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 26 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.159092070597590753323.1	x^18 - 6x^14 - 3x^13 - 3x^12 + 16x^10 + 12x^9 + 16x^8 - 9x^7 - 14x^6 - 18x^5 - 4x^4 + 3x^3 + 6x^2 + 3x + 1	\( -\,23^{6}\cdot 10243^{3} \)	18T779	Trivial
18.2.4893256305960227824373.1	x^18 - 4x^15 - 5x^13 + 8x^12 + 2x^11 + 6x^10 + 6x^9 - 12x^8 + 4x^7 - 19x^6 + 14x^5 - 6x^4 + 13x^3 - x^2 + 2x - 1	\( 23^{6}\cdot 67^{3}\cdot 479^{3} \)	18T779	Trivial (GRH)
18.0.13183222503484789096448.1	x^18 - 6x^17 + 22x^16 - 60x^15 + 138x^14 - 272x^13 + 454x^12 - 666x^11 + 902x^10 - 1124x^9 + 1248x^8 - 1212x^7 + 1010x^6 - 702x^5 + 396x^4 - 172x^3 + 54x^2 - 12x + 2	\( -\,2^{22}\cdot 37^{6}\cdot 107^{3} \)	18T779	Trivial
18.6.43369397037232870916096.1	x^18 - 6x^17 + 15x^16 - 18x^15 + 3x^14 + 26x^13 - 60x^12 + 94x^11 - 96x^10 + 56x^9 - 9x^8 - 96x^7 + 257x^6 - 254x^5 + 67x^4 + 50x^3 - 38x^2 + 10x - 1	\( 2^{18}\cdot 37^{6}\cdot 401^{3} \)	18T779	Trivial (GRH)
18.0.115604473758345840295936.2	x^18 - 8x^17 + 39x^16 - 134x^15 + 364x^14 - 794x^13 + 1444x^12 - 2174x^11 + 2756x^10 - 2884x^9 + 2508x^8 - 1760x^7 + 1004x^6 - 456x^5 + 178x^4 - 60x^3 + 15x^2 - 2x + 1	\( -\,2^{24}\cdot 37^{6}\cdot 139^{3} \)	18T779	Trivial
18.2.254331344722610381338249.1	x^18 - 4x^17 + 5x^16 + 3x^15 - 9x^14 + 22x^13 - 62x^12 - 28x^11 + 432x^10 - 597x^9 - 260x^8 + 1372x^7 - 1186x^6 - 537x^5 + 1524x^4 - 829x^3 - 326x^2 + 565x - 211	\( 23^{8}\cdot 59^{3}\cdot 251^{3} \)	18T779	$[2]$ (GRH)
18.0.514687157793406972592128.3	x^18 + 8x^16 + 46x^14 + 200x^12 + 650x^10 + 1701x^8 + 3498x^6 + 4901x^4 + 3909x^2 + 1303	\( -\,2^{18}\cdot 31^{6}\cdot 1303^{3} \)	18T779	Trivial (GRH)
18.2.927698508499559379439616.1	x^18 - 5x^17 + 16x^16 - 30x^15 + 28x^14 + 14x^13 - 128x^12 + 352x^11 - 663x^10 + 955x^9 - 1204x^8 + 1298x^7 - 1154x^6 + 944x^5 - 632x^4 + 336x^3 - 168x^2 + 40x - 8	\( 2^{12}\cdot 37^{8}\cdot 401^{3} \)	18T779	$[2]$
18.2.2775641410382903738630144.1	x^18 - 4x^17 + 10x^16 - 12x^15 + 5x^14 - 19x^12 + 20x^11 - 79x^10 + 354x^9 - 472x^8 + 944x^7 - 972x^6 + 1714x^5 - 1669x^4 + 1754x^3 - 777x^2 + 1220x - 1019	\( 2^{24}\cdot 37^{6}\cdot 401^{3} \)	18T779	$[2]$ (GRH)
18.4.3774188503911341795967351.1	x^18 - 3x^17 - 2x^16 + 10x^15 + 3x^14 - 8x^13 - 19x^12 + 14x^11 - 14x^10 + 17x^9 + 30x^8 + 28x^7 - 54x^6 - 55x^5 - 8x^4 + 28x^3 + 22x^2 + 10x + 1	\( -\,3^{6}\cdot 107^{6}\cdot 1511^{3} \)	18T779	$[2]$ (GRH)
18.4.11990706065651031116494523.1	x^18 - 9x^17 + 45x^16 - 156x^15 + 404x^14 - 812x^13 + 1279x^12 - 1564x^11 + 1418x^10 - 809x^9 + 11x^8 + 580x^7 - 739x^6 + 552x^5 - 270x^4 + 80x^3 - 8x^2 - 3x + 1	\( -\,7^{2}\cdot 257^{6}\cdot 947^{3} \)	18T779	Trivial (GRH)
18.8.30582621154749211119190016.2	x^18 - 6x^16 - 4x^15 - 31x^14 - 34x^13 + 97x^12 - 20x^11 + 89x^10 + 358x^9 - 794x^8 + 134x^7 + 690x^6 - 1276x^5 + 1219x^4 - 394x^3 - 49x^2 + 22x - 1	\( -\,2^{18}\cdot 101^{6}\cdot 479^{3} \)	18T779	Trivial (GRH)
18.8.30582621154749211119190016.3	x^18 - 8x^17 + 25x^16 - 38x^15 + 35x^14 - 78x^13 + 322x^12 - 848x^11 + 1170x^10 - 76x^9 - 2749x^8 + 5146x^7 - 4737x^6 + 1984x^5 + 595x^4 - 1084x^3 + 300x^2 + 68x - 29	\( -\,2^{18}\cdot 101^{6}\cdot 479^{3} \)	18T779	Trivial (GRH)
18.10.46025638949152433124675584.1	x^18 - 4x^17 - 11x^16 + 57x^15 + 15x^14 - 234x^13 + 70x^12 + 317x^11 + 9x^10 - 327x^9 - 172x^8 + 468x^7 - 218x^6 - 8x^5 + 84x^4 - 32x^3 - 32x^2 + 8x + 8	\( 2^{12}\cdot 37^{6}\cdot 16361^{3} \)	18T779	Trivial (GRH)
18.6.46025638949152433124675584.1	x^18 - 6x^17 + 18x^16 - 41x^15 + 80x^14 - 169x^13 + 320x^12 - 334x^11 - 94x^10 + 1363x^9 - 3313x^8 + 4431x^7 - 3914x^6 + 2253x^5 - 432x^4 - 168x^3 - 177x^2 + 279x - 89	\( 2^{12}\cdot 37^{6}\cdot 16361^{3} \)	18T779	$[2]$ (GRH)
18.10.46025638949152433124675584.2	x^18 - 2x^17 - 7x^16 + 24x^15 - 17x^14 - 52x^13 + 138x^12 - 100x^11 + 86x^10 - 82x^9 - 457x^8 + 748x^7 - 137x^6 - 346x^5 + 781x^4 - 408x^3 - 528x^2 + 158x + 97	\( 2^{12}\cdot 37^{6}\cdot 16361^{3} \)	18T779	Trivial (GRH)
18.6.68697349292420119212064768.3	x^18 - 5x^16 + 31x^14 - 527x^12 + 2934x^10 - 5475x^8 - 2054x^6 + 13113x^4 - 12097	\( 2^{18}\cdot 23^{6}\cdot 12097^{3} \)	18T779	Trivial (GRH)
18.6.68697349292420119212064768.4	x^18 - 8x^16 + x^14 - 65x^12 - 153x^10 + 365x^8 + 37x^6 + 360x^4 + 6998x^2 - 12097	\( 2^{18}\cdot 23^{6}\cdot 12097^{3} \)	18T779	$[2]$ (GRH)
18.6.177641050264505839272329216.3	x^18 + 9x^16 + 27x^14 - 2x^12 - 254x^10 - 625x^8 - 329x^6 + 355x^4 + 888x^2 - 401	\( 2^{30}\cdot 37^{6}\cdot 401^{3} \)	18T779	$[2]$ (GRH)
18.12.1957287753903949511628161024.1	x^18 - 13x^16 + 24x^14 + 208x^12 - 630x^10 - 170x^8 - 528x^6 + 6408x^4 - 6227x^2 + 479	\( -\,2^{24}\cdot 101^{6}\cdot 479^{3} \)	18T779	Trivial (GRH)
18.6.2945640892745755719979237376.4	x^18 - 6x^17 + 11x^16 + 6x^15 - 23x^14 - 90x^13 + 236x^12 + 304x^11 - 1016x^10 - 780x^9 + 2279x^8 + 2720x^7 - 4133x^6 - 3966x^5 + 3065x^4 + 1570x^3 + 872x^2 - 196x - 493	\( 2^{18}\cdot 37^{6}\cdot 16361^{3} \)	18T779	$[2]$ (GRH)
18.12.115477161257477740631527784448.2	x^18 - 23x^16 + 212x^14 - 969x^12 + 2116x^10 - 1210x^8 - 2712x^6 + 3888x^4 - 1008x^2 + 72	\( -\,2^{39}\cdot 3^{6}\cdot 257^{6} \)	18T779	Trivial (GRH)
18.14.188521017135728366078671192064.2	x^18 - 6x^17 - 3x^16 + 92x^15 - 155x^14 - 418x^13 + 1514x^12 + 10x^11 - 5512x^10 + 4838x^9 + 9077x^8 - 14020x^7 - 6115x^6 + 16428x^5 + 589x^4 - 7688x^3 + 644x^2 + 864x + 59	\( 2^{24}\cdot 37^{6}\cdot 16361^{3} \)	18T779	Trivial (GRH)
18.14.188521017135728366078671192064.3	x^18 - 6x^17 - 13x^16 + 124x^15 - 61x^14 - 642x^13 + 1146x^12 - 330x^11 - 3680x^10 + 8454x^9 + 31x^8 - 10742x^7 + 12217x^6 - 5494x^5 + 141x^4 + 700x^3 - 224x^2 + 26x - 1	\( 2^{24}\cdot 37^{6}\cdot 16361^{3} \)	18T779	$[2]$ (GRH)
18.18.12065345096686615429034956292096.1	x^18 - 48x^16 + 873x^14 - 8175x^12 + 43777x^10 - 137970x^8 + 250326x^6 - 242159x^4 + 106935x^2 - 16361	\( 2^{30}\cdot 37^{6}\cdot 16361^{3} \)	18T779	$[2]$ (GRH)
18.18.2939487800594529948360199110656000.1	x^18 - 68x^16 + 1627x^14 - 19505x^12 + 131697x^10 - 516410x^8 + 1146558x^6 - 1326597x^4 + 683179x^2 - 102185	\( 2^{30}\cdot 5^{3}\cdot 37^{6}\cdot 107^{3}\cdot 191^{3} \)	18T779	$[2]$ (GRH)