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 4594)

Label	Polynomial	Discriminant	Galois group	Class group
18.18.12267617659000607237787648.1	x^18 - 30x^16 - 37x^15 + 204x^14 + 294x^13 - 604x^12 - 858x^11 + 984x^10 + 1201x^9 - 984x^8 - 858x^7 + 604x^6 + 294x^5 - 204x^4 - 37x^3 + 30x^2 - 1	\( 2^{12}\cdot 3^{24}\cdot 13^{9} \)	$S_3 \times C_3$ (as 18T3)	Trivial (GRH)
18.18.13314770360250302126953125.1	x^18 - 24x^16 - 3x^15 + 216x^14 + 42x^13 - 943x^12 - 180x^11 + 2190x^10 + 272x^9 - 2772x^8 - 54x^7 + 1819x^6 - 180x^5 - 522x^4 + 110x^3 + 36x^2 - 6x - 1	\( 3^{24}\cdot 5^{9}\cdot 17^{6} \)	$S_3 \times C_6$ (as 18T6)	Trivial (GRH)
18.18.14824161510814728000000000.1	x^18 - 3x^17 - 24x^16 + 57x^15 + 237x^14 - 381x^13 - 1143x^12 + 1122x^11 + 2523x^10 - 1987x^9 - 2604x^8 + 2118x^7 + 1038x^6 - 1077x^5 - 12x^4 + 162x^3 - 21x^2 - 6x + 1	\( 2^{12}\cdot 3^{32}\cdot 5^{9} \)	$S_3 \times C_3$ (as 18T3)	Trivial (GRH)
18.18.17706519352529288000000000.1	x^18 - 6x^17 - 10x^16 + 97x^15 + 2x^14 - 560x^13 + 222x^12 + 1460x^11 - 630x^10 - 1983x^9 + 630x^8 + 1460x^7 - 222x^6 - 560x^5 - 2x^4 + 97x^3 + 10x^2 - 6x - 1	\( 2^{12}\cdot 5^{9}\cdot 19^{12} \)	$S_3 \times C_3$ (as 18T3)	Trivial (GRH)
18.18.21106009685505727678262841.1	x^18 - 3x^17 - 24x^16 + 96x^15 + 111x^14 - 861x^13 + 529x^12 + 2301x^11 - 3117x^10 - 1647x^9 + 4395x^8 - 453x^7 - 2235x^6 + 573x^5 + 474x^4 - 100x^3 - 45x^2 + 3x + 1	\( 3^{24}\cdot 73^{3}\cdot 577^{3} \)	18T207	Trivial (GRH)
18.18.23380151989531222748958669.1	x^18 - 4x^17 - 14x^16 + 71x^15 + 53x^14 - 472x^13 + 33x^12 + 1522x^11 - 555x^10 - 2661x^9 + 1098x^8 + 2705x^7 - 839x^6 - 1574x^5 + 194x^4 + 435x^3 + 27x^2 - 22x + 1	\( 3^{9}\cdot 7^{5}\cdot 643^{6} \)	18T284	Trivial (GRH)
18.18.36202993110042424993725741.1	x^18 - 18x^16 - x^15 + 135x^14 + 15x^13 - 546x^12 - 90x^11 + 1287x^10 + 276x^9 - 1782x^8 - 459x^7 + 1385x^6 + 405x^5 - 534x^4 - 170x^3 + 72x^2 + 24x + 1	\( 3^{27}\cdot 7^{15} \)	$C_6 \times C_3$ (as 18T2)	Trivial (GRH)
18.18.36408330967717863107914121.1	x^18 - 2x^17 - 28x^16 + 40x^15 + 301x^14 - 276x^13 - 1523x^12 + 872x^11 + 3837x^10 - 1473x^9 - 4871x^8 + 1489x^7 + 3019x^6 - 864x^5 - 779x^4 + 222x^3 + 44x^2 - 7x - 1	\( 7^{12}\cdot 138041^{3} \)	18T207	Trivial (GRH)
18.18.45672975569536652017399733.1	x^18 - 8x^17 - x^16 + 141x^15 - 219x^14 - 798x^13 + 2016x^12 + 1242x^11 - 6472x^10 + 2028x^9 + 7364x^8 - 5183x^7 - 2609x^6 + 2861x^5 - 66x^4 - 342x^3 + 35x^2 + 10x - 1	\( 7^{12}\cdot 53^{9} \)	$S_3 \times C_3$ (as 18T3)	Trivial (GRH)
18.18.46025638949152433124675584.1	x^18 - 7x^17 - 6x^16 + 144x^15 - 189x^14 - 975x^13 + 2404x^12 + 1953x^11 - 10054x^10 + 3451x^9 + 15638x^8 - 14529x^7 - 5420x^6 + 10671x^5 - 2089x^4 - 1318x^3 + 248x^2 + 75x + 1	\( 2^{12}\cdot 37^{6}\cdot 16361^{3} \)	18T314	Trivial (GRH)
18.18.70853239618582582520971264.1	x^18 - 17x^16 + 115x^14 - 404x^12 + 802x^10 - 911x^8 + 568x^6 - 176x^4 + 24x^2 - 1	\( 2^{18}\cdot 37^{4}\cdot 229^{6} \)	18T203	Trivial (GRH)
18.18.80421398252924334225227776.1	x^18 - 17x^16 + 117x^14 - 421x^12 + 854x^10 - 979x^8 + 601x^6 - 177x^4 + 23x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 53^{6} \)	$C_3\times S_4$ (as 18T33)	Trivial (GRH)
18.18.102094231502838405721411584.1	x^18 - 3x^17 - 27x^16 + 93x^15 + 240x^14 - 1056x^13 - 675x^12 + 5580x^11 - 1083x^10 - 15058x^9 + 9870x^8 + 20628x^7 - 20619x^6 - 12441x^5 + 18096x^4 + 1416x^3 - 6102x^2 + 654x + 487	\( 2^{12}\cdot 3^{31}\cdot 7^{9} \)	$S_3 \times C_3$ (as 18T3)	Trivial (GRH)
18.18.104192253035948620552339456.1	x^18 - 17x^16 + 114x^14 - 389x^12 + 728x^10 - 758x^8 + 433x^6 - 131x^4 + 19x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 169457^{2} \)	18T703	Trivial (GRH)
18.18.107870454521778261425837337.1	x^18 - x^17 - 18x^16 + 18x^15 + 134x^14 - 134x^13 - 531x^12 + 531x^11 + 1198x^10 - 1198x^9 - 1519x^8 + 1519x^7 + 989x^6 - 989x^5 - 265x^4 + 265x^3 + 20x^2 - 20x + 1	\( 3^{9}\cdot 19^{17} \)	$C_{18}$ (as 18T1)	Trivial (GRH)
18.18.110730297608000000000000000.1	x^18 - 3x^17 - 25x^16 + 86x^15 + 210x^14 - 928x^13 - 506x^12 + 4615x^11 - 1713x^10 - 10195x^9 + 9755x^8 + 7035x^7 - 12770x^6 + 2985x^5 + 2555x^4 - 1109x^3 - 13x^2 + 20x + 1	\( 2^{18}\cdot 5^{15}\cdot 7^{12} \)	$S_3 \times C_6$ (as 18T6)	Trivial (GRH)
18.18.111420547765458558938468352.1	x^18 - 6x^17 - 14x^16 + 114x^15 + 112x^14 - 925x^13 - 833x^12 + 3876x^11 + 4484x^10 - 7794x^9 - 12791x^8 + 4448x^7 + 15963x^6 + 4714x^5 - 6240x^4 - 4367x^3 - 319x^2 + 381x + 79	\( 2^{12}\cdot 3^{12}\cdot 13^{15} \)	$C_3^2\times S_3$ (as 18T17)	Trivial (GRH)
18.18.128096283147594231961387008.1	x^18 - 24x^16 + 207x^14 - 876x^12 + 2046x^10 - 2748x^8 + 2099x^6 - 852x^4 + 156x^2 - 8	\( 2^{15}\cdot 3^{24}\cdot 7^{12} \)	$C_6\times A_4$ (as 18T25)	Trivial (GRH)
18.18.142493532772533353405304832.1	x^18 - 3x^17 - 18x^16 + 43x^15 + 143x^14 - 223x^13 - 603x^12 + 508x^11 + 1359x^10 - 505x^9 - 1624x^8 + 146x^7 + 1012x^6 + 93x^5 - 302x^4 - 70x^3 + 31x^2 + 12x + 1	\( 2^{12}\cdot 37^{9}\cdot 16361^{2} \)	18T319	Trivial (GRH)
18.18.183239187763363936033203125.1	x^18 - 2x^17 - 25x^16 + 26x^15 + 214x^14 - 115x^13 - 823x^12 + 231x^11 + 1560x^10 - 284x^9 - 1556x^8 + 238x^7 + 826x^6 - 122x^5 - 220x^4 + 30x^3 + 25x^2 - 2x - 1	\( 5^{9}\cdot 9685993193^{2} \)	18T913	Trivial (GRH)
18.18.203412153331596396123869184.1	x^18 - 6x^17 - 18x^16 + 178x^15 - 126x^14 - 1323x^13 + 2437x^12 + 2646x^11 - 8874x^10 + 1316x^9 + 10665x^8 - 6174x^7 - 4241x^6 + 4158x^5 - 84x^4 - 765x^3 + 243x^2 - 27x + 1	\( 2^{12}\cdot 3^{21}\cdot 7^{15} \)	$S_3 \times C_3$ (as 18T3)	Trivial (GRH)
18.18.279992823820843547402730217.1	x^18 - 4x^17 - 19x^16 + 93x^15 + 70x^14 - 668x^13 + 255x^12 + 1811x^11 - 1506x^10 - 2121x^9 + 2524x^8 + 876x^7 - 1788x^6 + 174x^5 + 468x^4 - 169x^3 - 4x^2 + 9x - 1	\( 7^{12}\cdot 53^{6}\cdot 97^{3} \)	$C_6\times S_4$ (as 18T61)	Trivial (GRH)
18.18.314080936086007337997242368.1	x^18 - 9x^17 + 12x^16 + 102x^15 - 283x^14 - 341x^13 + 1564x^12 + 355x^11 - 3972x^10 - 17x^9 + 5382x^8 + 199x^7 - 3798x^6 - 569x^5 + 1139x^4 + 236x^3 - 114x^2 - 25x - 1	\( 2^{12}\cdot 37^{6}\cdot 31033^{3} \)	18T314	Trivial (GRH)
18.18.431008431261766353738330112.1	x^18 - 5x^17 - 17x^16 + 116x^15 + 28x^14 - 898x^13 + 729x^12 + 2639x^11 - 3688x^10 - 2725x^9 + 6303x^8 - 110x^7 - 4279x^6 + 1433x^5 + 961x^4 - 464x^3 - 59x^2 + 35x + 1	\( 2^{12}\cdot 7^{15}\cdot 53^{6} \)	$C_6\times S_4$ (as 18T61)	Trivial (GRH)
18.18.453551299002368000000000000.1	x^18 - 30x^16 + 349x^14 - 2006x^12 + 6022x^10 - 9096x^8 + 6089x^6 - 1684x^4 + 196x^2 - 8	\( 2^{27}\cdot 5^{12}\cdot 7^{12} \)	$S_3 \times C_3$ (as 18T3)	Trivial (GRH)
18.18.456487940826035155404146917.1	x^18 - x^17 - 17x^16 + 16x^15 + 120x^14 - 105x^13 - 455x^12 + 364x^11 + 1001x^10 - 715x^9 - 1287x^8 + 792x^7 + 924x^6 - 462x^5 - 330x^4 + 120x^3 + 45x^2 - 9x - 1	\( 37^{17} \)	$C_{18}$ (as 18T1)	Trivial (GRH)
18.18.512652391182435784215973888.1	x^18 - 25x^16 - 4x^15 + 230x^14 + 55x^13 - 996x^12 - 244x^11 + 2176x^10 + 393x^9 - 2413x^8 - 90x^7 + 1367x^6 - 175x^5 - 347x^4 + 95x^3 + 24x^2 - 11x + 1	\( 2^{12}\cdot 37^{9}\cdot 31033^{2} \)	18T319	Trivial (GRH)
18.18.543924745232899335442661376.1	x^18 - 36x^16 - 18x^15 + 432x^14 + 342x^13 - 1995x^12 - 1530x^11 + 4203x^10 + 2810x^9 - 4293x^8 - 2628x^7 + 2097x^6 + 1296x^5 - 414x^4 - 294x^3 + 9x^2 + 18x + 1	\( 2^{27}\cdot 3^{39} \)	$S_3 \times C_3$ (as 18T3)	Trivial (GRH)
18.18.563362135874260093126953125.1	x^18 - x^17 - 25x^16 + 20x^15 + 232x^14 - 137x^13 - 1018x^12 + 403x^11 + 2291x^10 - 566x^9 - 2742x^8 + 387x^7 + 1711x^6 - 131x^5 - 505x^4 + 30x^3 + 55x^2 - 5x - 1	\( 5^{9}\cdot 19^{16} \)	$C_{18}$ (as 18T1)	Trivial (GRH)
18.18.708478645847689707516501157.1	x^18 - x^17 - 27x^16 + 22x^15 + 269x^14 - 180x^13 - 1259x^12 + 711x^11 + 2914x^10 - 1420x^9 - 3300x^8 + 1287x^7 + 1831x^6 - 522x^5 - 466x^4 + 89x^3 + 45x^2 - 6x - 1	\( 7^{12}\cdot 13^{15} \)	$C_6 \times C_3$ (as 18T2)	Trivial (GRH)
18.18.737445455454227457309147136.1	x^18 - 17x^16 + 115x^14 - 400x^12 + 776x^10 - 851x^8 + 511x^6 - 157x^4 + 22x^2 - 1	\( 2^{30}\cdot 37^{6}\cdot 16361^{2} \)	18T776	Trivial (GRH)
18.18.774455350146061749097070592.1	x^18 - 18x^16 + 135x^14 - 546x^12 + 1287x^10 - 1782x^8 + 1386x^6 - 540x^4 + 81x^2 - 3	\( 2^{18}\cdot 3^{45} \)	$C_{18}$ (as 18T1)	Trivial (GRH)
18.18.781553895537094671760883712.1	x^18 - 30x^16 - 18x^15 + 342x^14 + 384x^13 - 1776x^12 - 2898x^11 + 3831x^10 + 9322x^9 - 1350x^8 - 12804x^7 - 5103x^6 + 5976x^5 + 4440x^4 - 276x^3 - 828x^2 - 168x - 8	\( 2^{18}\cdot 3^{31}\cdot 13^{6} \)	$C_3^2\times S_3$ (as 18T17)	Trivial (GRH)
18.18.822466862771545065687732224.1	x^18 - 3x^17 - 30x^16 + 79x^15 + 385x^14 - 819x^13 - 2727x^12 + 4210x^11 + 11347x^10 - 11183x^9 - 27282x^8 + 14876x^7 + 35618x^6 - 8833x^5 - 21852x^4 + 2338x^3 + 4189x^2 - 986x + 29	\( 2^{12}\cdot 7^{12}\cdot 29^{9} \)	$S_3 \times C_3$ (as 18T3)	Trivial (GRH)
18.18.965654874530970632000000000.1	x^18 - 2x^17 - 22x^16 + 35x^15 + 174x^14 - 218x^13 - 650x^12 + 630x^11 + 1268x^10 - 931x^9 - 1322x^8 + 732x^7 + 728x^6 - 302x^5 - 200x^4 + 59x^3 + 24x^2 - 4x - 1	\( 2^{12}\cdot 5^{9}\cdot 19^{6}\cdot 37^{6} \)	$C_3\times S_3^2$ (as 18T46)	Trivial (GRH)
18.18.984061123004931663569977889.1	x^18 - 9x^17 + 18x^16 + 60x^15 - 243x^14 - 63x^13 + 1112x^12 - 471x^11 - 2680x^10 + 1773x^9 + 3874x^8 - 2611x^7 - 3495x^6 + 1802x^5 + 1864x^4 - 499x^3 - 469x^2 + 36x + 37	\( 2836601\cdot 18625670317^{2} \)	18T968	Trivial (GRH)
18.18.1112524081631721433112434461.1	x^18 - 6x^17 - 21x^16 + 195x^15 - 87x^14 - 1848x^13 + 3708x^12 + 3330x^11 - 16686x^10 + 12758x^9 + 9624x^8 - 17265x^7 + 4149x^6 + 4521x^5 - 2802x^4 + 384x^3 + 63x^2 - 18x + 1	\( 3^{31}\cdot 23^{9} \)	$S_3 \times C_3$ (as 18T3)	Trivial (GRH)
18.18.1272623169716040941204406272.1	x^18 - 22x^16 + 195x^14 - 905x^12 + 2407x^10 - 3777x^8 + 3444x^6 - 1699x^4 + 374x^2 - 17	\( 2^{18}\cdot 17^{3}\cdot 994046201^{2} \)	18T968	Trivial (GRH)
18.18.1284203548600251267926125629.1	x^18 - 3x^17 - 27x^16 + 86x^15 + 198x^14 - 618x^13 - 806x^12 + 1917x^11 + 2124x^10 - 2696x^9 - 3204x^8 + 1365x^7 + 2209x^6 + 24x^5 - 561x^4 - 123x^3 + 30x^2 + 12x + 1	\( 3^{27}\cdot 7^{12}\cdot 23^{3} \)	$C_6\times A_4$ (as 18T25)	Trivial (GRH)
18.18.1365795913530635497834467328.1	x^18 - 35x^16 + 421x^14 - 2148x^12 + 5568x^10 - 7923x^8 + 6263x^6 - 2627x^4 + 518x^2 - 37	\( 2^{12}\cdot 37^{15} \)	$S_3 \times C_3$ (as 18T3)	Trivial (GRH)
18.18.1373804974140802360768493281.1	x^18 - 9x^17 + 16x^16 + 76x^15 - 296x^14 + 28x^13 + 1181x^12 - 1340x^11 - 1305x^10 + 3126x^9 - 756x^8 - 2054x^7 + 1651x^6 - 80x^5 - 370x^4 + 141x^3 - 3x^2 - 7x + 1	\( 7^{12}\cdot 71^{2}\cdot 281^{2}\cdot 15791^{2} \)	18T703	Trivial (GRH)
18.18.1436650532447139184230793216.1	x^18 - 19x^16 + 152x^14 - 665x^12 + 1729x^10 - 2717x^8 + 2508x^6 - 1254x^4 + 285x^2 - 19	\( 2^{18}\cdot 19^{17} \)	$C_{18}$ (as 18T1)	Trivial (GRH)
18.18.1580292385193027308673828125.1	x^18 - 2x^17 - 28x^16 + 48x^15 + 282x^14 - 420x^13 - 1262x^12 + 1718x^11 + 2548x^10 - 3446x^9 - 2165x^8 + 3163x^7 + 695x^6 - 1290x^5 - 24x^4 + 203x^3 - 13x^2 - 10x + 1	\( 5^{9}\cdot 7^{12}\cdot 3881^{3} \)	$C_3\times S_3\wr C_2$ (as 18T93)	Trivial (GRH)
18.18.1773946662392078824692561309.1	x^18 - 42x^16 - 14x^15 + 567x^14 + 378x^13 - 3339x^12 - 3402x^11 + 8505x^10 + 12726x^9 - 5481x^8 - 18417x^7 - 8008x^6 + 5796x^5 + 7770x^4 + 3731x^3 + 945x^2 + 126x + 7	\( 3^{27}\cdot 7^{17} \)	$C_2\times C_9:C_3$ (as 18T14)	Trivial (GRH)
18.18.1819145441046500375949998389.1	x^18 - 4x^17 - 25x^16 + 105x^15 + 200x^14 - 957x^13 - 568x^12 + 4008x^11 - 85x^10 - 8113x^9 + 2772x^8 + 7493x^7 - 3445x^6 - 3093x^5 + 1357x^4 + 499x^3 - 146x^2 - x + 1	\( 7^{12}\cdot 53^{6}\cdot 181^{3} \)	$C_2\times S_3\times A_4$ (as 18T60)	Trivial (GRH)
18.18.1923380668327365689220703125.1	x^18 - 27x^16 + 270x^14 - 1269x^12 + 3042x^10 - 76x^9 - 3888x^8 + 261x^7 + 2601x^6 - 297x^5 - 810x^4 + 120x^3 + 81x^2 - 9x - 1	\( 3^{44}\cdot 5^{9} \)	$C_{18}$ (as 18T1)	Trivial (GRH)
18.18.1946879194440836203367827049.1	x^18 - 9x^17 + 18x^16 + 60x^15 - 245x^14 - 49x^13 + 1095x^12 - 551x^11 - 2499x^10 + 1935x^9 + 3304x^8 - 2755x^7 - 2633x^6 + 1881x^5 + 1204x^4 - 546x^3 - 244x^2 + 33x - 1	\( 7^{12}\cdot 1583\cdot 4663\cdot 138041^{2} \)	18T879	Trivial (GRH)
18.18.2637116370088050448669881277.1	x^18 - 3x^17 - 31x^16 + 89x^15 + 346x^14 - 876x^13 - 2020x^12 + 3762x^11 + 7196x^10 - 7031x^9 - 15065x^8 + 2957x^7 + 14804x^6 + 4714x^5 - 3305x^4 - 1621x^3 + 195x^2 + 128x - 1	\( 13^{15}\cdot 61^{6} \)	$S_3 \times C_6$ (as 18T6)	Trivial (GRH)
18.18.2797687878976007885081018368.1	x^18 - 21x^16 + 177x^14 - 780x^12 + 1970x^10 - 2950x^8 + 2615x^6 - 1323x^4 + 349x^2 - 37	\( 2^{18}\cdot 19^{16}\cdot 37 \)	18T460	Trivial (GRH)
18.18.2881346768906705526417803981.1	x^18 - x^17 - 27x^16 + 22x^15 + 256x^14 - 167x^13 - 1098x^12 + 558x^11 + 2290x^10 - 951x^9 - 2405x^8 + 807x^7 + 1283x^6 - 333x^5 - 327x^4 + 62x^3 + 34x^2 - 4x - 1	\( 7^{12}\cdot 592661^{3} \)	18T362	Trivial (GRH)