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 50 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.6.148204394789719081222144.2	x^18 + 4x^16 + 5x^14 - 53x^12 - 189x^10 - 210x^8 + 74x^6 + 243x^4 + 169x^2 - 151	\( 2^{24}\cdot 37^{6}\cdot 151^{3} \)	18T837	Trivial (GRH)
18.6.148204394789719081222144.3	x^18 - 2x^17 + 3x^16 + 2x^15 - 33x^14 + 32x^13 - 54x^12 - 8x^11 + 58x^10 - 176x^9 - 13x^8 - 88x^7 + 211x^6 - 120x^5 + 55x^4 - 2x^3 + 4x^2 + 6x - 1	\( 2^{24}\cdot 37^{6}\cdot 151^{3} \)	18T837	Trivial (GRH)
18.2.514687157793406972592128.3	x^18 + 8x^16 + 20x^14 - 19x^12 - 274x^10 - 980x^8 - 2183x^6 - 3258x^4 - 2985x^2 - 1303	\( 2^{18}\cdot 31^{6}\cdot 1303^{3} \)	18T837	Trivial (GRH)
18.2.514687157793406972592128.4	x^18 + 7x^16 + 20x^14 + 23x^12 - 50x^10 - 412x^8 - 981x^6 - 2080x^4 - 2606x^2 - 1303	\( 2^{18}\cdot 31^{6}\cdot 1303^{3} \)	18T837	Trivial (GRH)
18.4.962209182221468210036736.1	x^18 - 9x^16 + 45x^14 - 147x^12 + 330x^10 - 4x^9 - 516x^8 + 36x^7 + 540x^6 - 72x^5 - 348x^4 + 40x^3 + 120x^2 - 8	\( -\,2^{24}\cdot 3^{18}\cdot 23^{6} \)	18T837	Trivial (GRH)
18.8.2775641410382903738630144.1	x^18 - 2x^17 - 8x^16 + 8x^15 + 53x^14 - 16x^13 - 225x^12 + 66x^11 + 519x^10 - 258x^9 - 792x^8 + 698x^7 + 1026x^6 - 900x^5 - 1011x^4 + 352x^3 + 377x^2 - 44x - 37	\( -\,2^{24}\cdot 37^{6}\cdot 401^{3} \)	18T837	Trivial (GRH)
18.4.2775641410382903738630144.2	x^18 + 6x^16 - 9x^14 - 133x^12 - 293x^10 - 8x^8 + 880x^6 + 1553x^4 + 1203x^2 + 401	\( -\,2^{24}\cdot 37^{6}\cdot 401^{3} \)	18T837	Trivial (GRH)
18.8.2775641410382903738630144.2	x^18 - 7x^16 - 16x^14 + 196x^12 - 54x^10 - 1282x^8 + 1720x^6 + 308x^4 - 1203x^2 + 401	\( -\,2^{24}\cdot 37^{6}\cdot 401^{3} \)	18T837	Trivial (GRH)
18.0.15955301891595616150355968.1	x^18 + 17x^16 + 143x^14 + 826x^12 + 3463x^10 + 10771x^8 + 25249x^6 + 40474x^4 + 49934x^2 + 40393	\( -\,2^{18}\cdot 31^{7}\cdot 1303^{3} \)	18T837	$[2]$ (GRH)
18.0.15955301891595616150355968.2	x^18 + 3x^16 + 17x^14 + 27x^12 + 66x^10 + 770x^8 + 5156x^6 + 14947x^4 + 37787x^2 + 40393	\( -\,2^{18}\cdot 31^{7}\cdot 1303^{3} \)	18T837	Trivial (GRH)
18.0.22378863613247581264543744.1	x^18 - 4x^17 + 15x^16 - 42x^15 + 92x^14 - 162x^13 + 248x^12 - 386x^11 + 594x^10 - 806x^9 + 1014x^8 - 662x^7 - 936x^6 + 1698x^5 + 428x^4 - 5774x^3 + 14953x^2 - 12726x + 7151	\( -\,2^{24}\cdot 37^{6}\cdot 151^{4} \)	18T837	Trivial (GRH)
18.0.22378863613247581264543744.2	x^18 - 4x^17 + 11x^16 + 6x^15 - 35x^14 + 60x^13 - 116x^12 + 482x^11 - 1052x^10 + 674x^9 + 2187x^8 - 7202x^7 + 11603x^6 - 12444x^5 + 11069x^4 - 7876x^3 + 5784x^2 - 2412x + 823	\( -\,2^{24}\cdot 37^{6}\cdot 151^{4} \)	18T837	Trivial (GRH)
18.4.25979647919979641670991872.1	x^18 - 3x^16 - 15x^14 - 69x^12 - 171x^10 - 621x^8 + 504x^6 - 270x^4 + 81x^2 + 27	\( -\,2^{24}\cdot 3^{21}\cdot 23^{6} \)	18T837	Trivial (GRH)
18.0.68697349292420119212064768.1	x^18 + 22x^16 + 194x^14 + 918x^12 + 3000x^10 + 9387x^8 + 25861x^6 + 43240x^4 + 36291x^2 + 12097	\( -\,2^{18}\cdot 23^{6}\cdot 12097^{3} \)	18T837	Trivial (GRH)
18.0.68697349292420119212064768.2	x^18 + 25x^16 + 279x^14 + 1849x^12 + 8017x^10 + 23434x^8 + 45462x^6 + 55856x^4 + 39329x^2 + 12097	\( -\,2^{18}\cdot 23^{6}\cdot 12097^{3} \)	18T837	$[2]$ (GRH)
18.4.102698732184167438329315328.1	x^18 - 2x^17 - x^16 - 12x^15 - x^14 - 132x^13 - 26x^12 + 156x^11 + 954x^10 + 526x^9 + 39x^8 - 2266x^7 - 3307x^6 + 2644x^5 + 3665x^4 + 2688x^3 - 3696x^2 - 20x + 1531	\( -\,2^{24}\cdot 37^{7}\cdot 401^{3} \)	18T837	Trivial (GRH)
18.2.899278084981108087628637469.1	x^18 - 8x^17 + 10x^16 + 32x^15 - 44x^14 + 133x^13 - 49x^12 - 606x^11 + 408x^10 - 2556x^9 - 3321x^8 + 7460x^7 + 3307x^6 + 30x^5 + 11772x^4 - 124x^3 - 20735x^2 - 72486x - 79357	\( 23^{7}\cdot 43^{6}\cdot 347^{3} \)	18T837	$[2]$ (GRH)
18.8.1242692251627115694366240768.1	x^18 - 8x^17 + 26x^16 - 26x^15 - 148x^14 + 809x^13 - 2085x^12 + 3308x^11 - 2908x^10 + 242x^9 + 2353x^8 - 2596x^7 + 2995x^6 - 2762x^5 + 70x^4 + 1189x^3 - 939x^2 + 619x - 139	\( -\,2^{12}\cdot 3^{3}\cdot 37^{6}\cdot 16361^{3} \)	18T837	$[2]$ (GRH)
18.8.1242692251627115694366240768.2	x^18 - 3x^17 - 4x^16 + 11x^15 - 68x^14 + 180x^13 - 236x^12 + 513x^11 - 1051x^10 + 1101x^9 - 606x^8 + 91x^7 + 574x^6 - 1131x^5 + 889x^4 - 245x^3 - 45x^2 + 29x - 1	\( -\,2^{12}\cdot 3^{3}\cdot 37^{6}\cdot 16361^{3} \)	18T837	$[2]$ (GRH)
18.2.1580039033725662741877489664.1	x^18 + 7x^16 + 25x^14 - 284x^12 - 3652x^10 - 25497x^8 - 113993x^6 - 389225x^4 - 573914x^2 - 278231	\( 2^{18}\cdot 23^{7}\cdot 12097^{3} \)	18T837	$[2]$ (GRH)
18.6.1580039033725662741877489664.1	x^18 - 32x^16 + 364x^14 - 1605x^12 - 302x^10 + 22373x^8 - 32877x^6 - 143293x^4 + 423395x^2 - 278231	\( 2^{18}\cdot 23^{7}\cdot 12097^{3} \)	18T837	Trivial (GRH)
18.6.1580039033725662741877489664.2	x^18 + 2x^16 - 2x^14 - 180x^12 - 737x^10 - 1092x^8 + 12114x^6 + 49162x^4 + 107352x^2 - 278231	\( 2^{18}\cdot 23^{7}\cdot 12097^{3} \)	18T837	$[2]$ (GRH)
18.2.1804330644648089697367621632.2	x^18 + 23x^16 + 212x^14 + 969x^12 + 2116x^10 + 1210x^8 - 2712x^6 - 3888x^4 - 1008x^2 - 72	\( 2^{33}\cdot 3^{6}\cdot 257^{6} \)	18T837	Trivial (GRH)
18.2.1957287753903949511628161024.2	x^18 + 13x^16 + 24x^14 - 208x^12 - 630x^10 + 170x^8 - 528x^6 - 6408x^4 - 6227x^2 - 479	\( 2^{24}\cdot 101^{6}\cdot 479^{3} \)	18T837	Trivial (GRH)
18.6.1957287753903949511628161024.2	x^18 + 7x^16 - 27x^14 - 256x^12 - 16x^10 + 1895x^8 - 377x^6 - 6025x^4 + 4790x^2 - 479	\( 2^{24}\cdot 101^{6}\cdot 479^{3} \)	18T837	Trivial (GRH)
18.10.1957287753903949511628161024.3	x^18 - 12x^16 + 49x^14 - 61x^12 - 149x^10 + 646x^8 - 466x^6 - 817x^4 + 1289x^2 - 479	\( 2^{24}\cdot 101^{6}\cdot 479^{3} \)	18T837	Trivial (GRH)
18.6.1957287753903949511628161024.3	x^18 + x^16 - 6x^15 + 54x^14 + 34x^13 + 24x^12 - 410x^11 - 252x^10 + 110x^9 + 446x^8 + 1454x^7 - 1814x^6 + 1438x^5 - 3120x^4 + 2914x^3 - 1021x^2 + 146x - 7	\( 2^{24}\cdot 101^{6}\cdot 479^{3} \)	18T837	Trivial (GRH)
18.10.1957287753903949511628161024.4	x^18 - 6x^16 + x^14 + 47x^12 - 125x^10 + 192x^8 + 294x^6 - 1363x^4 + 1437x^2 - 479	\( 2^{24}\cdot 101^{6}\cdot 479^{3} \)	18T837	Trivial (GRH)
18.6.2808264301657526235515846656.1	x^18 - 14x^16 + 46x^14 + 72x^12 - 334x^10 - 290x^8 + 890x^6 + 572x^4 - 1066x^2 - 634	\( 2^{35}\cdot 37^{6}\cdot 317^{3} \)	18T837	$[2]$ (GRH)
18.12.14434645157184717578940973056.1	x^18 - 16x^16 + 103x^14 - 341x^12 + 603x^10 - 488x^8 - 24x^6 + 297x^4 - 135x^2 + 9	\( -\,2^{36}\cdot 3^{6}\cdot 257^{6} \)	18T837	Trivial (GRH)
18.4.14434645157184717578940973056.1	x^18 + 11x^16 + 43x^14 + 58x^12 - 54x^10 - 245x^8 - 237x^6 - 27x^4 + 54x^2 + 9	\( -\,2^{36}\cdot 3^{6}\cdot 257^{6} \)	18T837	Trivial (GRH)
18.8.14434645157184717578940973056.1	x^18 - 9x^16 - 9x^14 + 180x^12 + 109x^10 - 444x^8 + 29x^6 + 232x^4 - 90x^2 + 9	\( -\,2^{36}\cdot 3^{6}\cdot 257^{6} \)	18T837	Trivial (GRH)
18.6.77901699621606951968309248000.1	x^18 - 16x^16 + 28x^14 + 876x^12 - 6605x^10 + 16370x^8 - 1907x^6 - 46345x^4 + 46825x^2 - 12625	\( 2^{22}\cdot 5^{3}\cdot 101^{3}\cdot 229^{6} \)	18T837	$[2]$ (GRH)
18.2.100269240783317624614817890304.1	x^18 + 16x^16 + 76x^14 - 170x^12 - 2484x^10 - 568x^8 + 26412x^6 - 11320x^4 - 39296x^2 - 13256	\( 2^{33}\cdot 37^{6}\cdot 1657^{3} \)	18T837	$[2]$ (GRH)
18.12.188521017135728366078671192064.1	x^18 - 2x^17 - 12x^16 + 30x^15 - 43x^14 - 274x^13 + 411x^12 + 3842x^11 + 4641x^10 - 25884x^9 - 44398x^8 + 66212x^7 + 128668x^6 - 42920x^5 - 126227x^4 - 31720x^3 + 1733x^2 + 446x - 1	\( -\,2^{24}\cdot 37^{6}\cdot 16361^{3} \)	18T837	Trivial (GRH)
18.4.188521017135728366078671192064.1	x^18 - 6x^17 + 32x^16 - 90x^15 + 160x^14 - 20x^13 - 832x^12 + 1632x^11 - 5288x^10 + 6204x^9 - 24324x^8 - 12936x^7 - 8508x^6 - 50048x^5 - 184088x^4 - 100864x^3 + 76488x^2 + 87792x - 10888	\( -\,2^{24}\cdot 37^{6}\cdot 16361^{3} \)	18T837	$[2]$ (GRH)
18.12.188521017135728366078671192064.2	x^18 + 8x^16 - 91x^14 - 409x^12 + 3051x^10 - 1142x^8 - 21910x^6 + 53243x^4 - 49083x^2 + 16361	\( -\,2^{24}\cdot 37^{6}\cdot 16361^{3} \)	18T837	Trivial (GRH)
18.4.188521017135728366078671192064.2	x^18 - 6x^17 + 21x^16 - 66x^15 + 157x^14 - 364x^13 + 702x^12 - 1226x^11 + 1914x^10 - 2324x^9 + 3761x^8 - 2024x^7 + 5585x^6 + 1520x^5 + 6499x^4 + 1320x^3 + 6742x^2 - 2004x - 857	\( -\,2^{24}\cdot 37^{6}\cdot 16361^{3} \)	18T837	$[2]$ (GRH)
18.12.923817290059821925052222275584.1	x^18 - 6x^16 - 66x^14 + 292x^12 + 1496x^10 - 3968x^8 - 6072x^6 + 16848x^4 - 8640x^2 + 576	\( -\,2^{42}\cdot 3^{6}\cdot 257^{6} \)	18T837	Trivial (GRH)
18.4.923817290059821925052222275584.1	x^18 + 30x^16 + 324x^14 + 1400x^12 + 956x^10 - 7336x^8 - 8280x^6 + 6640x^4 + 1920x^2 + 576	\( -\,2^{42}\cdot 3^{6}\cdot 257^{6} \)	18T837	$[2]$ (GRH)
18.0.12065345096686615429034956292096.1	x^18 + 48x^16 + 873x^14 + 8175x^12 + 43777x^10 + 137970x^8 + 250326x^6 + 242159x^4 + 106935x^2 + 16361	\( -\,2^{30}\cdot 37^{6}\cdot 16361^{3} \)	18T837	$[4, 560]$ (GRH)
18.2.372427769099646360301475650076672.1	x^18 - 8x^17 + 84x^16 - 424x^15 + 1921x^14 - 5644x^13 + 5853x^12 + 27036x^11 - 403385x^10 + 1487836x^9 - 7335706x^8 + 16115138x^7 - 59107418x^6 + 80135026x^5 - 271007145x^4 + 191575958x^3 - 735906741x^2 + 146184984x - 949668003	\( 2^{18}\cdot 37^{6}\cdot 97^{5}\cdot 401^{3} \)	18T837	$[2]$ (GRH)
18.6.479938219387244670821417298690048.1	x^18 - 27x^14 - 18x^12 + 207x^10 + 276x^8 - 340x^6 - 864x^4 - 576x^2 - 128	\( 2^{33}\cdot 3^{18}\cdot 229^{6} \)	18T837	Trivial (GRH)
18.10.2688406910504947110220610513666048.1	x^18 - 2x^17 - 37x^16 + 4x^15 - 36x^14 + 2434x^13 - 1714x^12 + 8608x^11 - 16694x^10 + 35326x^9 - 1022016x^8 + 297560x^7 + 3842036x^6 + 2139914x^5 + 4488290x^4 - 3418788x^3 - 15652523x^2 - 6314160x + 1380893	\( 2^{18}\cdot 37^{6}\cdot 97^{3}\cdot 16361^{3} \)	18T837	$[2]$ (GRH)
18.6.2688406910504947110220610513666048.1	x^18 - 8x^17 + 51x^16 - 236x^15 + 681x^14 - 1198x^13 - 3534x^12 + 18560x^11 - 50254x^10 + 36650x^9 + 194059x^8 - 165414x^7 + 1640355x^6 + 3243870x^5 + 1978647x^4 + 8119890x^3 + 14798234x^2 - 8630734x - 21520927	\( 2^{18}\cdot 37^{6}\cdot 97^{3}\cdot 16361^{3} \)	18T837	$[2]$ (GRH)
18.10.2688406910504947110220610513666048.2	x^18 - 6x^17 - 13x^16 + 250x^15 - 963x^14 - 532x^13 + 17244x^12 - 53770x^11 - 14136x^10 + 500498x^9 - 1071849x^8 - 549232x^7 + 6055735x^6 - 6621332x^5 - 14303083x^4 + 23745820x^3 + 26536272x^2 - 31151478x - 24981067	\( 2^{18}\cdot 37^{6}\cdot 97^{3}\cdot 16361^{3} \)	18T837	$[2]$ (GRH)
18.0.2939487800594529948360199110656000.1	x^18 + 68x^16 + 1627x^14 + 19505x^12 + 131697x^10 + 516410x^8 + 1146558x^6 + 1326597x^4 + 683179x^2 + 102185	\( -\,2^{30}\cdot 5^{3}\cdot 37^{6}\cdot 107^{3}\cdot 191^{3} \)	18T837	$[2, 2, 2, 1444]$ (GRH)
18.8.245022226642631606722468388649566208.1	x^18 - 35x^16 + 66x^14 + 9337x^12 - 76953x^10 - 590965x^8 + 6333625x^6 + 9667826x^4 - 118095612x^2 + 152771337	\( -\,2^{36}\cdot 3^{6}\cdot 257^{9} \)	18T837	$[4]$ (GRH)
18.18.6545151312217316349292450273696940032.1	x^18 - 87x^16 + 2877x^14 - 47683x^12 + 432199x^10 - 2182202x^8 + 6023730x^6 - 8496112x^4 + 5190808x^2 - 843712	\( 2^{28}\cdot 7^{6}\cdot 67^{6}\cdot 13183^{3} \)	18T837	Trivial (GRH)
18.14.43985025462771439670319408614090211328.1	x^18 - 6x^17 - 93x^16 + 854x^15 - 3061x^14 - 41886x^13 + 612274x^12 + 982052x^11 - 25727268x^10 - 18424230x^9 + 481948659x^8 + 393242142x^7 - 4171202649x^6 - 5609525286x^5 + 12169951277x^4 + 35299641836x^3 + 19566863748x^2 - 62055591982x - 61237993441	\( 2^{18}\cdot 37^{6}\cdot 97^{3}\cdot 16361^{4} \)	18T837	Trivial (GRH)