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 52)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.78781672174688898630480.1	x^18 - 9x^14 - 18x^13 + 6x^12 + 27x^11 + 18x^10 + 102x^9 + 144x^8 + 63x^7 + 39x^6 + 81x^5 + 36x^4 - 108x^3 + 36x + 8	\( -\,2^{4}\cdot 3^{44}\cdot 5 \)	18T658	Trivial
18.2.86659839392157788493528.1	x^18 - 3x^15 - 18x^13 + 30x^12 + 9x^11 - 18x^10 - 61x^9 + 90x^8 + 90x^7 - 117x^6 - 18x^5 + 27x^4 + 9x^3 - 3	\( 2^{3}\cdot 3^{44}\cdot 11 \)	18T658	Trivial
18.2.236345016524066695891440.1	x^18 - 12x^15 - 36x^14 - 90x^13 - 156x^12 - 243x^11 - 297x^10 - 334x^9 - 297x^8 - 243x^7 - 156x^6 - 90x^5 - 36x^4 - 12x^3 + 1	\( 2^{4}\cdot 3^{45}\cdot 5 \)	18T658	Trivial
18.0.259979518176473365480584.1	x^18 - 9x^15 + 9x^14 + 54x^12 - 135x^11 + 81x^10 - 6x^9 + 243x^8 - 729x^7 + 999x^6 - 756x^5 + 243x^4 + 81x^3 - 81x^2 + 9	\( -\,2^{3}\cdot 3^{45}\cdot 11 \)	18T658	$[2]$
18.12.59566164710710547949317538803712.2	x^18 - 9x^17 + 18x^16 + 60x^15 - 360x^14 + 756x^13 - 171x^12 - 3420x^11 + 9252x^10 - 11335x^9 + 1791x^8 + 18468x^7 - 33390x^6 + 30231x^5 - 14301x^4 + 1293x^3 + 1890x^2 - 774x + 89	\( -\,2^{12}\cdot 3^{36}\cdot 7^{13} \)	18T658	Trivial (GRH)
18.8.102113425218360939341687209377792.1	x^18 - 18x^16 - 33x^15 + 99x^14 + 180x^13 - 483x^12 + 324x^11 + 2961x^10 + 1041x^9 + 1827x^8 + 8829x^7 + 3507x^6 - 2466x^5 - 25164x^4 - 18954x^3 + 21906x^2 - 1014	\( -\,2^{14}\cdot 3^{37}\cdot 7^{12} \)	18T658	Trivial (GRH)
18.8.102113425218360939341687209377792.2	x^18 - 9x^16 - 6x^15 - 99x^14 + 180x^13 + 819x^12 - 36x^11 - 2304x^10 - 8420x^9 + 22572x^8 - 216x^7 + 3612x^6 - 104400x^5 + 97344x^4 + 50496x^3 - 44928x^2 - 17280x - 1472	\( -\,2^{14}\cdot 3^{37}\cdot 7^{12} \)	18T658	Trivial (GRH)
18.12.136151233624481252455582945837056.2	x^18 - 18x^16 + 27x^14 + 996x^12 - 5337x^10 + 4446x^8 + 13533x^6 - 10512x^4 - 7488x^2 + 256	\( -\,2^{16}\cdot 3^{36}\cdot 7^{12} \)	18T658	Trivial (GRH)
18.16.195717398335191800404900484640768.1	x^18 - 45x^16 - 45x^15 + 630x^14 + 819x^13 - 3363x^12 - 1323x^11 + 17001x^10 - 4536x^9 - 58050x^8 + 14364x^7 + 92466x^6 - 27216x^5 - 61209x^4 + 28728x^3 + 9234x^2 - 7047x + 963	\( -\,2^{12}\cdot 3^{36}\cdot 7^{12}\cdot 23 \)	18T658	Trivial (GRH)
18.8.238264658842842191797270155214848.1	x^18 - 9x^16 - 54x^14 + 447x^12 + 18x^10 - 2025x^8 - 1035x^6 + 1512x^4 + 1296x^2 + 252	\( -\,2^{14}\cdot 3^{36}\cdot 7^{13} \)	18T658	Trivial (GRH)
18.8.238264658842842191797270155214848.2	x^18 + 18x^16 - 48x^15 + 72x^14 - 342x^13 - 411x^12 + 468x^11 - 6480x^10 + 20816x^9 - 22680x^8 + 44892x^7 + 108897x^6 - 331110x^5 - 11358x^4 + 366870x^3 - 125676x^2 - 58104x + 17557	\( -\,2^{14}\cdot 3^{36}\cdot 7^{13} \)	18T658	Trivial (GRH)
18.10.246774110944372270075744089329664.1	x^18 - 36x^16 - 60x^15 + 387x^14 + 1440x^13 + 198x^12 - 9000x^11 - 17397x^10 + 10068x^9 + 54396x^8 + 46332x^7 + 23469x^6 - 140832x^5 - 307530x^4 + 210408x^3 + 379908x^2 - 215316x - 36644	\( 2^{12}\cdot 3^{36}\cdot 7^{12}\cdot 29 \)	18T658	Trivial (GRH)
18.6.246774110944372270075744089329664.1	x^18 - 9x^16 - 24x^15 + 72x^14 + 414x^13 - 1143x^12 + 594x^11 - 4842x^10 + 5538x^9 + 45603x^8 - 28512x^7 + 2277x^6 - 269352x^5 - 276102x^4 + 194256x^3 + 405972x^2 + 315684x + 25452	\( 2^{12}\cdot 3^{36}\cdot 7^{12}\cdot 29 \)	18T658	Trivial (GRH)
18.6.408453700873443757366748837511168.2	x^18 - 9x^17 + 27x^16 + 27x^15 - 360x^14 + 585x^13 + 1647x^12 - 7227x^11 + 6669x^10 + 2428x^9 + 8109x^8 - 11529x^7 - 59439x^6 + 8613x^5 + 397998x^4 - 762951x^3 + 608751x^2 - 225693x + 31747	\( 2^{16}\cdot 3^{37}\cdot 7^{12} \)	18T658	Trivial (GRH)
18.6.451000961381094148759118508085248.1	x^18 - 9x^17 + 18x^16 - 45x^15 + 378x^14 + 63x^13 - 1995x^12 - 6462x^11 + 1458x^10 + 22256x^9 + 99144x^8 - 10080x^7 - 173964x^6 - 458640x^5 + 110736x^4 + 596352x^3 + 821952x^2 - 956160x - 399616	\( 2^{12}\cdot 3^{36}\cdot 7^{12}\cdot 53 \)	18T658	Trivial (GRH)
18.6.451000961381094148759118508085248.2	x^18 - 27x^16 - 42x^15 + 360x^14 + 531x^13 - 1785x^12 - 3402x^11 + 2772x^10 + 5369x^9 + 19656x^8 + 3150x^7 - 51450x^6 - 73647x^5 + 3087x^4 + 198303x^3 + 74970x^2 - 145530x - 61054	\( 2^{12}\cdot 3^{36}\cdot 7^{12}\cdot 53 \)	18T658	Trivial (GRH)
18.10.519076578193334774986909981003776.1	x^18 - 18x^16 - 12x^15 + 36x^14 + 396x^13 - 285x^12 - 1584x^11 + 4716x^10 - 1612x^9 + 10836x^8 - 93276x^7 + 96003x^6 + 131976x^5 - 194670x^4 - 15228x^3 + 81648x^2 - 24948x + 2889	\( 2^{12}\cdot 3^{36}\cdot 7^{12}\cdot 61 \)	18T658	Trivial (GRH)
18.2.587152195005575401214701453922304.1	x^18 - 9x^16 - 84x^15 + 72x^14 + 828x^13 + 648x^12 - 1548x^11 - 8766x^10 - 19708x^9 + 32670x^8 + 78804x^7 + 80160x^6 - 141084x^5 - 452880x^4 + 177516x^3 + 64629x^2 + 480636x - 721709	\( 2^{12}\cdot 3^{37}\cdot 7^{12}\cdot 23 \)	18T658	$[2]$ (GRH)
18.12.604171099208635557771649322151936.1	x^18 - 45x^16 - 72x^15 + 603x^14 + 2286x^13 + 201x^12 - 17172x^11 - 44208x^10 - 26514x^9 + 72036x^8 + 171720x^7 + 154548x^6 + 10368x^5 - 111456x^4 - 76680x^3 + 8640x^2 + 18144x + 2016	\( -\,2^{12}\cdot 3^{36}\cdot 7^{12}\cdot 71 \)	18T658	Trivial (GRH)
18.12.604171099208635557771649322151936.2	x^18 - 18x^16 - 60x^15 + 225x^14 + 738x^13 - 564x^12 - 7416x^11 + 5751x^10 + 28444x^9 - 81666x^8 + 151092x^7 - 51033x^6 - 337950x^5 + 344628x^4 + 135384x^3 - 179928x^2 - 25992x + 19212	\( -\,2^{12}\cdot 3^{36}\cdot 7^{12}\cdot 71 \)	18T658	Trivial (GRH)
18.14.655227811817816027442492926840832.1	x^18 - 9x^17 - 9x^16 + 216x^15 - 18x^14 - 2214x^13 - 477x^12 + 13770x^11 + 12258x^10 - 56943x^9 - 83349x^8 + 146934x^7 + 265896x^6 - 202419x^5 - 421848x^4 + 110079x^3 + 292572x^2 - 13122x - 68202	\( 2^{12}\cdot 3^{36}\cdot 7^{13}\cdot 11 \)	18T658	Trivial (GRH)
18.14.655227811817816027442492926840832.2	x^18 - 27x^16 - 18x^15 + 108x^14 + 810x^13 + 1929x^12 - 11214x^11 - 16416x^10 + 54282x^9 + 53505x^8 - 99594x^7 - 96009x^6 + 57726x^5 + 71064x^4 + 7980x^3 - 1512x^2 + 4032x + 1372	\( 2^{12}\cdot 3^{36}\cdot 7^{13}\cdot 11 \)	18T658	Trivial (GRH)
18.8.740322332833116810227232267988992.1	x^18 - 9x^17 + 36x^16 - 84x^15 - 162x^14 + 1890x^13 - 7644x^12 + 20124x^11 - 25695x^10 - 8233x^9 + 163296x^8 - 464400x^7 + 835464x^6 - 1050840x^5 + 897840x^4 - 502416x^3 + 169056x^2 - 28224x + 1408	\( -\,2^{12}\cdot 3^{37}\cdot 7^{12}\cdot 29 \)	18T658	Trivial (GRH)
18.2.757341237036176966784180136218624.1	x^18 + 9x^16 - 36x^15 - 18x^14 + 915x^12 + 540x^11 - 5598x^10 - 7596x^9 + 17631x^8 + 62964x^7 - 43587x^6 - 218592x^5 + 5778x^4 + 343116x^3 + 242676x^2 - 37908x - 155268	\( 2^{12}\cdot 3^{36}\cdot 7^{12}\cdot 89 \)	18T658	Trivial (GRH)
18.12.782869593340767201619601938563072.1	x^18 - 54x^16 - 9x^15 + 1035x^14 + 378x^13 - 8811x^12 - 4536x^11 + 33399x^10 + 19467x^9 - 39933x^8 - 6237x^7 - 42957x^6 - 115668x^5 + 43254x^4 + 122472x^3 + 156492x^2 + 52488x + 5022	\( -\,2^{14}\cdot 3^{36}\cdot 7^{12}\cdot 23 \)	18T658	Trivial (GRH)
18.8.782869593340767201619601938563072.1	x^18 - 30x^15 - 54x^14 - 144x^13 - 417x^12 - 1422x^11 - 4446x^10 - 6708x^9 - 3726x^8 + 2754x^7 + 3825x^6 - 540x^5 - 486x^4 + 432x^3 - 324x^2 + 27	\( -\,2^{14}\cdot 3^{36}\cdot 7^{12}\cdot 23 \)	18T658	$[2]$ (GRH)
18.10.859454662254537906125867345596416.1	x^18 - 18x^16 - 12x^15 + 99x^14 + 144x^13 - 264x^12 - 324x^11 + 2007x^10 + 488x^9 - 8946x^8 - 9108x^7 + 2385x^6 + 3960x^5 + 9576x^4 + 59700x^3 - 9324x^2 - 40320x - 1276	\( 2^{12}\cdot 3^{36}\cdot 7^{12}\cdot 101 \)	18T658	Trivial (GRH)
18.16.953058635371368767189080620859392.1	x^18 - 9x^17 + 195x^15 - 387x^14 - 972x^13 + 2835x^12 + 261x^11 - 2817x^10 + 342x^9 - 2817x^8 + 261x^7 + 2835x^6 - 972x^5 - 387x^4 + 195x^3 - 9x + 1	\( -\,2^{16}\cdot 3^{36}\cdot 7^{13} \)	18T658	Trivial (GRH)
18.8.953058635371368767189080620859392.1	x^18 + 18x^16 - 9x^14 - 1560x^12 - 7137x^10 + 954x^8 + 30393x^6 - 14580x^4 - 7056x^2 + 112	\( -\,2^{16}\cdot 3^{36}\cdot 7^{13} \)	18T658	$[2]$ (GRH)
18.10.953058635371368767189080620859392.1	x^18 - 18x^16 - 261x^14 + 2028x^12 + 2583x^10 - 40446x^8 + 76797x^6 - 9072x^4 - 51408x^2 - 252	\( 2^{16}\cdot 3^{36}\cdot 7^{13} \)	18T658	Trivial (GRH)
18.10.961568087472898845467554554974208.1	x^18 - 9x^17 + 18x^16 + 54x^15 - 198x^14 - 36x^13 - 375x^12 + 4626x^11 - 864x^10 - 33075x^9 + 39609x^8 + 56466x^7 - 99594x^6 - 24471x^5 + 90081x^4 - 31563x^3 - 9018x^2 + 9522x + 1729	\( 2^{12}\cdot 3^{36}\cdot 7^{12}\cdot 113 \)	18T658	Trivial (GRH)
18.10.1089209868995850019644663566696448.1	x^18 - 9x^16 - 126x^14 + 1071x^12 + 3654x^10 - 32193x^8 - 26691x^6 + 263772x^4 + 42480x^2 - 76832	\( 2^{19}\cdot 3^{36}\cdot 7^{12} \)	18T658	Trivial (GRH)
18.12.1114738225300440254480085369040896.1	x^18 - 9x^17 + 18x^16 + 30x^15 - 171x^14 + 261x^13 - 1245x^12 + 3753x^11 + 8163x^10 - 34437x^9 - 15525x^8 + 113427x^7 - 18810x^6 - 134514x^5 + 44307x^4 + 53649x^3 - 13284x^2 - 6318x + 1026	\( -\,2^{12}\cdot 3^{36}\cdot 7^{12}\cdot 131 \)	18T658	Trivial (GRH)
18.8.1216851650518801193821772578418688.1	x^18 - 9x^17 + 36x^16 - 84x^15 - 324x^14 + 3024x^13 - 10665x^12 + 23508x^11 - 34398x^10 + 31289x^9 - 10359x^8 - 16020x^7 + 30048x^6 - 26505x^5 + 14769x^4 - 5391x^3 + 1242x^2 - 162x + 9	\( -\,2^{12}\cdot 3^{36}\cdot 7^{12}\cdot 11\cdot 13 \)	18T658	Trivial (GRH)
18.4.2859175906114106301567241862578176.2	x^18 + 63x^16 + 1467x^14 + 15405x^12 + 71316x^10 + 123480x^8 - 15960x^6 - 212688x^4 - 119952x^2 + 336	\( -\,2^{16}\cdot 3^{37}\cdot 7^{13} \)	18T658	$[4]$ (GRH)
18.4.2859175906114106301567241862578176.3	x^18 + 9x^16 - 54x^15 + 36x^14 - 162x^13 + 825x^12 - 1116x^11 - 2430x^10 - 10890x^9 + 7443x^8 + 38700x^7 + 22317x^6 - 188082x^5 - 283806x^4 - 116766x^3 + 101286x^2 + 132408x + 18678	\( -\,2^{16}\cdot 3^{37}\cdot 7^{13} \)	18T658	$[4]$ (GRH)
18.12.26141036855900400471471925600714752.1	x^18 - 18x^16 - 162x^14 + 5325x^12 - 33462x^10 - 5364x^8 + 634065x^6 - 1461330x^4 - 15300x^2 + 363	\( -\,2^{22}\cdot 3^{37}\cdot 7^{12} \)	18T658	Trivial (GRH)
18.12.26141036855900400471471925600714752.2	x^18 + 36x^16 + 234x^14 - 1857x^12 - 1728x^10 + 20394x^8 - 27417x^6 + 7794x^4 - 342x^2 + 3	\( -\,2^{22}\cdot 3^{37}\cdot 7^{12} \)	18T658	Trivial (GRH)
18.0.60995752663767601100101159735001088.1	x^18 + 63x^16 + 1530x^14 + 19224x^12 + 138096x^10 + 582498x^8 + 1409982x^6 + 1801800x^4 + 984375x^2 + 109375	\( -\,2^{22}\cdot 3^{36}\cdot 7^{13} \)	18T658	$[2, 188]$ (GRH)
18.10.60995752663767601100101159735001088.1	x^18 + 27x^16 - 162x^14 - 1269x^12 + 7938x^10 + 5355x^8 - 91119x^6 + 145908x^4 - 43344x^2 - 448	\( 2^{22}\cdot 3^{36}\cdot 7^{13} \)	18T658	Trivial (GRH)
18.14.60995752663767601100101159735001088.1	x^18 - 27x^16 - 36x^14 + 5991x^12 - 47880x^10 + 104643x^8 - 73017x^6 + 5922x^4 + 5544x^2 - 28	\( 2^{22}\cdot 3^{36}\cdot 7^{13} \)	18T658	Trivial (GRH)
18.10.60995752663767601100101159735001088.2	x^18 + 27x^16 - 162x^14 - 1017x^12 + 4914x^10 + 5355x^8 - 21315x^6 - 5292x^4 + 24696x^2 - 5488	\( 2^{22}\cdot 3^{36}\cdot 7^{13} \)	18T658	Trivial (GRH)
18.4.80056925371194976443882772152188928.1	x^18 - 9x^17 + 9x^16 + 87x^15 - 81x^14 - 972x^13 + 4071x^12 - 8820x^11 + 12267x^10 - 26013x^9 + 32706x^8 + 70866x^7 - 35265x^6 - 428886x^5 + 484812x^4 - 141066x^3 + 456012x^2 - 473040x + 18678	\( -\,2^{18}\cdot 3^{37}\cdot 7^{14} \)	18T658	$[2, 2]$ (GRH)
18.4.80056925371194976443882772152188928.2	x^18 - 27x^16 - 78x^15 - 144x^14 - 342x^13 - 63x^12 - 1008x^11 - 9450x^10 - 13720x^9 + 6993x^8 + 13104x^7 - 56385x^6 - 96894x^5 - 5040x^4 + 46704x^3 + 138474x^2 + 223272x - 20678	\( -\,2^{18}\cdot 3^{37}\cdot 7^{14} \)	18T658	$[2, 4]$ (GRH)
18.6.212199018096157133978664638054891712.1	x^18 - 7x^17 - 13x^16 + 195x^15 - 89x^14 - 3583x^13 + 2731x^12 + 52828x^11 + 32843x^10 - 315955x^9 - 446625x^8 + 832169x^7 + 1856844x^6 - 774826x^5 - 3534412x^4 - 428865x^3 + 3069393x^2 + 847425x - 976461	\( 2^{6}\cdot 3^{9}\cdot 7^{8}\cdot 643^{8} \)	18T658	$[6]$ (GRH)
18.6.212199018096157133978664638054891712.2	x^18 + 41x^16 + 404x^14 + 165x^12 - 8703x^10 - 4607x^8 + 24181x^6 - 1524x^4 - 948x^2 - 27	\( 2^{6}\cdot 3^{9}\cdot 7^{8}\cdot 643^{8} \)	18T658	$[3]$ (GRH)
18.14.243983010655070404400404638940004352.1	x^18 - 36x^16 + 189x^14 + 1596x^12 - 16821x^10 + 51660x^8 - 65289x^6 + 30744x^4 - 1764x^2 - 1372	\( 2^{24}\cdot 3^{36}\cdot 7^{13} \)	18T658	Trivial (GRH)
18.6.418256589694406407543550809611436032.1	x^18 - 36x^16 + 234x^14 + 1857x^12 - 1728x^10 - 20394x^8 - 27417x^6 - 7794x^4 - 342x^2 - 3	\( 2^{26}\cdot 3^{37}\cdot 7^{12} \)	18T658	$[2]$ (GRH)
18.6.418256589694406407543550809611436032.2	x^18 + 18x^16 - 162x^14 - 5325x^12 - 33462x^10 + 5364x^8 + 634065x^6 + 1461330x^4 - 15300x^2 - 363	\( 2^{26}\cdot 3^{37}\cdot 7^{12} \)	18T658	Trivial (GRH)
18.18.975932042620281617601618555760017408.1	x^18 - 63x^16 + 1530x^14 - 19224x^12 + 138096x^10 - 582498x^8 + 1409982x^6 - 1801800x^4 + 984375x^2 - 109375	\( 2^{26}\cdot 3^{36}\cdot 7^{13} \)	18T658	Trivial (GRH)