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 56)

Label	Polynomial	Discriminant	Galois group	Class group
18.4.745373357556319719171.1	x^18 - 9x^16 - 3x^15 + 36x^14 + 24x^13 - 79x^12 - 81x^11 + 93x^10 + 145x^9 - 39x^8 - 132x^7 - 23x^6 + 60x^5 + 9x^4 - 16x^3 - 3x^2 + 3x + 1	\( -\,3^{18}\cdot 7^{12}\cdot 139 \)	18T657	Trivial (GRH)
18.2.20125080654020632417617.1	x^18 - 3x^17 + 6x^16 - 14x^15 + 36x^14 - 96x^13 + 191x^12 - 297x^11 + 435x^10 - 690x^9 + 945x^8 - 813x^7 + 297x^6 + 105x^5 - 147x^4 + 44x^3 + 6x^2 - 6x + 1	\( 3^{21}\cdot 7^{12}\cdot 139 \)	18T657	Trivial (GRH)
18.4.21964383255760327839744.1	x^18 - 9x^16 + 36x^14 - 82x^12 + 114x^10 - 96x^8 + 43x^6 - 3x^4 - 6x^2 + 1	\( -\,2^{12}\cdot 3^{18}\cdot 7^{12} \)	18T657	Trivial (GRH)
18.2.593038347905528851673088.1	x^18 + 6x^16 + 6x^14 - 69x^12 - 441x^10 - 1341x^8 - 2241x^6 - 1998x^4 - 783x^2 - 27	\( 2^{12}\cdot 3^{21}\cdot 7^{12} \)	18T657	Trivial (GRH)
18.6.8939016006853175552398509.1	x^18 - 9x^17 + 27x^16 - 12x^15 - 90x^14 + 126x^13 + 125x^12 - 282x^11 - 126x^10 + 355x^9 + 147x^8 - 282x^7 - 169x^6 + 126x^5 + 120x^4 - 12x^3 - 36x^2 - 9x + 1	\( 3^{18}\cdot 7^{12}\cdot 43\cdot 38767 \)	18T657	Trivial (GRH)
18.0.155442283494504211376990784.1	x^18 - 6x^17 + 27x^16 - 114x^15 + 384x^14 - 1113x^13 + 3033x^12 - 7215x^11 + 15258x^10 - 29916x^9 + 52227x^8 - 80064x^7 + 112022x^6 - 137937x^5 + 140685x^4 - 120978x^3 + 87003x^2 - 40815x + 8191	\( -\,2^{6}\cdot 3^{18}\cdot 7^{12}\cdot 673^{2} \)	18T657	Trivial (GRH)
18.0.162353894693600708894966751.1	x^18 - 9x^17 + 54x^16 - 228x^15 + 774x^14 - 2142x^13 + 5039x^12 - 10110x^11 + 17622x^10 - 26609x^9 + 35103x^8 - 40098x^7 + 39737x^6 - 33534x^5 + 23970x^4 - 13926x^3 + 6444x^2 - 2088x + 433	\( -\,3^{18}\cdot 7^{12}\cdot 30276359 \)	18T657	Trivial (GRH)
18.6.2226460253813357741787856689.1	x^18 - 9x^17 + 18x^16 + 60x^15 - 234x^14 - 126x^13 + 1175x^12 - 30x^11 - 3522x^10 + 439x^9 + 7083x^8 - 18x^7 - 9551x^6 - 2262x^5 + 7674x^4 + 4138x^3 - 2364x^2 - 2472x - 559	\( 3^{18}\cdot 7^{12}\cdot 587\cdot 673\cdot 1051 \)	18T657	Trivial (GRH)
18.14.4290206164020174191198626271232.1	x^18 - 36x^16 + 504x^14 - 3457x^12 + 11952x^10 - 18639x^8 + 7076x^6 + 4929x^4 + 435x^2 - 13	\( 2^{12}\cdot 3^{6}\cdot 7^{12}\cdot 13\cdot 41^{8} \)	18T657	Trivial (GRH)
18.6.4290206164020174191198626271232.1	x^18 - 3x^17 + 16x^16 - 11x^15 - 58x^14 + 602x^13 - 2525x^12 + 7117x^11 - 17122x^10 + 25336x^9 - 31167x^8 - 8792x^7 + 64573x^6 - 180540x^5 + 206756x^4 - 195420x^3 + 80668x^2 + 13688x - 6728	\( 2^{12}\cdot 3^{6}\cdot 7^{12}\cdot 13\cdot 41^{8} \)	18T657	Trivial (GRH)
18.14.9570459904352696272673858605056.1	x^18 - 6x^17 + 20x^15 - 68x^14 + 749x^13 - 662x^12 - 4726x^11 + 7018x^10 + 4742x^9 - 9379x^8 - 2513x^7 + 4898x^6 + 1214x^5 - 976x^4 - 333x^3 + 15x^2 + 13x + 1	\( 2^{12}\cdot 3^{6}\cdot 7^{12}\cdot 29\cdot 41^{8} \)	18T657	Trivial (GRH)
18.6.9570459904352696272673858605056.1	x^18 - 3x^17 + 22x^16 - 27x^15 + 97x^14 + 133x^13 - 250x^12 + 1300x^11 - 1214x^10 + 1140x^9 - 100x^8 - 3235x^7 + 4766x^6 - 13591x^5 + 5393x^4 + 7078x^3 - 6478x^2 + 3813x - 533	\( 2^{12}\cdot 3^{6}\cdot 7^{12}\cdot 29\cdot 41^{8} \)	18T657	Trivial (GRH)
18.10.13530650209602087833780282855424.1	x^18 - 8x^17 - 7x^16 + 268x^15 - 925x^14 - 102x^13 + 7776x^12 - 19220x^11 + 14670x^10 + 15362x^9 - 48195x^8 + 71380x^7 - 74449x^6 - 1652x^5 + 123525x^4 - 119096x^3 - 2336x^2 + 51566x - 18509	\( 2^{12}\cdot 3^{6}\cdot 7^{12}\cdot 41^{9} \)	18T657	Trivial (GRH)
18.10.13530650209602087833780282855424.2	x^18 - 4x^17 - 24x^16 + 120x^15 + 189x^14 - 1648x^13 + 155x^12 + 12484x^11 - 12466x^10 - 50728x^9 + 85024x^8 + 89376x^7 - 240584x^6 + 5264x^5 + 238688x^4 - 116032x^3 + 25856x^2 - 89088x + 53248	\( 2^{12}\cdot 3^{6}\cdot 7^{12}\cdot 41^{9} \)	18T657	Trivial (GRH)
18.12.14190681927143653093964686897152.1	x^18 - 3x^17 + 2x^16 - 39x^15 + 10x^14 + 280x^13 + 243x^12 + 601x^11 - 3258x^10 - 7976x^9 + 7391x^8 + 16054x^7 + 2558x^6 + 10817x^5 + 579x^4 - 37304x^3 - 29743x^2 - 3766x + 889	\( -\,2^{12}\cdot 3^{6}\cdot 7^{12}\cdot 41^{8}\cdot 43 \)	18T657	Trivial (GRH)
18.4.14190681927143653093964686897152.1	x^18 - 6x^17 + 30x^16 - 112x^15 + 229x^14 - 105x^13 - 1402x^12 + 5066x^11 - 10956x^10 + 15747x^9 - 17607x^8 + 17447x^7 - 10931x^6 + 8040x^5 - 26x^4 - 2972x^3 + 72x^2 + 488x - 104	\( -\,2^{12}\cdot 3^{6}\cdot 7^{12}\cdot 41^{8}\cdot 43 \)	18T657	Trivial (GRH)
18.8.14190681927143653093964686897152.1	x^18 - 3x^17 - 12x^16 + 59x^15 - 169x^14 + 315x^13 + 250x^12 - 1177x^11 + 998x^10 + 277x^9 - 1342x^8 + 1251x^7 - 12x^6 - 683x^5 - 83x^4 + 534x^3 - 218x^2 + 28x - 1	\( -\,2^{12}\cdot 3^{6}\cdot 7^{12}\cdot 41^{8}\cdot 43 \)	18T657	Trivial (GRH)
18.12.14190681927143653093964686897152.2	x^18 - 2x^17 - 21x^16 + 112x^15 - 177x^14 - 532x^13 + 2595x^12 - 3640x^11 + 917x^10 + 9022x^9 - 23967x^8 + 20478x^7 + 10715x^6 - 33726x^5 + 25254x^4 - 7100x^3 - 512x^2 + 688x - 104	\( -\,2^{12}\cdot 3^{6}\cdot 7^{12}\cdot 41^{8}\cdot 43 \)	18T657	Trivial (GRH)
18.8.21121014961330088325900929335296.1	x^18 - 6x^17 - 13x^16 + 138x^15 - 14x^14 - 1296x^13 + 1281x^12 + 6782x^11 - 18134x^10 + 4664x^9 + 93135x^8 - 239644x^7 + 71013x^6 + 360096x^5 - 198902x^4 - 193004x^3 + 24342x^2 + 62774x + 19403	\( -\,2^{18}\cdot 3^{6}\cdot 7^{12}\cdot 41^{8} \)	18T657	Trivial (GRH)
18.4.23431125972725566736546343481344.1	x^18 - 6x^17 + 42x^16 - 155x^15 + 458x^14 - 1099x^13 + 628x^12 - 142x^11 - 11420x^10 + 22741x^9 - 52371x^8 + 49129x^7 - 35570x^6 - 39513x^5 + 97174x^4 - 84904x^3 + 149163x^2 - 19523x + 118391	\( -\,2^{12}\cdot 3^{6}\cdot 7^{12}\cdot 41^{8}\cdot 71 \)	18T657	Trivial (GRH)
18.8.27391316277974958297652767731712.1	x^18 - 3x^17 + 3x^16 + 33x^15 - 249x^14 + 567x^13 - 683x^12 - 1586x^11 + 14135x^10 - 39902x^9 + 58263x^8 + 20603x^7 - 269950x^6 + 507631x^5 - 520446x^4 + 353670x^3 - 159449x^2 + 44075x - 6929	\( -\,2^{12}\cdot 3^{6}\cdot 7^{12}\cdot 41^{8}\cdot 83 \)	18T657	Trivial (GRH)
18.8.27391316277974958297652767731712.2	x^18 - 4x^17 - 13x^16 + 64x^15 - 115x^14 + 434x^13 + 807x^12 - 8638x^11 + 8287x^10 + 26362x^9 - 34315x^8 - 38698x^7 + 35307x^6 + 61776x^5 - 12272x^4 - 58160x^3 + 1968x^2 - 8448x + 4544	\( -\,2^{12}\cdot 3^{6}\cdot 7^{12}\cdot 41^{8}\cdot 83 \)	18T657	Trivial (GRH)
18.8.45640439727204768655041586119744.1	x^18 + 11x^16 - 150x^14 - 621x^12 + 3167x^10 + 10627x^8 - 10601x^6 - 36666x^4 - 1944x^2 + 729	\( -\,2^{6}\cdot 3^{6}\cdot 7^{12}\cdot 643^{6} \)	18T657	$[3]$ (GRH)
18.12.55112648414720699225397737484288.1	x^18 + 15x^16 - 132x^14 - 1017x^12 + 7503x^10 + 8103x^8 - 119593x^6 + 194262x^4 - 32400x^2 + 167	\( -\,2^{12}\cdot 3^{6}\cdot 7^{12}\cdot 41^{8}\cdot 167 \)	18T657	Trivial (GRH)
18.8.55112648414720699225397737484288.1	x^18 - 3x^17 + 7x^16 + 6x^15 - 221x^14 + 714x^13 - 2165x^12 + 3597x^11 + 463x^10 - 10670x^9 + 60028x^8 - 110341x^7 + 102391x^6 - 13206x^5 - 193454x^4 + 324269x^3 - 250469x^2 + 118258x - 29261	\( -\,2^{12}\cdot 3^{6}\cdot 7^{12}\cdot 41^{8}\cdot 167 \)	18T657	Trivial (GRH)
18.10.59732870437511656046688565776384.1	x^18 - 5x^17 - 13x^16 + 164x^15 - 343x^14 - 723x^13 + 5442x^12 - 11744x^11 - 3122x^10 + 70943x^9 - 148329x^8 + 93136x^7 + 135322x^6 - 290598x^5 + 213196x^4 - 67385x^3 + 7128x^2 + 234x - 27	\( 2^{12}\cdot 3^{6}\cdot 7^{12}\cdot 41^{8}\cdot 181 \)	18T657	Trivial (GRH)
18.6.59732870437511656046688565776384.1	x^18 - 4x^17 - 5x^16 + 32x^15 + 64x^14 - 570x^13 + 854x^12 + 3082x^11 - 12409x^10 + 5448x^9 + 32474x^8 - 34944x^7 - 22696x^6 - 17496x^5 + 129553x^4 - 42044x^3 - 76656x^2 - 31780x + 75223	\( 2^{12}\cdot 3^{6}\cdot 7^{12}\cdot 41^{8}\cdot 181 \)	18T657	Trivial (GRH)
18.8.94714551467214614836461979987968.1	x^18 - 3x^17 - 20x^16 + 8x^15 + 346x^14 + 140x^13 - 3254x^12 + 5201x^11 - 14475x^10 + 13996x^9 + 60144x^8 - 33496x^7 - 56755x^6 - 77665x^5 - 56371x^4 - 26905x^3 - 53273x^2 - 15253x + 4493	\( -\,2^{12}\cdot 3^{6}\cdot 7^{13}\cdot 41^{9} \)	18T657	Trivial (GRH)
18.10.663001860270502303855233859915776.1	x^18 - 3x^17 - 3x^16 - 198x^14 + 665x^13 - 1035x^12 + 1680x^11 + 8425x^10 - 13464x^9 + 6284x^8 - 61792x^7 + 76447x^6 - 23603x^5 + 72610x^4 - 90727x^3 + 16016x^2 + 10176x - 1247	\( 2^{12}\cdot 3^{6}\cdot 7^{14}\cdot 41^{9} \)	18T657	Trivial (GRH)
18.10.663001860270502303855233859915776.2	x^18 - 3x^17 - 29x^16 + 133x^15 - 18x^14 - 810x^13 + 2764x^12 - 8967x^11 + 13513x^10 + 46545x^9 - 229417x^8 + 283982x^7 + 253555x^6 - 1149513x^5 + 1413873x^4 - 819117x^3 + 215019x^2 - 27351x + 4509	\( 2^{12}\cdot 3^{6}\cdot 7^{14}\cdot 41^{9} \)	18T657	Trivial (GRH)
18.12.865961613414533621361938102747136.1	x^18 - 6x^17 - 33x^16 + 230x^15 + 290x^14 - 3178x^13 + 936x^12 + 15544x^11 - 23453x^10 + 48204x^9 + 73884x^8 - 850430x^7 + 244572x^6 + 3611310x^5 - 1822347x^4 - 6573762x^3 + 3621940x^2 + 4327624x - 2563673	\( -\,2^{18}\cdot 3^{6}\cdot 7^{12}\cdot 41^{9} \)	18T657	Trivial (GRH)
18.4.865961613414533621361938102747136.1	x^18 + 30x^16 - 59x^14 - 3582x^12 - 1154x^10 + 83692x^8 + 218745x^6 + 174548x^4 + 41152x^2 + 2624	\( -\,2^{18}\cdot 3^{6}\cdot 7^{12}\cdot 41^{9} \)	18T657	Trivial (GRH)
18.8.865961613414533621361938102747136.1	x^18 + 2x^16 - 336x^14 + 1759x^12 + 13268x^10 - 92043x^8 - 68268x^6 + 806593x^4 + 13735x^2 + 41	\( -\,2^{18}\cdot 3^{6}\cdot 7^{12}\cdot 41^{9} \)	18T657	Trivial (GRH)
18.12.865961613414533621361938102747136.2	x^18 + 4x^16 - 337x^14 - 1097x^12 + 19399x^10 + 35318x^8 - 262504x^6 + 264491x^4 - 82041x^2 + 6929	\( -\,2^{18}\cdot 3^{6}\cdot 7^{12}\cdot 41^{9} \)	18T657	Trivial (GRH)
18.10.865961613414533621361938102747136.1	x^18 - 32x^16 + 142x^14 + 4366x^12 - 45575x^10 + 70434x^8 + 185481x^6 + 89832x^4 + 5456x^2 - 2624	\( 2^{18}\cdot 3^{6}\cdot 7^{12}\cdot 41^{9} \)	18T657	Trivial (GRH)
18.14.865961613414533621361938102747136.1	x^18 - 4x^17 - 43x^16 + 140x^15 + 697x^14 - 1332x^13 - 5877x^12 + 286x^11 + 24651x^10 + 46224x^9 - 7313x^8 - 142480x^7 - 209892x^6 - 124454x^5 + 64828x^4 + 183050x^3 + 109343x^2 + 14314x - 587	\( 2^{18}\cdot 3^{6}\cdot 7^{12}\cdot 41^{9} \)	18T657	Trivial (GRH)
18.6.865961613414533621361938102747136.1	x^18 - 4x^17 + 2x^16 + 50x^15 - 215x^14 - 246x^13 + 275x^12 - 2704x^11 - 5369x^10 - 10048x^9 - 13776x^8 - 20162x^7 - 58102x^6 - 24494x^5 + 64909x^4 + 120254x^3 + 63621x^2 + 9614x + 461	\( 2^{18}\cdot 3^{6}\cdot 7^{12}\cdot 41^{9} \)	18T657	Trivial (GRH)
18.10.865961613414533621361938102747136.2	x^18 - 4x^17 - 12x^16 + 64x^15 - 96x^14 + 14x^13 + 1598x^12 - 6098x^11 + 203x^10 + 44230x^9 - 68772x^8 - 114360x^7 + 266857x^6 + 144262x^5 - 157848x^4 - 649120x^3 - 153716x^2 + 1686168x - 999832	\( 2^{18}\cdot 3^{6}\cdot 7^{12}\cdot 41^{9} \)	18T657	Trivial (GRH)
18.6.865961613414533621361938102747136.2	x^18 - 4x^17 + 13x^16 - 8x^15 - 29x^14 + 130x^13 - 514x^12 - 668x^11 + 4063x^10 - 18830x^9 + 37846x^8 - 15000x^7 + 66773x^6 - 57922x^5 - 204442x^4 + 200028x^3 - 233624x^2 + 512050x - 283207	\( 2^{18}\cdot 3^{6}\cdot 7^{12}\cdot 41^{9} \)	18T657	Trivial (GRH)
18.10.865961613414533621361938102747136.3	x^18 - 3x^17 - 26x^16 - x^15 + 134x^14 + 1373x^13 - 851x^12 - 17411x^11 + 17249x^10 + 81126x^9 - 104951x^8 - 162914x^7 + 195573x^6 + 175749x^5 - 35028x^4 - 125407x^3 - 127059x^2 + 16766x - 26711	\( 2^{18}\cdot 3^{6}\cdot 7^{12}\cdot 41^{9} \)	18T657	Trivial (GRH)
18.16.1232291872634528753686122825233088.1	x^18 - 2x^17 - 30x^16 + 31x^15 + 87x^14 - 479x^13 + 4347x^12 + 16476x^11 - 25670x^10 - 155287x^9 - 113286x^8 + 327929x^7 + 691759x^6 + 409110x^5 - 151292x^4 - 339196x^3 - 191533x^2 - 49101x - 4901	\( -\,2^{6}\cdot 3^{9}\cdot 7^{12}\cdot 643^{6} \)	18T657	$[3]$ (GRH)
18.16.1232291872634528753686122825233088.2	x^18 - 8x^17 - 8x^16 + 208x^15 - 360x^14 - 1588x^13 + 6842x^12 + 1448x^11 - 55094x^10 + 23367x^9 + 257071x^8 - 22604x^7 - 643655x^6 - 289443x^5 + 596828x^4 + 503735x^3 - 104560x^2 - 214976x - 56953	\( -\,2^{6}\cdot 3^{9}\cdot 7^{12}\cdot 643^{6} \)	18T657	$[3]$ (GRH)
18.2.1880277683523991122651614897504256.1	x^18 + 48x^16 + 912x^14 + 8540x^12 + 38304x^10 + 45584x^8 - 226016x^6 - 799936x^4 - 876032x^2 - 313664	\( 2^{18}\cdot 3^{6}\cdot 7^{14}\cdot 29^{9} \)	18T657	$[2]$ (GRH)
18.2.1880277683523991122651614897504256.2	x^18 + 70x^16 + 1539x^14 + 15597x^12 + 79203x^10 + 187072x^8 + 135204x^6 - 49689x^4 - 12989x^2 - 29	\( 2^{18}\cdot 3^{6}\cdot 7^{14}\cdot 29^{9} \)	18T657	Trivial (GRH)
18.12.6061731293901735349533566719229952.1	x^18 - 6x^17 - 51x^16 + 254x^15 + 972x^14 - 2700x^13 - 9201x^12 + 4554x^11 + 26824x^10 + 36468x^9 + 1365x^8 - 107848x^7 - 42441x^6 + 89742x^5 - 3586x^4 - 30696x^3 + 25776x^2 + 6872x - 3683	\( -\,2^{18}\cdot 3^{6}\cdot 7^{13}\cdot 41^{9} \)	18T657	Trivial (GRH)
18.6.6061731293901735349533566719229952.1	x^18 - 4x^17 + 20x^16 - 68x^15 + 96x^14 - 224x^13 + 917x^12 - 4540x^11 + 19647x^10 - 46266x^9 + 29537x^8 + 227232x^7 - 1003323x^6 + 1600790x^5 + 38116x^4 - 3327590x^3 + 3988171x^2 - 1664262x + 145319	\( 2^{18}\cdot 3^{6}\cdot 7^{13}\cdot 41^{9} \)	18T657	Trivial (GRH)
18.12.9462214702675879570003616342212608.1	x^18 - 35x^16 + 187x^14 + 3052x^12 - 15317x^10 - 24724x^8 + 76749x^6 + 88732x^4 - 27020x^2 + 1183	\( -\,2^{24}\cdot 3^{6}\cdot 7^{13}\cdot 41^{8} \)	18T657	Trivial (GRH)
18.12.9462214702675879570003616342212608.2	x^18 + 2x^16 - 270x^14 - 313x^12 + 17021x^10 - 17547x^8 - 100465x^6 + 172382x^4 - 93639x^2 + 16807	\( -\,2^{24}\cdot 3^{6}\cdot 7^{13}\cdot 41^{8} \)	18T657	Trivial (GRH)
18.4.23380963562192407776772328774172672.1	x^18 + 34x^16 + 92x^14 - 6351x^12 - 55632x^10 - 20461x^8 + 1073368x^6 + 3333423x^4 + 3320091x^2 + 930987	\( -\,2^{18}\cdot 3^{9}\cdot 7^{12}\cdot 41^{9} \)	18T657	Trivial (GRH)
18.14.23380963562192407776772328774172672.1	x^18 - 34x^16 + 92x^14 + 6351x^12 - 55632x^10 + 20461x^8 + 1073368x^6 - 3333423x^4 + 3320091x^2 - 930987	\( 2^{18}\cdot 3^{9}\cdot 7^{12}\cdot 41^{9} \)	18T657	Trivial (GRH)