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 62)

Label	Polynomial	Discriminant	Galois group	Class group
18.2.480777589267694482681.1	x^18 - x^16 - 4x^15 + 10x^14 - 4x^13 - 8x^12 + 12x^11 - 20x^10 + 68x^9 - 155x^8 + 229x^7 - 264x^6 + 251x^5 - 189x^4 + 104x^3 - 39x^2 + 9x - 1	\( 23^{6}\cdot 59^{3}\cdot 251^{3} \)	18T885	Trivial
18.2.491768613745854528329.1	x^18 - 2x^17 + 2x^16 - 2x^15 - 5x^13 + 8x^12 - 12x^9 + 12x^8 - 6x^7 - 2x^6 + 17x^5 + 17x^4 - 35x^3 - 29x^2 - 6x - 1	\( 23^{6}\cdot 43^{3}\cdot 347^{3} \)	18T885	Trivial
18.0.1452394220449307475463.1	x^18 - 4x^17 + 9x^16 - 26x^15 + 47x^14 - 61x^13 + 104x^12 - 104x^11 + 98x^10 - 125x^9 + 69x^8 - 79x^7 + 94x^6 - 35x^5 + 77x^4 - 29x^3 + 22x^2 - 6x + 1	\( -\,23^{8}\cdot 2647^{3} \)	18T885	Trivial
18.4.2315693668589360644096.2	x^18 - 2x^17 - 2x^16 - 4x^15 + 25x^14 - 2x^13 - 27x^12 - 42x^11 + 65x^10 + 42x^9 - 82x^8 + 20x^7 + 34x^6 - 38x^5 + 3x^4 + 16x^3 - 5x^2 - 2x + 1	\( -\,2^{18}\cdot 37^{6}\cdot 151^{3} \)	18T885	Trivial
18.4.2315693668589360644096.3	x^18 - 2x^17 - 2x^16 + 8x^15 - 19x^14 + 18x^13 - 3x^12 - 26x^11 + 49x^10 - 40x^9 - 2x^8 + 72x^7 - 126x^6 + 142x^5 - 121x^4 + 74x^3 - 33x^2 + 10x - 1	\( -\,2^{18}\cdot 37^{6}\cdot 151^{3} \)	18T885	Trivial
18.0.28901118439586460073984.1	x^18 - 2x^17 + 2x^16 - 4x^15 - 16x^14 + 28x^13 + 42x^12 - 56x^11 - 6x^10 - 2x^9 + 54x^8 - 46x^7 + 68x^6 - 62x^5 + 24x^4 - 8x^3 + 4x^2 + 4x + 2	\( -\,2^{22}\cdot 37^{6}\cdot 139^{3} \)	18T885	Trivial
18.2.43369397037232870916096.2	x^18 - 2x^16 - 2x^15 + 3x^14 - 14x^13 - 65x^12 - 32x^11 + 183x^10 + 340x^9 + 168x^8 - 78x^7 - 40x^6 + 82x^5 + 37x^4 - 22x^3 - 5x^2 + 4x - 1	\( 2^{18}\cdot 37^{6}\cdot 401^{3} \)	18T885	Trivial
18.0.115604473758345840295936.1	x^18 - 8x^17 + 33x^16 - 98x^15 + 238x^14 - 474x^13 + 772x^12 - 1050x^11 + 1168x^10 - 1018x^9 + 782x^8 - 654x^7 + 478x^6 - 286x^5 + 224x^4 - 142x^3 + 59x^2 - 30x + 13	\( -\,2^{24}\cdot 37^{6}\cdot 139^{3} \)	18T885	Trivial
18.0.514687157793406972592128.2	x^18 + 7x^16 + 19x^14 + 13x^12 - 22x^10 - 11x^8 + 396x^6 + 1109x^4 + 1804x^2 + 1303	\( -\,2^{18}\cdot 31^{6}\cdot 1303^{3} \)	18T885	Trivial
18.6.2775641410382903738630144.1	x^18 + 7x^16 + 7x^14 + 14x^12 + 290x^10 + 109x^8 - 1413x^6 - 369x^4 + 1604x^2 - 401	\( 2^{24}\cdot 37^{6}\cdot 401^{3} \)	18T885	Trivial
18.6.2775641410382903738630144.2	x^18 - 5x^16 - 15x^14 + 82x^12 + 92x^10 - 483x^8 - 385x^6 + 1451x^4 + 502x^2 - 401	\( 2^{24}\cdot 37^{6}\cdot 401^{3} \)	18T885	Trivial
18.4.30582621154749211119190016.1	x^18 - 4x^17 + 9x^16 - 18x^15 + 30x^14 - 34x^13 + 56x^12 - 70x^11 + 64x^10 + 42x^9 + 82x^8 - 510x^7 + 818x^6 - 174x^5 - 1104x^4 + 1886x^3 - 1401x^2 + 426x - 43	\( -\,2^{18}\cdot 101^{6}\cdot 479^{3} \)	18T885	Trivial
18.8.30582621154749211119190016.1	x^18 - 8x^17 + 29x^16 - 80x^15 + 188x^14 - 364x^13 + 626x^12 - 920x^11 + 1158x^10 - 1196x^9 + 972x^8 - 600x^7 - 548x^6 + 1212x^5 - 170x^4 - 176x^3 - 95x^2 - 20x - 1	\( -\,2^{18}\cdot 101^{6}\cdot 479^{3} \)	18T885	$[2]$
18.4.30582621154749211119190016.2	x^18 - 4x^17 + 20x^16 - 30x^15 + 72x^14 - 14x^13 + 80x^12 - 80x^11 + 192x^10 - 628x^9 + 64x^8 + 256x^7 - 2052x^6 + 1936x^5 - 1984x^4 + 848x^3 - 384x^2 + 96x - 8	\( -\,2^{18}\cdot 101^{6}\cdot 479^{3} \)	18T885	Trivial
18.10.59372704543971800284135424.1	x^18 - 10x^16 - 6x^15 + 23x^14 + 100x^13 + x^12 - 832x^11 - 401x^10 + 3106x^9 + 1994x^8 - 5666x^7 - 3266x^6 + 7628x^5 + 5609x^4 - 3800x^3 - 4543x^2 - 1182x - 59	\( 2^{18}\cdot 37^{8}\cdot 401^{3} \)	18T885	Trivial (GRH)
18.2.59372704543971800284135424.1	x^18 - 2x^17 + 17x^16 - 36x^15 + 137x^14 - 186x^13 + 520x^12 - 152x^11 + 856x^10 + 1448x^9 + 731x^8 + 4914x^7 + 2609x^6 + 6010x^5 + 7771x^4 + 4498x^3 + 6252x^2 + 6198x + 691	\( 2^{18}\cdot 37^{8}\cdot 401^{3} \)	18T885	$[2]$
18.10.59372704543971800284135424.2	x^18 - 6x^17 + 8x^16 - 8x^15 + 31x^14 + 40x^13 - 143x^12 + 4x^11 - 261x^10 + 96x^9 + 1124x^8 + 130x^7 - 682x^6 - 1392x^5 - 573x^4 + 1696x^3 + 409x^2 - 600x + 23	\( 2^{18}\cdot 37^{8}\cdot 401^{3} \)	18T885	Trivial (GRH)
18.6.68697349292420119212064768.1	x^18 - 10x^16 + 41x^14 - 280x^12 + 2697x^10 - 13580x^8 + 33294x^6 - 40319x^4 + 26772x^2 - 12097	\( 2^{18}\cdot 23^{6}\cdot 12097^{3} \)	18T885	$[2]$ (GRH)
18.6.68697349292420119212064768.2	x^18 - 23x^16 + 239x^14 - 1505x^12 + 6320x^10 - 18318x^8 + 36493x^6 - 47757x^4 + 36480x^2 - 12097	\( 2^{18}\cdot 23^{6}\cdot 12097^{3} \)	18T885	$[2]$ (GRH)
18.6.177641050264505839272329216.1	x^18 - 9x^16 + 3x^14 + 130x^12 - 134x^10 - 619x^8 + 635x^6 + 1059x^4 - 802x^2 - 401	\( 2^{30}\cdot 37^{6}\cdot 401^{3} \)	18T885	Trivial (GRH)
18.6.177641050264505839272329216.2	x^18 - 2x^16 - 31x^14 + 127x^12 - 241x^10 + 556x^8 - 1034x^6 + 625x^4 + 401x^2 - 401	\( 2^{30}\cdot 37^{6}\cdot 401^{3} \)	18T885	Trivial (GRH)
18.2.408062656723324082449547264.1	x^18 - 2x^17 - 3x^16 - 10x^15 + 57x^14 - 14x^13 + 132x^12 - 736x^11 + 890x^10 - 1152x^9 + 3863x^8 - 8862x^7 + 12963x^6 - 13228x^5 + 16349x^4 - 10216x^3 - 11006x^2 + 2250x - 11393	\( 2^{18}\cdot 37^{6}\cdot 97^{2}\cdot 401^{3} \)	18T885	$[2]$
18.0.1957287753903949511628161024.1	x^18 + 30x^16 + 369x^14 + 2409x^12 + 9023x^10 + 19476x^8 + 22738x^6 + 11827x^4 + 1437x^2 + 479	\( -\,2^{24}\cdot 101^{6}\cdot 479^{3} \)	18T885	Trivial
18.8.1957287753903949511628161024.1	x^18 - x^16 - 12x^15 - 63x^14 + 48x^13 + 108x^12 + 668x^11 + 424x^10 - 1266x^9 - 4047x^8 - 3730x^7 + 5305x^6 + 14436x^5 + 5267x^4 - 8974x^3 - 11294x^2 - 4676x - 653	\( -\,2^{24}\cdot 101^{6}\cdot 479^{3} \)	18T885	Trivial (GRH)
18.10.2945640892745755719979237376.1	x^18 - 4x^17 - 13x^16 + 56x^15 + 20x^14 - 176x^13 + 180x^12 - 92x^11 + 86x^10 - 404x^9 + 6x^8 + 2268x^7 - 6676x^6 + 10396x^5 - 7732x^4 + 2784x^3 - 1807x^2 + 1524x - 409	\( 2^{18}\cdot 37^{6}\cdot 16361^{3} \)	18T885	$[2]$ (GRH)
18.14.2945640892745755719979237376.1	x^18 - 17x^16 - 32x^15 + 60x^14 + 286x^13 + 72x^12 - 916x^11 - 530x^10 + 1658x^9 + 698x^8 - 2244x^7 - 608x^6 + 1886x^5 + 628x^4 - 568x^3 - 211x^2 + 50x + 19	\( 2^{18}\cdot 37^{6}\cdot 16361^{3} \)	18T885	Trivial (GRH)
18.10.2945640892745755719979237376.2	x^18 - 2x^17 - 13x^16 + 2x^15 + 16x^14 + 14x^13 + 390x^12 + 1226x^11 + 1742x^10 + 2182x^9 + 2980x^8 + 1910x^7 - 1216x^6 - 2006x^5 - 134x^4 + 494x^3 + 25x^2 - 36x + 1	\( 2^{18}\cdot 37^{6}\cdot 16361^{3} \)	18T885	$[2]$ (GRH)
18.6.2945640892745755719979237376.2	x^18 - 6x^17 + 14x^16 - 20x^15 + 33x^14 + 4x^13 - 185x^12 + 22x^11 + 367x^10 + 952x^9 - 592x^8 - 2594x^7 - 2332x^6 - 678x^5 + 1625x^4 + 768x^3 + 845x^2 + 1098x + 311	\( 2^{18}\cdot 37^{6}\cdot 16361^{3} \)	18T885	Trivial
18.6.2945640892745755719979237376.3	x^18 - 6x^17 + 16x^16 - 28x^15 + 22x^14 + 68x^13 - 346x^12 + 820x^11 - 1248x^10 + 1348x^9 - 984x^8 + 200x^7 + 1040x^6 - 904x^5 + 680x^4 - 136x^3 - 968x^2 - 8x + 344	\( 2^{18}\cdot 37^{6}\cdot 16361^{3} \)	18T885	Trivial (GRH)
18.8.4874583099993698478544646144.1	x^18 - x^17 - 18x^16 + 12x^15 + 103x^14 + 43x^13 - 276x^12 - 1015x^11 + 1480x^10 + 2701x^9 - 2364x^8 - 7385x^7 + 4290x^6 + 7797x^5 - 2795x^4 - 2864x^3 + 264x^2 + 65x - 1	\( -\,2^{12}\cdot 101^{8}\cdot 479^{3} \)	18T885	$[2]$ (GRH)
18.8.4874583099993698478544646144.2	x^18 - x^17 - 18x^16 + 28x^15 + 87x^14 - 247x^13 + 116x^12 + 709x^11 - 1798x^10 + 421x^9 + 3328x^8 - 4625x^7 + 2010x^6 + 3945x^5 - 6903x^4 + 4600x^3 - 1828x^2 - 4901x + 4093	\( -\,2^{12}\cdot 101^{8}\cdot 479^{3} \)	18T885	Trivial (GRH)
18.12.12830795695275304514614198272.1	x^18 - 12x^16 + 59x^14 - 156x^12 + 244x^10 - 220x^8 + 71x^6 + 54x^4 - 48x^2 + 8	\( -\,2^{39}\cdot 3^{4}\cdot 257^{6} \)	18T885	Trivial (GRH)
18.12.115477161257477740631527784448.1	x^18 - 11x^16 + 46x^14 - 93x^12 + 104x^10 - 70x^8 - 72x^6 + 312x^4 - 288x^2 + 72	\( -\,2^{39}\cdot 3^{6}\cdot 257^{6} \)	18T885	Trivial (GRH)
18.4.115477161257477740631527784448.1	x^18 + 13x^16 + 52x^14 + 27x^12 - 340x^10 - 1194x^8 - 1888x^6 - 1136x^4 - 96x^2 + 72	\( -\,2^{39}\cdot 3^{6}\cdot 257^{6} \)	18T885	Trivial (GRH)
18.4.115477161257477740631527784448.2	x^18 + 24x^16 + 224x^14 + 968x^12 + 1424x^10 - 3168x^8 - 14016x^6 - 15104x^4 - 768x^2 + 4608	\( -\,2^{39}\cdot 3^{6}\cdot 257^{6} \)	18T885	Trivial (GRH)
18.0.125266416249852768744202305536.1	x^18 + 16x^16 + 57x^14 + 253x^12 + 1991x^10 + 6914x^8 + 11072x^6 + 8805x^4 + 3353x^2 + 479	\( -\,2^{30}\cdot 101^{6}\cdot 479^{3} \)	18T885	Trivial (GRH)
18.12.125266416249852768744202305536.1	x^18 - 9x^16 - 9x^14 + 256x^12 - 316x^10 - 2161x^8 + 5179x^6 - 1485x^4 - 1228x^2 + 479	\( -\,2^{30}\cdot 101^{6}\cdot 479^{3} \)	18T885	Trivial (GRH)
18.4.125266416249852768744202305536.1	x^18 + 25x^16 + 246x^14 + 1234x^12 + 3312x^10 + 4196x^8 + 398x^6 - 4326x^4 - 2741x^2 + 479	\( -\,2^{30}\cdot 101^{6}\cdot 479^{3} \)	18T885	Trivial (GRH)
18.8.125266416249852768744202305536.1	x^18 + 10x^16 - 33x^14 - 845x^12 - 263x^10 + 2876x^8 + 800x^6 - 2445x^4 - 173x^2 + 479	\( -\,2^{30}\cdot 101^{6}\cdot 479^{3} \)	18T885	Trivial (GRH)
18.8.125266416249852768744202305536.2	x^18 - 7x^16 - 5x^14 + 58x^12 + 46x^10 + 367x^8 - 647x^6 - 1197x^4 + 958x^2 + 479	\( -\,2^{30}\cdot 101^{6}\cdot 479^{3} \)	18T885	Trivial (GRH)
18.10.188521017135728366078671192064.1	x^18 - 28x^16 + 171x^14 + 989x^12 - 7481x^10 - 18602x^8 + 24388x^6 + 32901x^4 - 16361x^2 - 16361	\( 2^{24}\cdot 37^{6}\cdot 16361^{3} \)	18T885	Trivial (GRH)
18.14.188521017135728366078671192064.1	x^18 - 2x^17 - 27x^16 + 18x^15 + 279x^14 + 88x^13 - 1730x^12 - 2022x^11 + 8226x^10 + 14928x^9 - 23191x^8 - 56106x^7 + 15241x^6 + 85522x^5 + 31331x^4 - 31112x^3 - 22396x^2 - 3034x + 313	\( 2^{24}\cdot 37^{6}\cdot 16361^{3} \)	18T885	$[2]$ (GRH)
18.10.188521017135728366078671192064.2	x^18 - 6x^17 - 4x^16 + 60x^15 - 71x^14 + 110x^13 - 99x^12 - 226x^11 + 257x^10 - 2162x^9 + 3376x^8 - 986x^7 - 2972x^6 + 10206x^5 - 6397x^4 + 1468x^3 + 2991x^2 - 3162x - 961	\( 2^{24}\cdot 37^{6}\cdot 16361^{3} \)	18T885	Trivial (GRH)
18.2.243190597812108493963818696704.1	x^18 + 25x^16 + 205x^14 + 350x^12 - 3352x^10 - 12929x^8 + 27233x^6 + 152625x^4 - 70818x^2 - 548969	\( 2^{30}\cdot 37^{8}\cdot 401^{3} \)	18T885	$[2, 2]$ (GRH)
18.6.243190597812108493963818696704.1	x^18 - 29x^16 + 303x^14 - 892x^12 - 8444x^10 + 90365x^8 - 344615x^6 + 510119x^4 + 89022x^2 - 548969	\( 2^{30}\cdot 37^{8}\cdot 401^{3} \)	18T885	Trivial (GRH)
18.6.243190597812108493963818696704.2	x^18 + 36x^16 + 495x^14 + 2729x^12 + 577x^10 - 44084x^8 - 79110x^6 + 218855x^4 + 334073x^2 - 548969	\( 2^{30}\cdot 37^{8}\cdot 401^{3} \)	18T885	$[2]$ (GRH)
18.4.287751882445035327420458860544.1	x^18 + 17x^16 - 64x^15 + 83x^14 - 614x^13 - 136x^12 - 1682x^11 + 346x^10 + 898x^9 + 4897x^8 + 4488x^7 + 5075x^6 + 12286x^5 + 341x^4 - 5774x^3 - 5006x^2 + 6202x - 1811	\( -\,2^{18}\cdot 97^{2}\cdot 101^{6}\cdot 479^{3} \)	18T885	$[2]$ (GRH)
18.8.287751882445035327420458860544.1	x^18 - 2x^17 - 20x^16 + 122x^15 - 341x^14 + 306x^13 + 1365x^12 - 7340x^11 + 21481x^10 - 43444x^9 + 64290x^8 - 62292x^7 + 8410x^6 + 71812x^5 - 130595x^4 + 106800x^3 + 37555x^2 - 86446x + 19177	\( -\,2^{18}\cdot 97^{2}\cdot 101^{6}\cdot 479^{3} \)	18T885	$[2]$ (GRH)
18.2.12065345096686615429034956292096.1	x^18 + 55x^16 + 1243x^14 + 14896x^12 + 101720x^10 + 392939x^8 + 781309x^6 + 566197x^4 - 130888x^2 - 16361	\( 2^{30}\cdot 37^{6}\cdot 16361^{3} \)	18T885	$[2]$ (GRH)
18.6.12065345096686615429034956292096.1	x^18 + 4x^16 - 185x^14 - 871x^12 + 8447x^10 + 45580x^8 - 28944x^6 - 226899x^4 - 185053x^2 - 16361	\( 2^{30}\cdot 37^{6}\cdot 16361^{3} \)	18T885	$[2]$ (GRH)