + 24x^16 - 42x^15 + 50x^14 + 88x^13 - 244x^12 + 636x^11 - 920x^10 + 1560x^9 - 3316x^8 + 4672x^7 - 6748x^6 + 4432x^5 - 2680x^4 - 1080x^3 + 1240x^2 - 1176x + 392	\( -\,2^{18}\cdot 101^{7}\cdot 479^{3} \)	18T880	$[2]$
18.8.3088844736629670323038191616.1	x^18 - 4x^17 - 13x^16 + 96x^15 - 155x^14 - 90x^12 + 944x^11 + 118x^10 - 6404x^9 + 10729x^8 - 874x^7 - 14733x^6 + 14306x^5 - 1903x^4 - 1720x^3 - 1972x^2 + 2088x - 457	\( -\,2^{18}\cdot 101^{7}\cdot 479^{3} \)	18T880	Trivial (GRH)
18.4.3088844736629670323038191616.2	x^18 - 6x^17 + 22x^16 - 24x^15 + 6x^13 + 478x^12 - 1208x^11 + 1448x^10 - 764x^9 + 688x^8 - 3068x^7 + 3272x^6 - 712x^5 - 4344x^4 + 4328x^3 - 3776x^2 + 2072x - 392	\( -\,2^{18}\cdot 101^{7}\cdot 479^{3} \)	18T880	$[2]$
18.8.3088844736629670323038191616.2	x^18 - 8x^17 + 20x^16 - 34x^15 + 77x^14 - 50x^13 - 79x^12 + 116x^11 - 329x^10 + 430x^9 + 52x^8 - 394x^7 - 268x^6 + 1150x^5 + 257x^4 - 1918x^3 + 1075x^2 + 382x - 479	\( -\,2^{18}\cdot 101^{7}\cdot 479^{3} \)	18T880	Trivial (GRH)
18.4.3088844736629670323038191616.3	x^18 - 8x^17 + 33x^16 - 74x^15 + 54x^14 + 206x^13 - 738x^12 + 882x^11 + 588x^10 - 3762x^9 + 5624x^8 - 2154x^7 - 6510x^6 + 13254x^5 - 10574x^4 - 438x^3 + 11427x^2 - 9874x + 3031	\( -\,2^{18}\cdot 101^{7}\cdot 479^{3} \)	18T880	Trivial
18.8.3088844736629670323038191616.3	x^18 - 4x^17 - 4x^16 + 14x^15 + 39x^14 + 2x^13 - 261x^12 - 248x^11 + 763x^10 + 2972x^9 - 4434x^8 - 9216x^7 + 16160x^6 + 6048x^5 - 17103x^4 + 896x^3 + 5821x^2 - 2132x - 1397	\( -\,2^{18}\cdot 101^{7}\cdot 479^{3} \)	18T880	Trivial (GRH)
18.4.3088844736629670323038191616.4	x^18 - 6x^17 + 20x^16 - 60x^15 + 140x^14 - 262x^13 + 482x^12 - 648x^11 + 732x^10 - 1020x^9 - 40x^8 - 792x^7 - 1112x^6 + 680x^5 + 864x^4 + 2792x^3 + 3912x^2 + 1080x - 216	\( -\,2^{18}\cdot 101^{7}\cdot 479^{3} \)	18T880	$[2, 2]$
18.2.6572718859786716053076180992.1	x^18 + 26x^16 + 271x^14 + 1253x^12 + 1591x^10 - 4844x^8 - 9632x^6 + 11021x^4 + 14837x^2 - 14837	\( 2^{30}\cdot 37^{7}\cdot 401^{3} \)	18T880	Trivial (GRH)
18.6.6572718859786716053076180992.1	x^18 + 11x^16 - 4x^14 + 128x^12 - 522x^10 + 174x^8 - 672x^6 - 1652x^4 + 14837x^2 - 14837	\( 2^{30}\cdot 37^{7}\cdot 401^{3} \)	18T880	Trivial (GRH)
18.2.6572718859786716053076180992.2	x^18 + 23x^16 + 155x^14 + 248x^12 - 1882x^10 - 12131x^8 - 33129x^6 - 50227x^4 - 41588x^2 - 14837	\( 2^{30}\cdot 37^{7}\cdot 401^{3} \)	18T880	$[2]$ (GRH)
18.6.6572718859786716053076180992.2	x^18 - 7x^16 - 69x^14 + 384x^12 + 1300x^10 - 3283x^8 - 4197x^6 + 5581x^4 + 1776x^2 - 14837	\( 2^{30}\cdot 37^{7}\cdot 401^{3} \)	18T880	$[2]$ (GRH)
18.10.108988713031592961639231782912.1	x^18 - 2x^17 - 18x^16 - 20x^15 + 77x^14 + 398x^13 + 463x^12 - 830x^11 - 3717x^10 - 4082x^9 + 2588x^8 + 12988x^7 + 13638x^6 - 4144x^5 - 20439x^4 - 11752x^3 + 4693x^2 + 6356x + 1559	\( 2^{18}\cdot 37^{7}\cdot 16361^{3} \)	18T880	Trivial (GRH)
18.14.108988713031592961639231782912.1	x^18 - 6x^17 - 8x^16 + 98x^15 - 83x^14 - 298x^13 + 233x^12 + 248x^11 + 2137x^10 - 7876x^9 + 9540x^8 + 2002x^7 - 15970x^6 + 9750x^5 + 3345x^4 - 3624x^3 + 239x^2 + 204x - 29	\( 2^{18}\cdot 37^{7}\cdot 16361^{3} \)	18T880	Trivial (GRH)
18.2.108988713031592961639231782912.1	x^18 - 2x^17 + 18x^16 - 68x^15 + 147x^14 - 506x^13 + 1245x^12 - 1650x^11 + 2847x^10 - 7702x^9 + 4348x^8 + 1432x^7 + 44600x^6 - 38948x^5 - 39997x^4 + 10112x^3 + 26867x^2 - 51780x - 110251	\( 2^{18}\cdot 37^{7}\cdot 16361^{3} \)	18T880	$[2]$ (GRH)
18.6.108988713031592961639231782912.1	x^18 - 8x^17 + 21x^16 + 34x^15 - 498x^14 + 2278x^13 - 7232x^12 + 19210x^11 - 46648x^10 + 103070x^9 - 194866x^8 + 297646x^7 - 353770x^6 + 316106x^5 - 202748x^4 + 89142x^3 - 24453x^2 + 2794x + 137	\( 2^{18}\cdot 37^{7}\cdot 16361^{3} \)	18T880	Trivial (GRH)
18.10.108988713031592961639231782912.2	x^18 - 6x^17 + 4x^16 + 18x^15 - 43x^14 + 268x^13 - 375x^12 - 702x^11 + 773x^10 - 2580x^9 + 9942x^8 + 4626x^7 - 15466x^6 - 9672x^5 - 86265x^4 + 56318x^3 + 219287x^2 - 51510x - 125441	\( 2^{18}\cdot 37^{7}\cdot 16361^{3} \)	18T880	Trivial (GRH)
18.14.108988713031592961639231782912.2	x^18 - 6x^17 + 4x^16 + 52x^15 - 149x^14 - 48x^13 + 673x^12 - 354x^11 - 421x^10 - 678x^9 - 2210x^8 + 5586x^7 + 2500x^6 - 5560x^5 + 121x^4 + 994x^3 - 175x^2 - 8x + 1	\( 2^{18}\cdot 37^{7}\cdot 16361^{3} \)	18T880	$[2]$ (GRH)
18.6.108988713031592961639231782912.2	x^18 - 6x^17 + 7x^16 - 6x^15 + 101x^14 - 148x^13 - 68x^12 + 658x^11 - 6154x^10 + 6482x^9 + 14373x^8 + 9678x^7 - 23777x^6 - 67118x^5 + 34133x^4 - 36342x^3 + 52358x^2 - 22524x + 15061	\( 2^{18}\cdot 37^{7}\cdot 16361^{3} \)	18T880	$[2]$ (GRH)
18.10.108988713031592961639231782912.3	x^18 - 6x^17 + 8x^16 - 12x^15 + x^14 + 454x^13 - 1293x^12 + 1734x^11 - 3721x^10 + 5650x^9 - 5654x^8 + 7668x^7 - 3916x^6 + 3420x^5 - 3793x^4 - 2706x^3 + 2621x^2 + 26x - 193	\( 2^{18}\cdot 37^{7}\cdot 16361^{3} \)	18T880	Trivial (GRH)
18.10.108988713031592961639231782912.4	x^18 - 2x^17 - 4x^16 + 6x^15 - 131x^14 + 54x^13 - 69x^12 - 626x^11 + 3511x^10 - 2022x^9 + 7454x^8 + 9688x^7 - 19332x^6 + 21932x^5 - 37287x^4 - 42196x^3 + 22321x^2 + 8304x + 541	\( 2^{18}\cdot 37^{7}\cdot 16361^{3} \)	18T880	Trivial (GRH)
18.0.197686063144298900674444263424.1	x^18 + 22x^16 - 16x^15 + 263x^14 - 188x^13 + 1863x^12 - 1438x^11 + 7585x^10 - 8362x^9 + 18826x^8 - 50624x^7 + 40224x^6 - 113596x^5 + 67751x^4 - 75684x^3 + 380717x^2 + 309326x + 86293	\( -\,2^{24}\cdot 101^{7}\cdot 479^{3} \)	18T880	$[2, 2]$ (GRH)
18.8.197686063144298900674444263424.1	x^18 - 8x^17 + 24x^16 - 30x^15 - 47x^14 + 682x^13 - 3395x^12 + 7138x^11 + 1827x^10 - 38720x^9 + 78256x^8 - 78814x^7 + 49184x^6 - 10816x^5 - 8945x^4 + 6116x^3 - 4261x^2 - 1040x + 257	\( -\,2^{24}\cdot 101^{7}\cdot 479^{3} \)	18T880	Trivial (GRH)
18.12.12651908041235129643164432859136.1	x^18 - 38x^16 + 409x^14 - 539x^12 - 7247x^10 + 13026x^8 + 44226x^6 - 70005x^4 - 48379x^2 + 48379	\( -\,2^{30}\cdot 101^{7}\cdot 479^{3} \)	18T880	Trivial (GRH)
18.4.12651908041235129643164432859136.1	x^18 + 21x^16 - 179x^14 - 2390x^12 - 1514x^10 + 23545x^8 + 14197x^6 - 56259x^4 + 48379	\( -\,2^{30}\cdot 101^{7}\cdot 479^{3} \)	18T880	Trivial (GRH)
18.8.12651908041235129643164432859136.1	x^18 - 25x^16 + 60x^14 + 1200x^12 - 2474x^10 - 8998x^8 + 4448x^6 - 21020x^4 + 30805x^2 + 48379	\( -\,2^{30}\cdot 101^{7}\cdot 479^{3} \)	18T880	$[2]$ (GRH)
18.12.12651908041235129643164432859136.2	x^18 - 35x^16 + 356x^14 - 1134x^12 - 378x^10 + 4340x^8 + 5408x^6 - 5494x^4 - 48379x^2 + 48379	\( -\,2^{30}\cdot 101^{7}\cdot 479^{3} \)	18T880	Trivial (GRH)
18.4.12651908041235129643164432859136.2	x^18 + 23x^16 + 137x^14 - 222x^12 - 3402x^10 - 3153x^8 + 13375x^6 + 2133x^4 + 48379	\( -\,2^{30}\cdot 101^{7}\cdot 479^{3} \)	18T880	$[3]$ (GRH)