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
18.0.271903514215160479744.4	x^18 + x^14 + 2x^12 - x^10 + 8x^6 + 10x^4 + 5x^2 + 1	\( -\,2^{18}\cdot 23^{6}\cdot 2647^{2} \)	18T836	Trivial
18.0.271903514215160479744.5	x^18 - 4x^16 + 8x^14 - 8x^12 + x^10 + 6x^8 - 7x^6 + 5x^4 - 2x^2 + 1	\( -\,2^{18}\cdot 23^{6}\cdot 2647^{2} \)	18T836	Trivial
18.0.981486058210060140544.2	x^18 + 7x^16 + 19x^14 + 40x^12 + 90x^10 + 143x^8 + 123x^6 + 55x^4 + 12x^2 + 1	\( -\,2^{24}\cdot 37^{6}\cdot 151^{2} \)	18T836	Trivial
18.4.5678874869175838572544.2	x^18 + 2x^16 - x^14 - 4x^12 - x^10 + 5x^8 + 5x^6 - 3x^4 - 4x^2 + 1	\( -\,2^{18}\cdot 23^{6}\cdot 12097^{2} \)	18T836	Trivial (GRH)
18.0.5678874869175838572544.3	x^18 + 6x^16 + 16x^14 + 25x^12 + 26x^10 + 21x^8 + 9x^6 + 4x^4 + 4x^2 + 1	\( -\,2^{18}\cdot 23^{6}\cdot 12097^{2} \)	18T836	Trivial (GRH)
18.4.5678874869175838572544.3	x^18 - 5x^14 + x^12 + 10x^10 - 5x^6 - x^4 - x^2 + 1	\( -\,2^{18}\cdot 23^{6}\cdot 12097^{2} \)	18T836	Trivial (GRH)
18.0.5678874869175838572544.4	x^18 + 4x^16 + x^14 - 6x^12 + 10x^10 + 21x^8 - 3x^6 - 8x^4 + 4x^2 + 1	\( -\,2^{18}\cdot 23^{6}\cdot 12097^{2} \)	18T836	Trivial (GRH)
18.2.6253780826948691034112.1	x^18 - 6x^16 + 19x^14 - 45x^12 + 84x^10 - 120x^8 + 135x^6 - 117x^4 + 71x^2 - 23	\( 2^{18}\cdot 23^{7}\cdot 2647^{2} \)	18T836	Trivial (GRH)
18.2.6253780826948691034112.2	x^18 - 3x^16 + 6x^14 - 15x^12 + 27x^10 - 47x^8 + 68x^6 - 66x^4 + 51x^2 - 23	\( 2^{18}\cdot 23^{7}\cdot 2647^{2} \)	18T836	Trivial (GRH)
18.4.6921799028386293612544.2	x^18 + x^16 - x^14 + 6x^12 + 10x^10 - 5x^8 - 13x^6 - 3x^4 + 4x^2 + 1	\( -\,2^{24}\cdot 37^{6}\cdot 401^{2} \)	18T836	Trivial (GRH)
18.4.6921799028386293612544.3	x^18 - 5x^14 + 3x^12 - x^10 - 10x^8 + 4x^6 - x^4 - 5x^2 + 1	\( -\,2^{24}\cdot 37^{6}\cdot 401^{2} \)	18T836	Trivial (GRH)
18.0.7885291964701182263296.1	x^18 + 2x^16 - 8x^14 - 4x^12 + 36x^10 + 36x^8 - 4x^4 + 4x^2 + 4	\( -\,2^{28}\cdot 37^{6}\cdot 107^{2} \)	18T836	Trivial
18.2.60269290595878834369589.1	x^18 - 2x^17 - 8x^16 + 12x^15 + 20x^14 + 24x^13 - 49x^12 - 41x^11 - 81x^10 + 165x^9 + 57x^8 + 134x^7 - 150x^6 + 100x^5 - 103x^4 + 271x^3 - 114x^2 + 18x - 1	\( 23^{7}\cdot 43^{5}\cdot 347^{2} \)	18T836	Trivial (GRH)
18.8.75954541386658254041088.1	x^18 - 4x^17 + 2x^16 + 7x^15 - 12x^14 + 12x^13 + 6x^12 - 8x^11 + 10x^10 - x^9 + 10x^8 - 8x^7 + 6x^6 + 12x^5 - 12x^4 + 7x^3 + 2x^2 - 4x + 1	\( -\,2^{12}\cdot 3^{3}\cdot 37^{6}\cdot 16361^{2} \)	18T836	Trivial (GRH)
18.8.75954541386658254041088.2	x^18 - 2x^17 - 9x^16 + 19x^15 + 29x^14 - 55x^13 - 81x^12 + 101x^11 + 145x^10 - 94x^9 - 152x^8 - 13x^7 + 99x^6 + 89x^5 - 33x^4 - 52x^3 + 3x^2 + 7x - 1	\( -\,2^{12}\cdot 3^{3}\cdot 37^{6}\cdot 16361^{2} \)	18T836	Trivial (GRH)
18.2.130614121991044287168512.1	x^18 - 6x^16 + 19x^14 - 39x^12 + 33x^10 + 5x^8 - 64x^6 + 87x^4 - 14x^2 - 23	\( 2^{18}\cdot 23^{7}\cdot 12097^{2} \)	18T836	Trivial (GRH)
18.6.130614121991044287168512.1	x^18 - 2x^16 - x^14 - 4x^12 - 28x^8 - 22x^6 + 15x^4 + 47x^2 - 23	\( 2^{18}\cdot 23^{7}\cdot 12097^{2} \)	18T836	Trivial (GRH)
18.6.130614121991044287168512.2	x^18 - 10x^16 + 44x^14 - 126x^12 + 288x^10 - 507x^8 + 585x^6 - 388x^4 + 135x^2 - 23	\( 2^{18}\cdot 23^{7}\cdot 12097^{2} \)	18T836	Trivial (GRH)
18.0.256106564050292863664128.1	x^18 - 17x^14 + 15x^12 + 71x^10 - 62x^8 - 120x^6 + 79x^4 + 135x^2 + 37	\( -\,2^{24}\cdot 37^{7}\cdot 401^{2} \)	18T836	Trivial
18.0.442995137816722791202816.1	x^18 + 9x^16 + 29x^14 + 36x^12 - 33x^8 - 17x^6 + 5x^4 + 6x^2 + 1	\( -\,2^{30}\cdot 37^{6}\cdot 401^{2} \)	18T836	Trivial
18.4.4086195728400729669369856.2	x^18 + x^16 - 16x^14 - 4x^12 + 42x^10 - 90x^8 - 40x^6 + 28x^4 + 13x^2 + 1	\( -\,2^{24}\cdot 101^{6}\cdot 479^{2} \)	18T836	Trivial (GRH)
18.4.4086195728400729669369856.3	x^18 + 8x^16 - x^14 - 89x^12 - 9x^10 + 326x^8 + 296x^6 + 23x^4 - 17x^2 + 1	\( -\,2^{24}\cdot 101^{6}\cdot 479^{2} \)	18T836	Trivial (GRH)
18.8.4086195728400729669369856.3	x^18 - 9x^16 + 23x^14 + 8x^12 - 102x^10 + 99x^8 + 7x^6 - 21x^4 + 1	\( -\,2^{24}\cdot 101^{6}\cdot 479^{2} \)	18T836	Trivial (GRH)
18.8.4086195728400729669369856.4	x^18 + x^16 - 15x^14 - 26x^12 + 28x^10 + 91x^8 + 71x^6 + 9x^4 - 10x^2 + 1	\( -\,2^{24}\cdot 101^{6}\cdot 479^{2} \)	18T836	Trivial (GRH)
18.10.8858877923209861941690368.2	x^18 - 12x^16 + 66x^14 - 214x^12 + 430x^10 - 524x^8 + 366x^6 - 136x^4 + 26x^2 - 2	\( 2^{35}\cdot 37^{6}\cdot 317^{2} \)	18T836	Trivial (GRH)
18.4.11522585241472304020455424.1	x^18 + 4x^16 - 21x^14 - 81x^12 + 51x^10 + 374x^8 + 400x^6 + 155x^4 + 23x^2 + 1	\( -\,2^{24}\cdot 37^{6}\cdot 16361^{2} \)	18T836	Trivial (GRH)
18.12.11522585241472304020455424.2	x^18 - 6x^16 - 17x^14 + 51x^12 + 43x^10 - 136x^8 + 24x^6 + 57x^4 - 17x^2 + 1	\( -\,2^{24}\cdot 37^{6}\cdot 16361^{2} \)	18T836	Trivial (GRH)
18.12.11522585241472304020455424.3	x^18 - 2x^16 - 15x^14 + 43x^12 + 11x^10 - 108x^8 + 62x^6 + 17x^4 - 11x^2 + 1	\( -\,2^{24}\cdot 37^{6}\cdot 16361^{2} \)	18T836	Trivial (GRH)
18.6.13996497268824222166417408.2	x^18 - 6x^17 + 6x^16 + 36x^15 - 133x^14 + 128x^13 + 373x^12 - 1172x^11 + 721x^10 + 1202x^9 - 2058x^8 + 1872x^7 - 1906x^6 - 750x^5 + 3593x^4 - 1388x^3 - 915x^2 + 498x - 139	\( 2^{18}\cdot 37^{6}\cdot 97^{3}\cdot 151^{2} \)	18T836	Trivial (GRH)
18.6.60512517068990720950403072.1	x^18 - 4x^16 + 18x^12 - 16x^10 - 36x^8 + 24x^6 + 40x^4 - 8	\( 2^{33}\cdot 37^{6}\cdot 1657^{2} \)	18T836	Trivial (GRH)
18.0.225654932797645784457674752.1	x^18 + 18x^16 + 125x^14 + 415x^12 + 631x^10 + 240x^8 - 210x^6 + 237x^4 + 485x^2 + 37	\( -\,2^{24}\cdot 37^{7}\cdot 11903^{2} \)	18T836	Trivial (GRH)
18.0.261516526617646698839670784.1	x^18 + 13x^16 + 65x^14 + 164x^12 + 232x^10 + 203x^8 + 127x^6 + 57x^4 + 14x^2 + 1	\( -\,2^{30}\cdot 101^{6}\cdot 479^{2} \)	18T836	Trivial (GRH)
18.6.299393824390943127278522368.1	x^18 - x^17 - 18x^16 + 26x^15 + 79x^14 - 189x^13 + 132x^12 + 155x^11 - 1526x^10 + 2707x^9 + 1870x^8 - 3311x^7 + 9756x^6 - 19877x^5 - 1493x^4 + 3496x^3 - 1008x^2 + 17157x - 13781	\( 2^{12}\cdot 37^{8}\cdot 97^{3}\cdot 151^{2} \)	18T836	Trivial (GRH)
18.0.737445455454227457309147136.1	x^18 + 17x^16 + 115x^14 + 400x^12 + 776x^10 + 851x^8 + 511x^6 + 157x^4 + 22x^2 + 1	\( -\,2^{30}\cdot 37^{6}\cdot 16361^{2} \)	18T836	$[28]$ (GRH)
18.4.737445455454227457309147136.1	x^18 + 14x^16 + 71x^14 + 165x^12 + 167x^10 + 26x^8 - 64x^6 - 33x^4 - x^2 + 1	\( -\,2^{30}\cdot 37^{6}\cdot 16361^{2} \)	18T836	Trivial (GRH)
18.10.771303956649573781864448000.1	x^18 - 20x^16 + 174x^14 - 857x^12 + 2603x^10 - 4970x^8 + 5803x^6 - 3810x^4 + 1175x^2 - 125	\( 2^{22}\cdot 5^{3}\cdot 101^{2}\cdot 229^{6} \)	18T836	Trivial (GRH)
18.10.12830795695275304514614198272.1	x^18 - 12x^16 + 10x^14 + 90x^12 - 137x^10 - 6x^8 + 123x^6 - 104x^4 + 44x^2 - 8	\( 2^{39}\cdot 3^{4}\cdot 257^{6} \)	18T836	Trivial (GRH)
18.6.12830795695275304514614198272.1	x^18 - 41x^14 - 73x^12 + 248x^10 + 584x^8 + 76x^6 - 228x^4 + 72x^2 - 8	\( 2^{39}\cdot 3^{4}\cdot 257^{6} \)	18T836	Trivial (GRH)
18.14.24702741630550297604362600448.1	x^18 - 22x^16 + 204x^14 - 1040x^12 + 3176x^10 - 5908x^8 + 6468x^6 - 3760x^4 + 888x^2 - 8	\( 2^{33}\cdot 37^{6}\cdot 33479^{2} \)	18T836	Trivial (GRH)
18.6.24702741630550297604362600448.1	x^18 - 2x^16 - 6x^14 + 20x^12 - 36x^10 - 12x^8 + 92x^6 - 48x^2 - 8	\( 2^{33}\cdot 37^{6}\cdot 33479^{2} \)	18T836	Trivial (GRH)
18.0.28766333616426383014730137600.1	x^18 + 18x^16 + 123x^14 + 415x^12 + 763x^10 + 786x^8 + 446x^6 + 133x^4 + 19x^2 + 1	\( -\,2^{30}\cdot 5^{2}\cdot 37^{6}\cdot 107^{2}\cdot 191^{2} \)	18T836	$[72]$ (GRH)
18.10.164318006876410189488454893568.1	x^18 - 18x^16 - 8x^15 + 59x^14 + 194x^13 + 269x^12 - 668x^11 - 1645x^10 - 2406x^9 + 1558x^8 + 6584x^7 + 9918x^6 + 2652x^5 - 7905x^4 - 12080x^3 - 919x^2 + 4422x + 281	\( 2^{18}\cdot 37^{6}\cdot 97^{3}\cdot 16361^{2} \)	18T836	Trivial (GRH)
18.6.164318006876410189488454893568.1	x^18 - 4x^17 + 2x^15 - 23x^14 + 148x^13 - 99x^12 + 330x^11 + 37x^10 - 1594x^9 - 2198x^8 - 7014x^7 + 7264x^6 - 2550x^5 + 41819x^4 + 8272x^3 + 11531x^2 - 82036x - 5287	\( 2^{18}\cdot 37^{6}\cdot 97^{3}\cdot 16361^{2} \)	18T836	Trivial (GRH)
18.10.164318006876410189488454893568.2	x^18 - 28x^16 - 42x^15 + 257x^14 + 732x^13 - 371x^12 - 3174x^11 - 2813x^10 - 1406x^9 - 9552x^8 - 6906x^7 + 42982x^6 + 91268x^5 + 44005x^4 - 59440x^3 - 93513x^2 - 49916x - 9851	\( 2^{18}\cdot 37^{6}\cdot 97^{3}\cdot 16361^{2} \)	18T836	Trivial (GRH)
18.6.164318006876410189488454893568.2	x^18 - 6x^17 + 21x^16 - 22x^15 - 93x^14 + 524x^13 - 1344x^12 + 1690x^11 - 646x^10 - 5414x^9 + 17589x^8 - 46942x^7 + 96229x^6 - 128632x^5 + 136629x^4 - 5648x^3 + 77926x^2 + 148922x - 161657	\( 2^{18}\cdot 37^{6}\cdot 97^{3}\cdot 16361^{2} \)	18T836	Trivial (GRH)
18.6.928747553864454763844078927872.1	x^18 + 13x^16 - 42x^15 - 347x^14 - 582x^13 - 2124x^12 + 1276x^11 + 22904x^10 + 59282x^9 + 197557x^8 + 464924x^7 + 775763x^6 + 1424964x^5 + 1620523x^4 + 165110x^3 - 1335696x^2 - 1665358x - 1012069	\( 2^{18}\cdot 37^{6}\cdot 97^{5}\cdot 401^{2} \)	18T836	Trivial (GRH)
18.14.1039294451317299665683750060032.1	x^18 - 29x^16 + 272x^14 - 641x^12 - 2916x^10 + 9612x^8 + 16200x^6 - 34308x^4 + 10368x^2 - 648	\( 2^{39}\cdot 3^{8}\cdot 257^{6} \)	18T836	Trivial (GRH)
18.18.248242103929959658245181304471552.1	x^18 - 22x^16 + 203x^14 - 1018x^12 + 3001x^10 - 5237x^8 + 5136x^6 - 2442x^4 + 364x^2 - 8	\( 2^{27}\cdot 7^{6}\cdot 67^{6}\cdot 13183^{2} \)	18T836	Trivial (GRH)
18.10.548274266819953501843032253923328.1	x^18 + 3x^16 - 4x^15 - 657x^14 + 956x^13 - 1352x^12 + 4556x^11 + 120476x^10 - 409872x^9 + 174583x^8 + 1248426x^7 - 3121933x^6 + 2409572x^5 + 1634473x^4 - 5232806x^3 + 2559048x^2 + 1428746x - 77669	\( 2^{18}\cdot 97^{5}\cdot 101^{6}\cdot 479^{2} \)	18T836	Trivial (GRH)
18.14.1546068126700143472896872093581312.1	x^18 - 2x^17 - 70x^16 + 152x^15 + 1572x^14 - 3418x^13 - 13440x^12 + 29956x^11 + 19616x^10 - 81532x^9 + 261960x^8 - 158712x^7 - 825268x^6 + 701608x^5 - 295096x^4 + 415328x^3 + 634520x^2 - 689080x + 34072	\( 2^{18}\cdot 37^{6}\cdot 97^{5}\cdot 16361^{2} \)	18T836	Trivial (GRH)