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 40 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.2.8975765936889758489.1	x^18 - x^17 + 3x^15 - x^14 + x^13 + 7x^12 + 2x^11 + 3x^10 + 11x^9 + 3x^8 + 2x^7 + 7x^6 + x^5 - x^4 + 3x^3 - x + 1	\( 7^{12}\cdot 41^{3}\cdot 97^{2} \)	18T472	Trivial
18.2.21235348679958696913.1	x^18 - 3x^17 + 5x^16 - 6x^15 + 5x^14 + x^13 - 9x^12 + 18x^11 - 26x^10 + 29x^9 - 26x^8 + 18x^7 - 9x^6 + x^5 + 5x^4 - 6x^3 + 5x^2 - 3x + 1	\( 7^{12}\cdot 41^{2}\cdot 97^{3} \)	18T472	Trivial
18.8.3078687716353187161727.1	x^18 - 5x^17 + 4x^16 + 18x^15 - 42x^14 + 40x^13 - 48x^12 + 70x^11 - 69x^10 + 89x^9 - 67x^8 - 96x^7 + 187x^6 - 65x^5 - 54x^4 + 47x^3 - 3x^2 - 7x + 1	\( -\,7^{15}\cdot 41^{3}\cdot 97^{2} \)	18T472	Trivial
18.4.7101528447669869215744.1	x^18 - 4x^16 + 4x^14 + x^12 - 5x^10 + 11x^8 - 8x^6 + 5x^4 - 5x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 1399^{2} \)	18T472	Trivial
18.4.7101528447669869215744.2	x^18 - x^16 + 2x^14 + x^12 - 3x^10 + 2x^8 - x^6 - 4x^4 + x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 1399^{2} \)	18T472	Trivial
18.8.7283724597225833041159.1	x^18 + x^16 - 5x^15 - 13x^14 + 11x^13 - 2x^12 + 41x^11 + 6x^10 - 68x^9 + 53x^8 - 63x^7 + x^6 + 50x^5 - 28x^4 + 24x^3 - 5x^2 - 4x + 1	\( -\,7^{15}\cdot 41^{2}\cdot 97^{3} \)	18T472	Trivial
18.6.15088262539911684020009.1	x^18 - 3x^17 + x^15 + 5x^14 + 17x^13 - 28x^12 - 12x^11 + 6x^10 + 17x^9 - 23x^8 + 13x^7 + 33x^6 - 15x^5 - 24x^4 + 3x^3 + 10x^2 - x - 1	\( 7^{12}\cdot 41^{5}\cdot 97^{2} \)	18T472	Trivial
18.2.24724476901703653513873.1	x^18 - 2x^17 + 5x^16 - 12x^15 + 17x^14 - 27x^13 + 35x^12 - 23x^11 + 8x^10 + 21x^9 - 78x^8 + 130x^7 - 128x^6 + 164x^5 - 101x^4 + 86x^3 - 17x^2 + 5x - 1	\( 7^{12}\cdot 97^{3}\cdot 1399^{2} \)	18T472	Trivial
18.2.24724476901703653513873.2	x^18 - 2x^17 + 3x^16 - 12x^15 + 17x^14 - 11x^13 + 30x^12 - 31x^11 - 20x^10 - 14x^9 + 62x^8 - 30x^7 + 105x^6 - 209x^5 + 172x^4 - 33x^3 - 47x^2 - 9x - 1	\( 7^{12}\cdot 97^{3}\cdot 1399^{2} \)	18T472	Trivial
18.6.36578872938484796669433.1	x^18 - 6x^16 - x^15 + 9x^14 + 18x^13 - x^12 - 60x^11 + 33x^10 + 28x^9 - 66x^8 + 81x^7 - 44x^6 + 3x^5 + 15x^4 - 19x^3 + 6x^2 + 3x - 1	\( 3^{24}\cdot 73^{3}\cdot 577^{2} \)	18T472	Trivial
18.4.57388858189268996325376.1	x^18 + 4x^16 + 10x^14 + 4x^12 - 24x^10 - 23x^8 + 6x^6 + 15x^4 + 7x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T472	Trivial
18.4.124546058324322950578176.1	x^18 + 3x^16 - 7x^12 - 30x^10 - 72x^8 - 47x^6 + 30x^4 + 12x^2 + 1	\( -\,2^{18}\cdot 3^{24}\cdot 1297^{2} \)	18T472	Trivial
18.6.199803395729731379254417.1	x^18 - x^17 - 3x^16 + 7x^15 - 15x^14 - 39x^13 + 38x^12 + 19x^11 - 121x^10 - 27x^9 + 104x^8 + 12x^7 - 62x^6 - 26x^5 + 57x^4 + 74x^3 + 15x^2 - 5x - 1	\( 7^{12}\cdot 41^{2}\cdot 97^{5} \)	18T472	Trivial (GRH)
18.6.289123420349393529839217.1	x^18 - 3x^17 - 3x^16 + 24x^15 - 51x^14 + 69x^13 - 67x^12 + 48x^11 - 24x^10 + 13x^9 - 24x^8 + 48x^7 - 67x^6 + 69x^5 - 51x^4 + 24x^3 - 3x^2 - 3x + 1	\( 3^{24}\cdot 73^{2}\cdot 577^{3} \)	18T472	Trivial
18.12.987629569339089510074691.1	x^18 - 3x^17 - 12x^16 + 46x^15 + 15x^14 - 165x^13 + 11x^12 + 321x^11 - 9x^10 - 405x^9 - 60x^8 + 297x^7 + 126x^6 - 90x^5 - 93x^4 - 10x^3 + 21x^2 + 9x + 1	\( -\,3^{27}\cdot 73^{3}\cdot 577^{2} \)	18T472	Trivial
18.0.2352943185760028849340416.1	x^18 + 6x^16 - 3x^14 - 64x^12 - 75x^10 + 124x^8 + 366x^6 + 377x^4 + 194x^2 + 41	\( -\,2^{18}\cdot 7^{12}\cdot 41^{3}\cdot 97^{2} \)	18T472	$[4]$
18.10.2352943185760028849340416.1	x^18 - 6x^16 - 3x^14 + 64x^12 - 75x^10 - 124x^8 + 366x^6 - 377x^4 + 194x^2 - 41	\( 2^{18}\cdot 7^{12}\cdot 41^{3}\cdot 97^{2} \)	18T472	Trivial (GRH)
18.10.5566719244359092643561472.1	x^18 - 5x^16 + 31x^12 - 54x^10 - 100x^8 + 603x^6 - 886x^4 + 506x^2 - 97	\( 2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{3} \)	18T472	Trivial (GRH)
18.2.6497398218116128597530193.1	x^18 + 7x^16 - x^15 + 21x^14 + 42x^13 - 99x^12 + 364x^11 - 581x^10 + 1146x^9 - 1225x^8 + 1330x^7 - 754x^6 + 371x^5 - 84x^4 + 10x^3 - 1	\( 7^{12}\cdot 97^{3}\cdot 22679^{2} \)	18T472	Trivial
18.6.6497398218116128597530193.1	x^18 + 7x^16 - 8x^15 - 7x^14 - 28x^13 - 253x^12 - 168x^11 - 364x^10 - 639x^9 - 448x^8 - 350x^7 - 348x^6 - 112x^5 - 7x^4 - 32x^3 + 7x^2 + 7x - 1	\( 7^{12}\cdot 97^{3}\cdot 22679^{2} \)	18T472	Trivial
18.6.6497398218116128597530193.2	x^18 + 7x^16 - 13x^15 + 21x^14 - 49x^13 - 8x^12 - 49x^11 - 231x^10 + 310x^9 - 490x^8 + 364x^7 - 607x^6 + 98x^5 - 56x^4 - 164x^3 + 14x^2 + 14x - 1	\( 7^{12}\cdot 97^{3}\cdot 22679^{2} \)	18T472	Trivial
18.12.7806332349433625305658859.1	x^18 - 15x^16 - x^15 + 60x^14 + 48x^13 - 40x^12 - 375x^11 + 87x^10 + 729x^9 - 756x^8 + 336x^7 + 108x^6 - 279x^5 + 108x^4 + 28x^3 - 21x^2 + 1	\( -\,3^{27}\cdot 73^{2}\cdot 577^{3} \)	18T472	Trivial
18.12.10145719923049728269615104.1	x^18 - 3x^16 - 4x^14 - 23x^12 + 79x^10 + 139x^8 - 303x^6 + 135x^4 - 21x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T472	Trivial (GRH)
18.8.10145719923049728269615104.1	x^18 + x^16 - 30x^14 + 75x^12 - 87x^10 + 31x^8 + 40x^6 - 24x^4 - 7x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T472	Trivial (GRH)
18.8.10145719923049728269615104.2	x^18 + 2x^16 - 22x^14 + 19x^12 + 36x^10 - 170x^8 + 173x^6 - 20x^4 - 7x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T472	Trivial (GRH)
18.12.10161075065555921079107584.1	x^18 - 10x^16 + 36x^14 - 48x^12 - 27x^10 + 158x^8 - 180x^6 + 88x^4 - 18x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 52919^{2} \)	18T472	Trivial (GRH)
18.0.161536237646646866899894272.1	x^18 + 12x^16 + 54x^14 + 173x^12 + 681x^10 + 2232x^8 + 4894x^6 + 7221x^4 + 5484x^2 + 1297	\( -\,2^{18}\cdot 3^{24}\cdot 1297^{3} \)	18T472	$[20]$
18.0.2506638307140843254915898467.1	x^18 - 4x^17 + 27x^16 - 60x^15 + 184x^14 - 362x^13 + 1149x^12 - 2823x^11 + 6431x^10 - 8311x^9 + 12191x^8 - 16179x^7 + 72116x^6 - 64228x^5 - 9158x^4 + 235477x^3 + 50634x^2 - 611585x + 912673	\( -\,7^{12}\cdot 1399^{2}\cdot 4523^{3} \)	18T472	$[3]$ (GRH)
18.0.2506638307140843254915898467.2	x^18 - 3x^17 + 13x^16 - 38x^15 + 58x^14 - 100x^13 - 41x^12 + 1255x^11 - 2627x^10 + 6918x^9 - 10699x^8 - 9658x^7 + 36052x^6 - 83059x^5 + 215570x^4 - 28704x^3 - 43068x^2 - 639812x + 912673	\( -\,7^{12}\cdot 1399^{2}\cdot 4523^{3} \)	18T472	$[6]$ (GRH)
18.2.3479981933606056796477980672.1	x^18 + 7x^16 - 28x^14 - 182x^12 + 147x^10 - 2009x^8 - 14847x^6 - 13034x^4 - 3773x^2 - 343	\( 2^{18}\cdot 7^{15}\cdot 52879^{2} \)	18T472	Trivial (GRH)
18.0.9588932067586158538111844352.1	x^18 + 24x^16 + 222x^14 + 1049x^12 + 2799x^10 + 4389x^8 + 4075x^6 + 2187x^4 + 624x^2 + 73	\( -\,2^{18}\cdot 3^{24}\cdot 73^{3}\cdot 577^{2} \)	18T472	$[84]$ (GRH)
18.18.9588932067586158538111844352.1	x^18 - 24x^16 + 222x^14 - 1049x^12 + 2799x^10 - 4389x^8 + 4075x^6 - 2187x^4 + 624x^2 - 73	\( 2^{18}\cdot 3^{24}\cdot 73^{3}\cdot 577^{2} \)	18T472	Trivial (GRH)
18.0.75791969904071417486171701248.1	x^18 + 30x^16 + 357x^14 + 2216x^12 + 7917x^10 + 16836x^8 + 21078x^6 + 14613x^4 + 4866x^2 + 577	\( -\,2^{18}\cdot 3^{24}\cdot 73^{2}\cdot 577^{3} \)	18T472	$[3, 84]$ (GRH)
18.18.75791969904071417486171701248.1	x^18 - 30x^16 + 357x^14 - 2216x^12 + 7917x^10 - 16836x^8 + 21078x^6 - 14613x^4 + 4866x^2 - 577	\( 2^{18}\cdot 3^{24}\cdot 73^{2}\cdot 577^{3} \)	18T472	Trivial (GRH)
18.0.147354494188655680463387247047.1	x^18 + 28x^16 - 31x^15 + 343x^14 - 560x^13 + 2535x^12 - 4606x^11 + 14791x^10 - 17924x^9 + 29428x^8 + 15897x^7 - 50004x^6 + 185423x^5 - 114961x^4 + 122123x^3 + 237580x^2 - 217679x + 451879	\( -\,7^{12}\cdot 97^{3}\cdot 22679^{3} \)	18T472	$[104]$ (GRH)
18.6.331314408493551322443896061952.1	x^18 - 6x^16 + 15x^14 - 28x^12 + 47x^10 - 54x^8 + 52x^6 - 46x^4 + 19x^2 - 13	\( 2^{18}\cdot 7^{12}\cdot 13^{3}\cdot 239^{2}\cdot 853^{2} \)	18T472	Trivial (GRH)
18.14.536495523810946581168977084416.1	x^18 - 12x^16 - 38x^14 + 642x^12 + 1195x^10 - 28537x^8 + 111638x^6 - 195808x^4 + 163791x^2 - 52879	\( 2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T472	Trivial (GRH)
18.14.537713931394153787585294237696.1	x^18 - 26x^16 + 277x^14 - 1739x^12 + 8504x^10 - 34994x^8 + 100505x^6 - 170701x^4 + 150743x^2 - 52919	\( 2^{18}\cdot 7^{12}\cdot 52919^{3} \)	18T472	Trivial (GRH)
18.6.2223111032611629473532068233216.1	x^18 - 28x^16 + 210x^14 + 56x^12 - 27440x^10 + 350105x^8 + 1255282x^6 - 17267649x^4 - 48409305x^2 - 313046839	\( 2^{18}\cdot 7^{15}\cdot 97^{3}\cdot 1399^{2} \)	18T472	Trivial (GRH)
18.0.29902909752142884167850994584247.1	x^18 + 34x^16 - 13x^15 + 567x^14 - 279x^13 + 7100x^12 - 380x^11 + 71045x^10 + 25446x^9 + 522337x^8 + 265934x^7 + 2635061x^6 + 1204439x^5 + 8662708x^4 + 2593860x^3 + 16839843x^2 + 2010611x + 14591569	\( -\,7^{12}\cdot 71^{3}\cdot 113^{3}\cdot 64679^{2} \)	18T472	$[6]$ (GRH)