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 all 40 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.8.2014136652391101890074142784.1	x^18 - 63x^14 + 39x^12 + 675x^10 + 54x^8 - 1950x^6 - 1269x^4 + 441x^2 + 289	\( -\,2^{6}\cdot 3^{32}\cdot 19^{8} \)	18T585	Trivial (GRH)
18.8.2014136652391101890074142784.2	x^18 + 9x^16 - 171x^12 - 207x^10 + 1017x^8 + 981x^6 - 2268x^4 + 108x^2 + 9	\( -\,2^{6}\cdot 3^{32}\cdot 19^{8} \)	18T585	Trivial (GRH)
18.12.6042409957173305670222428352.1	x^18 + 3x^16 - 27x^14 - 51x^12 + 207x^10 + 153x^8 - 396x^6 + 216x^4 - 45x^2 + 3	\( -\,2^{6}\cdot 3^{33}\cdot 19^{8} \)	18T585	Trivial (GRH)
18.4.6042409957173305670222428352.1	x^18 - 6x^17 + 6x^16 + 42x^15 - 159x^14 + 177x^13 + 228x^12 - 969x^11 + 1032x^10 + 883x^9 - 4350x^8 + 6393x^7 - 4722x^6 + 1113x^5 + 363x^4 - 21x^3 - 84x^2 + 21x + 1	\( -\,2^{6}\cdot 3^{33}\cdot 19^{8} \)	18T585	Trivial (GRH)
18.12.6042409957173305670222428352.2	x^18 - 3x^17 - 21x^16 + 60x^15 + 168x^14 - 435x^13 - 675x^12 + 1437x^11 + 1428x^10 - 1991x^9 - 1464x^8 + 336x^7 + 399x^6 + 849x^5 + 588x^4 + 63x^3 - 96x^2 - 60x - 8	\( -\,2^{6}\cdot 3^{33}\cdot 19^{8} \)	18T585	Trivial (GRH)
18.10.6042409957173305670222428352.1	x^18 + 6x^16 - 18x^14 - 75x^12 + 153x^10 + 243x^8 - 531x^6 + 18x^4 + 225x^2 - 3	\( 2^{6}\cdot 3^{33}\cdot 19^{8} \)	18T585	Trivial (GRH)
18.10.6042409957173305670222428352.2	x^18 - 3x^17 - 9x^16 + 33x^15 + 21x^14 - 144x^13 + 3x^12 + 339x^11 - 117x^10 - 715x^9 + 474x^8 + 2727x^7 + 2697x^6 - 1032x^5 - 6219x^4 - 6063x^3 + 825x^2 + 4104x + 1567	\( 2^{6}\cdot 3^{33}\cdot 19^{8} \)	18T585	Trivial (GRH)
18.4.38268596395430935911408712896.1	x^18 - 6x^17 + 3x^16 + 42x^15 - 60x^14 - 147x^13 + 414x^12 + 360x^11 - 3171x^10 + 4141x^9 + 5901x^8 - 25989x^7 + 29664x^6 + 3096x^5 - 44430x^4 + 85779x^3 - 131538x^2 + 125604x - 39736	\( -\,2^{6}\cdot 3^{32}\cdot 19^{9} \)	18T585	Trivial (GRH)
18.8.38268596395430935911408712896.1	x^18 - 81x^14 - 231x^12 + 999x^10 + 4302x^8 + 2172x^6 - 3591x^4 + 171x^2 + 19	\( -\,2^{6}\cdot 3^{32}\cdot 19^{9} \)	18T585	$[2]$ (GRH)
18.8.38268596395430935911408712896.2	x^18 - 6x^17 + 9x^16 + 12x^15 - 36x^14 - 18x^13 - 243x^12 + 36x^11 - 423x^10 + 1362x^9 + 3897x^8 + 594x^7 - 3105x^6 - 972x^5 + 1404x^4 - 162x^3 - 270x^2 + 108x - 9	\( -\,2^{6}\cdot 3^{32}\cdot 19^{9} \)	18T585	Trivial (GRH)
18.10.38268596395430935911408712896.1	x^18 - 6x^17 + 3x^16 + 39x^15 - 60x^14 - 51x^13 + 135x^12 - 42x^11 + 21x^10 - 46x^9 - 72x^8 + 81x^7 - 108x^6 + 432x^5 - 432x^4 - 135x^3 + 243x^2 - 27	\( 2^{6}\cdot 3^{32}\cdot 19^{9} \)	18T585	Trivial (GRH)
18.2.38268596395430935911408712896.1	x^18 - 6x^17 + 15x^16 - 27x^15 + 42x^14 - 123x^13 + 618x^12 - 1680x^11 + 2526x^10 - 2582x^9 + 1017x^8 - 918x^6 - 1215x^5 + 486x^4 - 729x^3 - 1458x^2 - 2187x + 729	\( 2^{6}\cdot 3^{32}\cdot 19^{9} \)	18T585	$[3]$ (GRH)
18.6.38268596395430935911408712896.1	x^18 - 90x^14 - 417x^12 - 513x^10 + 459x^8 + 1479x^6 + 1026x^4 + 171x^2 - 19	\( 2^{6}\cdot 3^{32}\cdot 19^{9} \)	18T585	Trivial (GRH)
18.6.38268596395430935911408712896.2	x^18 - 15x^16 + 12x^14 + 309x^12 + 129x^10 - 2175x^8 - 4779x^6 - 3876x^4 - 1140x^2 - 19	\( 2^{6}\cdot 3^{32}\cdot 19^{9} \)	18T585	Trivial (GRH)
18.12.114805789186292807734226138688.1	x^18 - 18x^16 + 45x^14 + 603x^12 - 2457x^10 - 1836x^8 + 12906x^6 - 7695x^4 - 1539x^2 + 513	\( -\,2^{6}\cdot 3^{33}\cdot 19^{9} \)	18T585	Trivial (GRH)
18.16.114805789186292807734226138688.1	x^18 - 6x^16 - 72x^14 + 921x^12 - 4239x^10 + 10089x^8 - 12951x^6 + 8208x^4 - 1881x^2 + 57	\( -\,2^{6}\cdot 3^{33}\cdot 19^{9} \)	18T585	Trivial (GRH)
18.8.114805789186292807734226138688.1	x^18 - 3x^17 + 6x^16 + 6x^15 - 30x^14 + 42x^13 + 9x^12 + 15x^11 - 597x^10 + 358x^9 + 993x^8 - 1986x^7 + 210x^6 + 3612x^5 + 57x^4 - 2187x^3 - 456x^2 + 399x + 127	\( -\,2^{6}\cdot 3^{33}\cdot 19^{9} \)	18T585	$[2]$ (GRH)
18.12.114805789186292807734226138688.2	x^18 + 3x^16 - 99x^14 - 33x^12 + 2745x^10 - 6003x^8 + 3222x^6 + 684x^4 - 513x^2 + 57	\( -\,2^{6}\cdot 3^{33}\cdot 19^{9} \)	18T585	Trivial (GRH)
18.10.114805789186292807734226138688.1	x^18 - 12x^16 - 99x^14 + 204x^12 + 1998x^10 + 1224x^8 - 6570x^6 - 4275x^4 + 6498x^2 - 57	\( 2^{6}\cdot 3^{33}\cdot 19^{9} \)	18T585	Trivial (GRH)
18.14.114805789186292807734226138688.1	x^18 - 3x^17 - 21x^16 + 69x^15 + 180x^14 - 603x^13 - 1029x^12 + 1764x^11 + 3060x^10 + 465x^9 - 2502x^8 - 9162x^7 - 3600x^6 + 12348x^5 + 6048x^4 - 4086x^3 - 2493x^2 - 126x + 51	\( 2^{6}\cdot 3^{33}\cdot 19^{9} \)	18T585	Trivial (GRH)
18.6.114805789186292807734226138688.1	x^18 - 3x^17 + 6x^16 - 12x^15 + 69x^14 - 147x^13 - 108x^12 + 798x^11 - 1074x^10 - 1001x^9 + 2073x^8 - 393x^7 - 1797x^6 + 570x^5 + 2136x^4 + 225x^3 - 780x^2 + 660x + 568	\( 2^{6}\cdot 3^{33}\cdot 19^{9} \)	18T585	Trivial (GRH)
18.10.114805789186292807734226138688.2	x^18 - 3x^17 - 18x^16 + 87x^15 + 3x^14 - 666x^13 + 1263x^12 + 654x^11 - 5598x^10 + 7493x^9 + 510x^8 - 13248x^7 + 16287x^6 - 5586x^5 - 6498x^4 + 9120x^3 - 5016x^2 + 1368x - 152	\( 2^{6}\cdot 3^{33}\cdot 19^{9} \)	18T585	Trivial (GRH)
18.6.114805789186292807734226138688.2	x^18 - 6x^17 + 12x^16 - 9x^15 + 3x^14 - 177x^13 + 912x^12 - 2130x^11 + 3963x^10 - 4952x^9 + 4803x^8 - 7284x^7 + 7119x^6 + 4713x^5 - 17625x^4 + 16638x^3 - 7329x^2 + 1428x - 71	\( 2^{6}\cdot 3^{33}\cdot 19^{9} \)	18T585	$[2]$ (GRH)
18.16.386714237259091562894235414528.1	x^18 - 33x^16 + 423x^14 - 2733x^12 + 9531x^10 - 17685x^8 + 16020x^6 - 5760x^4 + 369x^2 + 3	\( -\,2^{12}\cdot 3^{33}\cdot 19^{8} \)	18T585	Trivial (GRH)
18.8.386714237259091562894235414528.3	x^18 + 12x^16 - 18x^14 - 519x^12 - 1107x^10 - 63x^8 + 765x^6 - 108x^4 - 27x^2 + 3	\( -\,2^{12}\cdot 3^{33}\cdot 19^{8} \)	18T585	$[2]$ (GRH)
18.14.386714237259091562894235414528.1	x^18 - 3x^16 - 108x^14 + 834x^12 - 2169x^10 + 2061x^8 - 207x^6 - 369x^4 + 99x^2 - 3	\( 2^{12}\cdot 3^{33}\cdot 19^{8} \)	18T585	Trivial (GRH)
18.10.2181309994539563346950296635072.1	x^18 - 6x^17 + 6x^16 + 39x^15 - 153x^14 + 243x^13 + 51x^12 - 1152x^11 + 2484x^10 - 3228x^9 + 1017x^8 + 5319x^7 - 12150x^6 + 16326x^5 - 13581x^4 + 5175x^3 - 198x^2 - 216x + 24	\( 2^{6}\cdot 3^{33}\cdot 19^{10} \)	18T585	$[2]$ (GRH)
18.4.2449190169307579898330157625344.1	x^18 + 21x^16 + 150x^14 + 432x^12 + 231x^10 - 1257x^8 - 2397x^6 - 1311x^4 - 57x^2 + 19	\( -\,2^{12}\cdot 3^{32}\cdot 19^{9} \)	18T585	$[2]$ (GRH)
18.4.2449190169307579898330157625344.2	x^18 + 36x^16 + 513x^14 + 3762x^12 + 15318x^10 + 34200x^8 + 36810x^6 + 9747x^4 - 7182x^2 + 171	\( -\,2^{12}\cdot 3^{32}\cdot 19^{9} \)	18T585	Trivial (GRH)
18.14.7347570507922739694990472876032.1	x^18 - 39x^16 + 603x^14 - 4719x^12 + 19755x^10 - 42237x^8 + 34173x^6 + 15732x^4 - 27360x^2 - 3648	\( 2^{12}\cdot 3^{33}\cdot 19^{9} \)	18T585	Trivial (GRH)
18.2.7347570507922739694990472876032.1	x^18 + 6x^16 - 72x^14 - 921x^12 - 4239x^10 - 10089x^8 - 12951x^6 - 8208x^4 - 1881x^2 - 57	\( 2^{12}\cdot 3^{33}\cdot 19^{9} \)	18T585	$[2, 4]$ (GRH)
18.14.7347570507922739694990472876032.2	x^18 - 27x^16 + 225x^14 - 621x^12 - 675x^10 + 6723x^8 - 12744x^6 + 9234x^4 - 1539x^2 - 513	\( 2^{12}\cdot 3^{33}\cdot 19^{9} \)	18T585	Trivial (GRH)
18.18.4450636533424095295669119045874041.1	x^18 - 9x^17 - 36x^16 + 402x^15 + 774x^14 - 7515x^13 - 13662x^12 + 69579x^11 + 157617x^10 - 275611x^9 - 923211x^8 + 22716x^7 + 1994634x^6 + 1659249x^5 - 182439x^4 - 400341x^3 + 50184x^2 + 2502x - 271	\( 3^{32}\cdot 19^{8}\cdot 521^{3} \)	18T585	Trivial (GRH)
18.18.4450636533424095295669119045874041.2	x^18 - 3x^17 - 57x^16 + 168x^15 + 1242x^14 - 3579x^13 - 13410x^12 + 37662x^11 + 77760x^10 - 211705x^9 - 247752x^8 + 648429x^7 + 423585x^6 - 1065453x^5 - 332010x^4 + 872259x^3 + 29415x^2 - 279408x + 65717	\( 3^{32}\cdot 19^{8}\cdot 521^{3} \)	18T585	Trivial (GRH)
18.0.47411780397590423575518108050443059.1	x^18 - 9x^17 + 105x^16 - 636x^15 + 4149x^14 - 18627x^13 + 85281x^12 - 295821x^11 + 1023900x^10 - 2783254x^9 + 7476363x^8 - 15822075x^7 + 32975607x^6 - 52653699x^5 + 83017335x^4 - 92460621x^3 + 103314213x^2 - 63862212x + 42671071	\( -\,3^{33}\cdot 19^{8}\cdot 53\cdot 71\cdot 133451 \)	18T585	$[2, 2, 1962]$ (GRH)
18.12.91430564233231293221640534671388672.1	x^18 - 18x^16 - 309x^14 + 8372x^12 - 55854x^10 + 119094x^8 + 17613x^6 - 202104x^4 + 27216x^2 + 448	\( -\,2^{12}\cdot 3^{24}\cdot 7^{13}\cdot 13^{8} \)	18T585	Trivial (GRH)
18.6.91430564233231293221640534671388672.1	x^18 + 18x^16 - 309x^14 - 8372x^12 - 55854x^10 - 119094x^8 + 17613x^6 + 202104x^4 + 27216x^2 - 448	\( 2^{12}\cdot 3^{24}\cdot 7^{13}\cdot 13^{8} \)	18T585	Trivial (GRH)
18.12.640013949632619052551483742699720704.1	x^18 - 18x^16 - 102x^14 + 3193x^12 - 6825x^10 - 132027x^8 + 642425x^6 + 294000x^4 - 5267451x^2 + 5564881	\( -\,2^{12}\cdot 3^{24}\cdot 7^{14}\cdot 13^{8} \)	18T585	Trivial (GRH)
18.0.932267093615745135240086188983816192.1	x^18 + 60x^16 + 1575x^14 + 23667x^12 + 223371x^10 + 1364166x^8 + 5334336x^6 + 12640491x^4 + 15851187x^2 + 7232217	\( -\,2^{12}\cdot 3^{33}\cdot 19^{9}\cdot 181\cdot 701 \)	18T585	$[2, 2, 2, 2, 3402]$ (GRH)
18.6.1188597335032006811881326950728052736.1	x^18 + 45x^16 + 90x^14 - 8463x^12 - 42246x^10 + 36774x^8 + 429843x^6 + 501228x^4 - 13104x^2 - 5824	\( 2^{12}\cdot 3^{24}\cdot 7^{13}\cdot 13^{9} \)	18T585	$[2]$ (GRH)