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 750)

Label	Polynomial	Discriminant	Galois group	Class group
20.6.185812470152989833691136.1	x^20 - 7x^18 - 6x^17 + 14x^16 + 22x^15 - 11x^14 - 8x^13 + 36x^12 + 8x^11 - 33x^10 - 90x^9 - 148x^8 - 68x^7 + 69x^6 + 194x^5 + 211x^4 + 110x^3 + 44x^2 + 14x + 1	\( -\,2^{20}\cdot 191\cdot 5519^{4} \)	20T992	Trivial (GRH)
20.6.301326738635234130859375.1	x^20 - 2x^19 - 7x^18 + 21x^17 + 2x^16 - 71x^15 + 88x^14 + 62x^13 - 251x^12 + 140x^11 + 180x^10 - 135x^9 - 230x^8 + 259x^7 + 7x^6 - 78x^5 - 8x^4 + 24x^3 + x^2 - 5x + 1	\( -\,5^{12}\cdot 1039^{3}\cdot 1049^{2} \)	20T1045	Trivial (GRH)
20.6.766830176824887223713792.1	x^20 - x^19 - 3x^18 + 5x^17 + 4x^16 - 11x^15 - 13x^14 + 21x^13 - 10x^12 - 25x^11 + 21x^10 - 25x^9 - 10x^8 + 21x^7 - 13x^6 - 11x^5 + 4x^4 + 5x^3 - 3x^2 - x + 1	\( -\,2^{16}\cdot 3^{16}\cdot 43^{7} \)	$S_5$ (as 20T30)	Trivial
20.6.1108181030652775972732928.1	x^20 - 3x^18 - 2x^17 - 7x^16 + 18x^15 - 9x^14 + 10x^13 - 5x^12 - 40x^11 + 99x^10 - 150x^9 + 155x^8 - 78x^7 - 34x^6 + 162x^5 - 248x^4 + 192x^3 - 75x^2 + 14x - 1	\( -\,2^{20}\cdot 11^{16}\cdot 23 \)	20T749	Trivial (GRH)
20.6.1180522086783240923185887.1	x^20 - x^19 - 3x^18 + 11x^17 - 5x^16 - 23x^15 + 41x^14 + 21x^13 - 82x^12 + 32x^11 + 123x^10 - 148x^9 - 25x^8 + 156x^7 - 55x^6 - 11x^5 - 8x^4 + 2x^3 + 12x^2 - 7x + 1	\( -\,3^{16}\cdot 223^{7} \)	$S_5$ (as 20T30)	Trivial
20.6.1666352755035916574867251.1	x^20 - 5x^19 + 11x^18 - 19x^17 + 21x^16 - 14x^15 - 4x^14 + 33x^13 - 63x^12 + 88x^11 - 97x^10 + 88x^9 - 63x^8 + 33x^7 - 4x^6 - 14x^5 + 21x^4 - 19x^3 + 11x^2 - 5x + 1	\( -\,11^{16}\cdot 331^{3} \)	20T303	Trivial (GRH)
20.6.1666352755035916574867251.2	x^20 - 6x^19 + 17x^18 - 34x^17 + 52x^16 - 52x^15 + 14x^14 + 52x^13 - 105x^12 + 123x^11 - 123x^10 + 123x^9 - 105x^8 + 52x^7 + 14x^6 - 52x^5 + 52x^4 - 34x^3 + 17x^2 - 6x + 1	\( -\,11^{16}\cdot 331^{3} \)	20T303	Trivial (GRH)
20.6.1667682586167898216778752.1	x^20 - 4x^19 + 2x^18 + 10x^17 - 23x^16 + 32x^15 - 8x^14 - 23x^13 - 33x^12 + 89x^11 - 83x^10 + 41x^9 + 51x^8 - 2x^7 - 88x^6 + 34x^5 - 6x^4 - 16x^3 + 23x^2 + 5x - 1	\( -\,2^{10}\cdot 11^{16}\cdot 23^{2}\cdot 67 \)	20T846	Trivial (GRH)
20.6.1691110832936975699766791.1	x^20 - 10x^19 + 55x^18 - 210x^17 + 612x^16 - 1428x^15 + 2740x^14 - 4390x^13 + 5906x^12 - 6654x^11 + 6177x^10 - 4535x^9 + 2336x^8 - 410x^7 - 677x^6 + 896x^5 - 623x^4 + 283x^3 - 83x^2 + 14x - 1	\( -\,137^{2}\cdot 5639\cdot 11243^{4} \)	20T1015	Trivial (GRH)
20.6.2060764600365471574508544.1	x^20 + 3x^18 + 5x^16 - 8x^14 - 39x^12 - 73x^10 - 22x^8 + 53x^6 + 15x^4 - 7x^2 - 1	\( -\,2^{10}\cdot 3^{4}\cdot 17^{4}\cdot 4153^{4} \)	20T992	Trivial (GRH)
20.6.2060764600365471574508544.2	x^20 - 6x^18 + 15x^16 - 3x^14 - 46x^12 + 49x^10 + 36x^8 - 53x^6 - 5x^4 + 14x^2 - 1	\( -\,2^{10}\cdot 3^{4}\cdot 17^{4}\cdot 4153^{4} \)	20T992	Trivial (GRH)
20.6.2060764600365471574508544.3	x^20 - 2x^18 + 4x^16 + 10x^14 - 18x^12 - 32x^10 - x^8 + 32x^6 + 24x^4 - 1	\( -\,2^{10}\cdot 3^{4}\cdot 17^{4}\cdot 4153^{4} \)	20T992	Trivial (GRH)
20.6.2164573914914857896089168.1	x^20 - x^19 + 2x^18 - 3x^17 - 14x^16 + 41x^15 - 55x^14 - 8x^13 + 123x^12 - 156x^11 + 86x^10 + 70x^9 - 133x^8 + 122x^7 - 56x^6 - 30x^5 + 2x^4 - 34x^3 + x^2 - 4x - 1	\( -\,2^{4}\cdot 53^{5}\cdot 4241^{4} \)	20T992	Trivial (GRH)
20.6.2732857610451081915433984.1	x^20 - 4x^18 - 2x^16 + 31x^14 - 51x^12 + 28x^10 - 12x^8 + 4x^6 + 10x^4 - 5x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 241^{2} \)	20T846	Trivial (GRH)
20.6.2732857610451081915433984.2	x^20 + 6x^18 + 6x^16 - 38x^14 - 105x^12 - 101x^10 - 37x^8 + 10x^6 + 14x^4 + 2x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 241^{2} \)	20T846	Trivial (GRH)
20.6.2732857610451081915433984.3	x^20 + 3x^18 + 7x^16 + 9x^14 - 10x^12 - 9x^10 - 53x^8 - 30x^6 + 45x^4 + 15x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 241^{2} \)	20T846	Trivial (GRH)
20.6.3053557556770074858882467.1	x^20 - 2x^19 - 5x^18 + 9x^17 + 16x^16 - 18x^15 - 39x^14 + 26x^13 + 57x^12 - 31x^11 - 47x^10 + 35x^9 + 14x^8 - 31x^7 + 7x^6 + 16x^5 - 5x^3 - 5x^2 + 1	\( -\,8123\cdot 16493^{2}\cdot 1175561^{2} \)	20T1110	Trivial (GRH)
20.6.4830858228494718956812959.1	x^20 - 3x^19 + 2x^18 + 7x^17 - 8x^16 - 11x^15 + 7x^14 + 48x^13 - 44x^12 - 80x^11 + 125x^10 + 54x^9 - 191x^8 + 36x^7 + 170x^6 - 140x^5 - 8x^4 + 66x^3 - 39x^2 + 10x - 1	\( -\,3^{3}\cdot 43\cdot 163^{2}\cdot 271\cdot 4903^{4} \)	20T1015	Trivial (GRH)
20.6.6719704070016640000000000.1	x^20 - 6x^18 + 12x^16 - 4x^14 - 25x^12 + 57x^10 - 66x^8 + 51x^6 - 26x^4 + 8x^2 - 1	\( -\,2^{16}\cdot 5^{10}\cdot 3240299^{2} \)	20T1045	Trivial (GRH)
20.6.6736516842429754982164739.1	x^20 - x^19 - 3x^18 - 5x^17 - 2x^16 + 10x^15 + 18x^14 + 18x^13 + 2x^12 - 19x^11 - 27x^10 - 19x^9 + 2x^8 + 18x^7 + 18x^6 + 10x^5 - 2x^4 - 5x^3 - 3x^2 - x + 1	\( -\,11\cdot 17^{4}\cdot 157^{2}\cdot 4153^{4} \)	20T1015	Trivial (GRH)
20.6.7372775235505820194045952.1	x^20 - 2x^19 - 5x^18 + 8x^17 + 8x^16 - 8x^14 + 6x^13 - 39x^12 - 40x^11 - 75x^10 + 86x^9 + 147x^8 + 52x^7 + 346x^6 + 180x^5 - 89x^4 + 14x^3 + 26x^2 + 8x + 1	\( -\,2^{20}\cdot 23^{3}\cdot 4903^{4} \)	20T1015	Trivial (GRH)
20.6.8447822482160435379306496.1	x^20 - 6x^19 + 8x^18 + 26x^17 - 104x^16 + 116x^15 + 94x^14 - 476x^13 + 668x^12 - 264x^11 - 608x^10 + 1126x^9 - 715x^8 - 208x^7 + 766x^6 - 582x^5 + 84x^4 + 146x^3 - 94x^2 + 22x - 1	\( -\,2^{30}\cdot 13^{4}\cdot 19\cdot 347^{4} \)	20T992	Trivial (GRH)
20.6.8628532102283831192126464.1	x^20 - 2x^19 - x^18 + x^17 - 8x^16 + 46x^15 - 64x^14 + 75x^13 - 127x^12 + 55x^11 + 46x^10 + 19x^9 + 40x^8 - 175x^7 + 94x^6 + 4x^5 + 15x^4 - 36x^3 + 25x^2 - 8x - 1	\( -\,2^{10}\cdot 13^{6}\cdot 347^{6} \)	20T808	Trivial (GRH)
20.6.8628532102283831192126464.2	x^20 - 11x^18 + 54x^16 - 152x^14 + 264x^12 - 284x^10 + 175x^8 - 39x^6 - 22x^4 + 16x^2 - 1	\( -\,2^{10}\cdot 13^{6}\cdot 347^{6} \)	20T808	Trivial (GRH)
20.6.8628532102283831192126464.3	x^20 - x^18 + 8x^16 - 19x^14 + 57x^12 - 113x^10 + 67x^8 + 47x^6 - 72x^4 + 25x^2 - 1	\( -\,2^{10}\cdot 13^{6}\cdot 347^{6} \)	20T808	Trivial (GRH)
20.6.10086602384511078995362816.1	x^20 - 8x^18 + 29x^16 - 57x^14 + 67x^12 - 42x^10 - 9x^8 + 47x^6 - 43x^4 + 15x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 463^{2} \)	20T846	Trivial (GRH)
20.6.10301685869703920569286656.1	x^20 - 5x^18 + x^16 + 26x^14 - 27x^12 - 31x^10 + 87x^8 - 82x^6 + 23x^4 + 7x^2 - 1	\( -\,2^{28}\cdot 13^{8}\cdot 19^{6} \)	20T991	Trivial (GRH)
20.6.11138046967442830397538304.1	x^20 + 2x^10 - 13x^8 + 19x^6 - 18x^4 + 9x^2 - 1	\( -\,2^{20}\cdot 107^{2}\cdot 5519^{4} \)	20T1015	Trivial (GRH)
20.6.11533713053509947520712704.1	x^20 - x^18 - 2x^14 + 14x^12 - 23x^10 + 9x^8 - 6x^6 + 8x^4 + 2x^2 - 1	\( -\,2^{20}\cdot 1483^{2}\cdot 2236369^{2} \)	20T1110	Trivial (GRH)
20.6.11533713053509947520712704.2	x^20 - 6x^18 + 11x^16 + 7x^14 - 68x^12 + 142x^10 - 158x^8 + 98x^6 - 29x^4 + 2x^2 - 1	\( -\,2^{20}\cdot 1483^{2}\cdot 2236369^{2} \)	20T1110	Trivial (GRH)
20.6.12164157316311040000000000.1	x^20 - 7x^18 + 23x^16 - 58x^14 + 110x^12 - 125x^10 + 63x^8 + 5x^6 - 16x^4 + 6x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 1039^{2}\cdot 1049^{2} \)	20T781	Trivial (GRH)
20.6.12164157316311040000000000.2	x^20 + 2x^18 - 2x^16 - 9x^14 + x^12 + 11x^10 + x^8 - 7x^6 + x^4 + 3x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 1039^{2}\cdot 1049^{2} \)	20T1045	Trivial (GRH)
20.6.12643669953134424130859375.1	x^20 - 4x^19 + 4x^18 + x^17 - 7x^15 - 3x^14 + 13x^13 + 12x^12 + 2x^11 - 48x^10 + 10x^9 + 23x^8 + 22x^7 - 34x^6 + 6x^5 + 2x^4 + 4x^3 - 2x^2 - 2x + 1	\( -\,5^{10}\cdot 1039^{3}\cdot 1049^{3} \)	20T540	Trivial (GRH)
20.6.12643669953134424130859375.2	x^20 - 6x^19 + 17x^18 - 26x^17 - x^16 + 108x^15 - 316x^14 + 596x^13 - 778x^12 + 593x^11 + 141x^10 - 1079x^9 + 1334x^8 - 706x^7 - 89x^6 + 406x^5 - 337x^4 + 144x^3 - 33x^2 - x + 1	\( -\,5^{10}\cdot 1039^{3}\cdot 1049^{3} \)	20T1022	Trivial (GRH)
20.6.12671809176594786122989568.1	x^20 - 2x^19 + 3x^18 - 4x^17 + 3x^16 + 6x^15 - 2x^14 - 6x^13 - 39x^12 - 50x^11 - 11x^10 + 12x^9 - 66x^8 - 124x^7 - 69x^6 + 104x^5 + 315x^4 + 258x^3 + 41x^2 - 18x + 1	\( -\,2^{20}\cdot 11^{16}\cdot 263 \)	20T846	Trivial (GRH)
20.6.12796294836209762099609375.1	x^20 - 2x^19 - 2x^18 + 4x^17 - 7x^16 - 7x^15 + 4x^14 - 6x^13 - 3x^12 + 7x^11 + 8x^10 + 3x^9 - 7x^8 + 16x^7 + 4x^6 - 14x^5 - 3x^4 - 2x^3 + 9x^2 - 5x + 1	\( -\,5^{10}\cdot 61^{3}\cdot 17939^{3} \)	20T540	Trivial (GRH)
20.6.13167225195265942636954624.1	x^20 + x^18 + 3x^16 + 7x^14 - 3x^12 - 4x^10 - 13x^8 - 25x^6 + 7x^4 + 4x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 23^{4} \)	20T749	Trivial (GRH)
20.6.13167225195265942636954624.2	x^20 - 3x^16 - 11x^14 - 3x^12 + 88x^10 - 29x^8 - 143x^6 + 89x^4 + 11x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 23^{4} \)	20T749	Trivial (GRH)
20.6.13167225195265942636954624.3	x^20 - 5x^18 - 6x^16 + 54x^14 - 48x^12 - 44x^10 + 26x^8 + 43x^6 + 6x^4 - 27x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 23^{4} \)	20T749	Trivial (GRH)
20.6.17537157059432067986358272.1	x^20 - 10x^19 + 46x^18 - 128x^17 + 222x^16 - 182x^15 - 183x^14 + 903x^13 - 1724x^12 + 2232x^11 - 2147x^10 + 1501x^9 - 608x^8 - 122x^7 + 474x^6 - 480x^5 + 309x^4 - 142x^3 + 45x^2 - 9x + 1	\( -\,2^{18}\cdot 19^{8}\cdot 83^{5} \)	20T989	Trivial (GRH)
20.6.17655750991471477605209863.1	x^20 - 2x^19 - 4x^18 + 11x^17 + 4x^16 - 32x^15 + 10x^14 + 84x^13 - 138x^12 + 18x^11 + 163x^10 - 146x^9 - 2x^8 + 43x^7 - 5x^6 + x^5 - 8x^4 - x^2 + x + 1	\( -\,11^{16}\cdot 727^{3} \)	20T303	Trivial (GRH)
20.6.17655750991471477605209863.2	x^20 - 5x^19 + 3x^18 + 24x^17 - 54x^16 + 43x^15 - 25x^14 + 40x^13 - 60x^12 + 80x^11 - 93x^10 + 80x^9 - 60x^8 + 40x^7 - 25x^6 + 43x^5 - 54x^4 + 24x^3 + 3x^2 - 5x + 1	\( -\,11^{16}\cdot 727^{3} \)	20T303	Trivial (GRH)
20.6.18546881403289244170576896.1	x^20 - 19x^16 + 19x^12 + 40x^8 - 15x^4 - 9	\( -\,2^{10}\cdot 3^{6}\cdot 17^{4}\cdot 4153^{4} \)	20T807	Trivial (GRH)
20.6.18783695020114406357421875.1	x^20 - 3x^19 + 3x^18 - 10x^17 + 18x^16 - 12x^15 + 27x^14 - 18x^13 + 32x^12 - 59x^11 - 5x^10 - 29x^9 - 66x^8 + 26x^7 - 4x^6 + 15x^5 + 39x^4 + 3x^3 - 15x^2 - 3x + 1	\( -\,5^{10}\cdot 11^{9}\cdot 13^{8} \)	20T547	Trivial (GRH)
20.6.22743500561450963169808384.1	x^20 - 2x^16 - 10x^14 - 14x^12 + 11x^10 + 51x^8 - 13x^6 - x^4 - 6x^2 - 1	\( -\,2^{12}\cdot 19^{8}\cdot 83^{6} \)	20T991	Trivial (GRH)
20.6.24868623129665465017517056.1	x^20 + 4x^18 - 2x^16 - 20x^14 - 18x^12 - 6x^10 + 43x^8 + 84x^6 + 10x^4 - 6x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 727^{2} \)	20T846	Trivial (GRH)
20.6.24868623129665465017517056.2	x^20 + 7x^18 + 8x^16 - 34x^14 - 108x^12 - 112x^10 - 13x^8 + 43x^6 + 14x^4 - 4x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 727^{2} \)	20T846	Trivial (GRH)
20.6.24868623129665465017517056.3	x^20 + x^18 - 9x^16 - 18x^14 + 3x^12 + 35x^10 + 30x^8 - 7x^6 - 24x^4 - 10x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 727^{2} \)	20T846	Trivial (GRH)
20.6.29495477290631717860845248.1	x^20 - 3x^19 + 10x^18 - 5x^17 + 2x^16 + 20x^15 - 22x^14 + 6x^13 - 53x^12 + 43x^11 - 84x^10 + 33x^9 + 70x^8 + 19x^7 + 18x^6 - 55x^5 - 12x^4 + 21x^3 - 3x^2 - 3x + 1	\( -\,2^{6}\cdot 19^{8}\cdot 83^{7} \)	20T674	Trivial (GRH)
20.6.29495477290631717860845248.2	x^20 - 5x^19 + 9x^18 - x^17 - 35x^16 + 114x^15 - 223x^14 + 235x^13 + 68x^12 - 669x^11 + 1137x^10 - 1105x^9 + 755x^8 - 461x^7 + 280x^6 - 126x^5 + 15x^4 + 34x^3 - 28x^2 + 3x + 1	\( -\,2^{6}\cdot 19^{8}\cdot 83^{7} \)	20T674	Trivial (GRH)