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 2501)

Label	Polynomial	Discriminant	Galois group	Class group
20.8.381390155774156971417921.1	x^20 - 3x^19 - x^18 + 10x^17 - 7x^16 - 7x^15 + 31x^14 - 30x^13 - 75x^12 + 104x^11 + 88x^10 - 139x^9 - 15x^8 + 81x^7 - 63x^6 - 18x^5 + 56x^4 + 2x^3 - 16x^2 - x + 1	\( 11^{16}\cdot 43^{2}\cdot 67^{2} \)	20T341	Trivial (GRH)
20.8.444622235903180809437184.1	x^20 - 4x^18 - 10x^17 - 3x^16 + 8x^15 + 48x^14 + 38x^13 + 48x^12 + 26x^11 - 20x^10 + 20x^9 - 53x^8 - 64x^7 - 14x^6 + 14x^5 + 51x^4 + 4x^3 - 18x^2 + 1	\( 2^{30}\cdot 13^{4}\cdot 347^{4} \)	20T669	Trivial (GRH)
20.8.444622235903180809437184.2	x^20 - 2x^19 - 6x^18 + 10x^17 + x^16 - 12x^15 + 48x^14 - 4x^13 - 2x^12 + 8x^11 - 116x^10 + 8x^9 - 2x^8 - 4x^7 + 48x^6 - 12x^5 + x^4 + 10x^3 - 6x^2 - 2x + 1	\( 2^{30}\cdot 13^{4}\cdot 347^{4} \)	20T669	Trivial (GRH)
20.8.487396615698744004253529.1	x^20 - 2x^19 - 3x^18 - x^17 + 28x^16 - 3x^15 - 102x^14 + 56x^13 + 145x^12 - 48x^11 - 143x^10 - 48x^9 + 145x^8 + 56x^7 - 102x^6 - 3x^5 + 28x^4 - x^3 - 3x^2 - 2x + 1	\( 3^{6}\cdot 401^{8} \)	$C_2\times C_2^4:D_5$ (as 20T85)	Trivial (GRH)
20.8.882316447948636312484929.1	x^20 - 4x^19 + 6x^18 - 4x^17 - 9x^16 + 35x^15 - 49x^14 + 25x^13 + 31x^12 - 93x^11 + 108x^10 - 17x^9 - 39x^8 + 9x^7 - 11x^6 + 8x^5 - 69x^4 + 80x^3 - 4x^2 - 4x - 1	\( 7^{6}\cdot 43^{4}\cdot 1217^{4} \)	20T994	Trivial (GRH)
20.8.1076309151404899342122481.1	x^20 - 10x^18 - x^17 + 37x^16 + 11x^15 - 49x^14 - x^13 - 26x^12 - 121x^11 + 145x^10 + 314x^9 - 151x^8 - 350x^7 + 55x^6 + 193x^5 + 3x^4 - 51x^3 - 6x^2 + 5x + 1	\( 29^{2}\cdot 61^{6}\cdot 397^{4} \)	20T799	Trivial (GRH)
20.8.1208667589881678916015625.1	x^20 - 8x^18 - 5x^17 + 24x^16 + 14x^15 - 54x^14 - 7x^13 + 138x^12 + 57x^11 - 201x^10 - 171x^9 + 159x^8 + 207x^7 - 95x^6 - 166x^5 + 24x^4 + 77x^3 + 14x^2 - 6x - 1	\( 5^{10}\cdot 109\cdot 149\cdot 2760559^{2} \)	20T1045	Trivial (GRH)
20.8.1555892820924979549874521.1	x^20 - 5x^19 + 6x^18 + 10x^17 - 43x^16 + 58x^15 + 65x^14 - 261x^13 + 4x^12 + 418x^11 - 21x^10 - 308x^9 - 85x^8 + 73x^7 + 51x^6 + 63x^5 + 25x^4 - 24x^3 - 25x^2 - 2x + 1	\( 11^{18}\cdot 23^{4} \)	$C_2\times C_2^4:C_5$ (as 20T41)	Trivial
20.8.1555892820924979549874521.2	x^20 - x^19 - 11x^18 + 12x^17 + 43x^16 - 44x^15 - 76x^14 + 65x^13 + 66x^12 - 32x^11 - 45x^10 - 32x^9 + 66x^8 + 65x^7 - 76x^6 - 44x^5 + 43x^4 + 12x^3 - 11x^2 - x + 1	\( 11^{18}\cdot 23^{4} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	Trivial (GRH)
20.8.1555892820924979549874521.3	x^20 - 5x^19 + 11x^18 - 7x^17 - 31x^16 + 121x^15 - 226x^14 + 239x^13 - 55x^12 - 277x^11 + 527x^10 - 490x^9 + 231x^8 + 7x^7 - 79x^6 + 66x^5 - 60x^4 + 25x^3 + 11x^2 - 9x + 1	\( 11^{18}\cdot 23^{4} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	Trivial (GRH)
20.8.1734361690558178085830656.1	x^20 - 4x^19 - 2x^18 + 30x^17 - 29x^16 - 88x^15 + 222x^14 - 70x^13 - 398x^12 + 668x^11 - 300x^10 - 382x^9 + 684x^8 - 460x^7 + 166x^6 - 78x^5 + 29x^4 + 44x^3 - 30x^2 - 8x + 1	\( 2^{20}\cdot 31^{4}\cdot 53^{4}\cdot 61^{3} \)	20T791	Trivial (GRH)
20.8.1860495326773308902342656.1	x^20 - 4x^18 - 2x^17 + x^16 + 28x^15 - 23x^14 - 32x^13 + 46x^12 - 54x^11 + 112x^10 - 72x^9 - 68x^8 + 94x^7 - 27x^6 + 26x^5 - 45x^4 + 18x^3 + 7x^2 - 6x + 1	\( 2^{20}\cdot 36497^{4} \)	20T994	Trivial (GRH)
20.8.2060764600365471574508544.1	x^20 - 5x^18 + 4x^16 + 14x^14 - 33x^12 - 3x^10 + 65x^8 - 14x^6 - 43x^4 + 4x^2 + 1	\( 2^{10}\cdot 3^{4}\cdot 17^{4}\cdot 4153^{4} \)	20T964	Trivial (GRH)
20.8.2320349626175642005405696.1	x^20 - 10x^19 + 45x^18 - 120x^17 + 209x^16 - 244x^15 + 182x^14 - 64x^13 - 38x^12 + 124x^11 - 222x^10 + 268x^9 - 171x^8 - 22x^7 + 137x^6 - 100x^5 + 13x^4 + 24x^3 - 12x^2 + 1	\( 2^{20}\cdot 38569^{4} \)	20T994	Trivial (GRH)
20.8.2721578286903708118793449.1	x^20 - 7x^18 + 15x^16 - 8x^14 - 47x^12 + 154x^10 - 239x^8 + 208x^6 - 77x^4 - 2x^2 + 1	\( 29^{2}\cdot 61^{4}\cdot 97^{2}\cdot 397^{4} \)	20T799	Trivial (GRH)
20.8.2732857610451081915433984.1	x^20 + 8x^18 + 23x^16 + 23x^14 - 24x^12 - 73x^10 - 28x^8 + 53x^6 + 27x^4 - 12x^2 + 1	\( 2^{10}\cdot 11^{16}\cdot 241^{2} \)	20T751	Trivial (GRH)
20.8.3919569348575304934929089.1	x^20 - 3x^19 - 4x^18 + 18x^17 + 9x^16 - 52x^15 - 27x^14 + 97x^13 + 71x^12 - 99x^11 - 131x^10 + 44x^9 + 108x^8 + 17x^7 - 14x^6 - 36x^5 - 18x^4 + 16x^3 + 10x^2 - 7x + 1	\( 11^{18}\cdot 89^{3} \)	20T432	Trivial (GRH)
20.8.4085400993762722886713344.1	x^20 - 5x^18 - 2x^17 + 21x^16 - 42x^14 - 30x^13 + 10x^12 + 40x^11 + 30x^10 + 66x^9 + 33x^8 - 58x^7 - 27x^6 + 2x^5 + 9x^4 + 16x^3 + 2x^2 - 4x - 1	\( 2^{20}\cdot 13^{4}\cdot 97^{2}\cdot 347^{4} \)	20T964	Trivial (GRH)
20.8.4226880044572534053535744.1	x^20 - 4x^19 - 4x^18 + 32x^17 - 13x^16 - 86x^15 + 66x^14 + 156x^13 - 181x^12 - 144x^11 + 266x^10 + 38x^9 - 198x^8 - 16x^7 + 92x^6 + 46x^5 - 34x^4 - 30x^3 + 8x^2 + 8x + 1	\( 2^{30}\cdot 89^{8} \)	20T555	Trivial (GRH)
20.8.4391182420642244613154093.1	x^20 - 10x^18 - 2x^17 + 36x^16 - 91x^14 + 5x^13 + 221x^12 + 163x^11 - 156x^10 - 264x^9 - 62x^8 + 22x^7 - 69x^6 - 26x^5 + 47x^4 + 2x^3 - 7x^2 + 10x - 1	\( 13^{13}\cdot 347^{4} \)	20T369	Trivial (GRH)
20.8.4902190169190997617688501.1	x^20 - 5x^19 + 8x^18 - 6x^16 - 34x^15 + 74x^14 + 102x^13 - 547x^12 + 775x^11 - 266x^10 - 574x^9 + 829x^8 - 424x^7 + 2x^6 + 142x^5 - 101x^4 + 22x^3 + 6x^2 - 4x + 1	\( 11^{16}\cdot 197^{2}\cdot 2749 \)	20T846	Trivial (GRH)
20.8.6130984268238865203986432.1	x^20 - 4x^19 + 3x^18 + 16x^17 - 33x^16 + 16x^15 - 6x^14 - 28x^13 + 93x^12 - 128x^11 + 157x^10 - 128x^9 + 93x^8 - 28x^7 - 6x^6 + 16x^5 - 33x^4 + 16x^3 + 3x^2 - 4x + 1	\( 2^{20}\cdot 17\cdot 61^{4}\cdot 397^{4} \)	20T1015	Trivial (GRH)
20.8.6486179365988627137555921.1	x^20 - 7x^19 + 24x^18 - 57x^17 + 109x^16 - 169x^15 + 180x^14 - 117x^13 + 63x^12 - 44x^11 - 32x^10 + 154x^9 - 177x^8 + 78x^7 + 42x^6 - 81x^5 + 35x^4 + 14x^3 - 16x^2 - 2x + 1	\( 11^{16}\cdot 109^{4} \)	$C_2\times C_2^4:C_5$ (as 20T41)	Trivial
20.8.6486179365988627137555921.2	x^20 - 3x^19 - 6x^18 + 19x^17 + 15x^16 - 24x^15 - 77x^14 + 18x^13 + 153x^12 + 37x^11 - 136x^10 - 174x^9 + 100x^8 + 140x^7 + 49x^6 - 99x^5 - 51x^4 + 14x^3 + 19x^2 + 7x - 1	\( 11^{16}\cdot 109^{4} \)	20T254	Trivial (GRH)
20.8.6802209109663753569286129.1	x^20 - x^19 + 8x^17 - 23x^16 + 46x^15 - 74x^14 + 79x^13 - 60x^12 - 6x^11 + 81x^10 - 206x^9 + 260x^8 - 124x^7 + 71x^6 - 108x^5 - 214x^4 + 189x^3 + 77x^2 - 20x + 1	\( 11^{16}\cdot 23^{6} \)	$C_2\times C_2^4:C_5$ (as 20T46)	Trivial (GRH)
20.8.6904360924896058824196096.1	x^20 - 6x^18 + 11x^16 + 8x^14 - 69x^12 + 108x^10 - 49x^8 - 34x^6 + 42x^4 - 12x^2 + 1	\( 2^{40}\cdot 1583^{4} \)	20T638	Trivial (GRH)
20.8.6904360924896058824196096.2	x^20 - 10x^18 + 41x^16 - 106x^14 + 184x^12 - 192x^10 + 91x^8 + 10x^6 - 21x^4 + 2x^2 + 1	\( 2^{40}\cdot 1583^{4} \)	20T638	Trivial (GRH)
20.8.6904360924896058824196096.3	x^20 - 4x^18 + 2x^16 + x^12 + 26x^10 - 40x^8 + 18x^6 - 4x^4 + 1	\( 2^{40}\cdot 1583^{4} \)	20T760	Trivial (GRH)
20.8.10211541282372040816328704.1	x^20 - 2x^18 + 2x^16 - 7x^14 + 8x^12 - 3x^10 + 8x^8 - 7x^6 + 2x^4 - 2x^2 + 1	\( 2^{20}\cdot 7^{4}\cdot 43^{2}\cdot 1217^{4} \)	20T799	Trivial (GRH)
20.8.10527014003350667272569856.1	x^20 - 7x^18 + 16x^16 - 2x^14 - 52x^12 + 100x^10 - 95x^8 + 49x^6 - 2x^4 - 8x^2 + 1	\( 2^{10}\cdot 11^{18}\cdot 43^{2} \)	20T751	Trivial (GRH)
20.8.10751439513964248879333376.1	x^20 - 6x^18 + 18x^16 - 40x^14 + 64x^12 - 64x^10 + 34x^8 - x^6 - 4x^4 - 4x^2 + 1	\( 2^{20}\cdot 53^{4}\cdot 59^{2}\cdot 139^{4} \)	20T994	Trivial (GRH)
20.8.11149939773041205947265625.1	x^20 - 3x^19 - x^18 + 14x^17 - 21x^16 + 20x^15 - 6x^14 - 91x^13 + 224x^12 - 130x^11 - 184x^10 + 330x^9 - 224x^8 + 85x^7 + 27x^6 - 99x^5 + 81x^4 - 13x^3 - 16x^2 + 8x - 1	\( 5^{10}\cdot 97^{2}\cdot 3319^{4} \)	20T760	Trivial (GRH)
20.8.11533713053509947520712704.1	x^20 - x^18 + 9x^16 - 10x^14 + 23x^12 - 26x^10 - 9x^8 + 5x^6 + 14x^4 - 8x^2 + 1	\( 2^{20}\cdot 1483^{2}\cdot 2236369^{2} \)	20T1105	Trivial (GRH)
20.8.11533713053509947520712704.2	x^20 - 3x^18 + x^14 + 5x^12 - 8x^6 + 8x^4 - 6x^2 + 1	\( 2^{20}\cdot 1483^{2}\cdot 2236369^{2} \)	20T1105	Trivial (GRH)
20.8.11611809929883435192549376.1	x^20 - 5x^18 - 4x^17 + 4x^16 + 16x^15 + 16x^14 + 26x^13 - 214x^12 + 146x^11 + 368x^10 - 570x^9 - 103x^8 + 618x^7 - 214x^6 - 304x^5 + 216x^4 + 98x^3 - 69x^2 - 26x + 1	\( 2^{20}\cdot 11^{16}\cdot 241 \)	20T749	Trivial (GRH)
20.8.12109442907327939057025024.1	x^20 - 9x^18 + 34x^16 - 88x^14 + 166x^12 - 234x^10 + 250x^8 - 179x^6 + 74x^4 - 15x^2 + 1	\( 2^{20}\cdot 13^{4}\cdot 167^{2}\cdot 347^{4} \)	20T799	Trivial (GRH)
20.8.12164157316311040000000000.1	x^20 - 4x^18 + 2x^16 + 7x^14 + x^12 - 27x^10 + 29x^8 - 4x^6 - 4x^4 - x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 1039^{2}\cdot 1049^{2} \)	20T1030	Trivial (GRH)
20.8.12164157316311040000000000.2	x^20 + x^14 - 17x^12 + 3x^10 + 34x^8 - 41x^6 + 25x^4 - 8x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 1039^{2}\cdot 1049^{2} \)	20T1030	Trivial (GRH)
20.8.13699542148527028116127744.1	x^20 - 4x^19 + 4x^18 + 6x^17 - 10x^16 + 4x^15 - 9x^14 - 14x^13 - 23x^12 + 88x^11 + 8x^10 - 80x^9 - 18x^8 + 52x^7 + 76x^6 - 148x^5 + 82x^4 - 28x^3 + 22x^2 - 12x + 2	\( 2^{38}\cdot 2657^{4} \)	20T1028	Trivial (GRH)
20.8.13928692418928729728745472.1	x^20 - 5x^19 + 9x^18 - 5x^17 - 23x^16 + 102x^15 - 254x^14 + 440x^13 - 517x^12 + 307x^11 + 313x^10 - 1221x^9 + 1967x^8 - 2052x^7 + 1492x^6 - 824x^5 + 399x^4 - 179x^3 + 63x^2 - 13x + 1	\( 2^{24}\cdot 13^{3}\cdot 4409^{4} \)	20T791	Trivial (GRH)
20.8.14880182395101510812616281.1	x^20 - x^19 - 7x^18 + 12x^17 + 19x^16 - 58x^15 - 30x^14 + 152x^13 + 41x^12 - 241x^11 - 49x^10 + 241x^9 + 41x^8 - 152x^7 - 30x^6 + 58x^5 + 19x^4 - 12x^3 - 7x^2 + x + 1	\( 23^{2}\cdot 97\cdot 9497\cdot 13219^{4} \)	20T1015	Trivial (GRH)
20.8.16793894275362398486328125.1	x^20 - 2x^19 - 10x^18 + 14x^17 + 43x^16 - 32x^15 - 102x^14 + 37x^13 + 167x^12 - 18x^11 - 195x^10 - 18x^9 + 167x^8 + 37x^7 - 102x^6 - 32x^5 + 43x^4 + 14x^3 - 10x^2 - 2x + 1	\( 5^{11}\cdot 61^{4}\cdot 397^{4} \)	20T802	Trivial (GRH)
20.8.18546881403289244170576896.1	x^20 - 5x^19 + 8x^18 - 10x^17 + 16x^16 - 4x^15 - x^14 + x^13 - 28x^12 + 24x^11 - 32x^10 + 15x^9 + 27x^8 - 10x^7 - 17x^6 - 38x^5 + 33x^4 + 19x^3 - 16x^2 - x + 1	\( 2^{10}\cdot 3^{6}\cdot 17^{4}\cdot 4153^{4} \)	20T964	Trivial (GRH)
20.8.20749170740660742431640625.1	x^20 - 3x^19 - 2x^18 + 11x^17 - 16x^16 + 15x^15 + 9x^14 - 32x^13 + 63x^12 - 75x^11 + 83x^10 - 75x^9 + 63x^8 - 32x^7 + 9x^6 + 15x^5 - 16x^4 + 11x^3 - 2x^2 - 3x + 1	\( 5^{12}\cdot 419^{2}\cdot 695771^{2} \)	20T1030	Trivial (GRH)
20.8.22313281250000000000000000.1	x^20 - 5x^19 + 10x^18 - 10x^17 + 9x^15 - 15x^14 + 60x^13 - 70x^12 - 15x^11 + 86x^10 - 105x^9 - 5x^8 + 80x^6 + 104x^5 - 80x^4 - 20x^3 - 20x - 4	\( 2^{16}\cdot 5^{23}\cdot 13^{4} \)	20T369	Trivial (GRH)
20.8.22789983804294045004464128.1	x^20 - 2x^19 - 8x^18 + 14x^17 + 15x^16 - 50x^15 - 6x^14 + 90x^13 + x^12 - 44x^11 + 43x^10 + 38x^9 + 8x^8 + 8x^7 + 20x^6 + 20x^5 - 29x^4 - 24x^3 + 11x^2 + 4x - 1	\( 2^{20}\cdot 11^{17}\cdot 43 \)	20T749	Trivial (GRH)
20.8.22958799056697995850416128.1	x^20 - 2x^19 - 2x^18 + 4x^17 - 23x^16 + 8x^15 + 36x^14 - 34x^13 + 13x^12 + 214x^11 + 322x^10 + 14x^9 - 339x^8 - 262x^7 + 2x^6 + 142x^5 + 36x^4 - 46x^3 + 4x^2 + 14x + 1	\( 2^{30}\cdot 37\cdot 4903^{4} \)	20T992	Trivial (GRH)
20.8.22958799056697995850416128.2	x^20 - 6x^19 + 8x^18 + 16x^17 - 31x^16 - 42x^15 + 22x^14 + 286x^13 - 199x^12 - 728x^11 + 844x^10 + 672x^9 - 1215x^8 - 182x^7 + 764x^6 + 22x^5 - 250x^4 - 32x^3 + 36x^2 + 12x + 1	\( 2^{30}\cdot 37\cdot 4903^{4} \)	20T992	Trivial (GRH)
20.8.22993730893173532944527721.1	x^20 - 10x^19 + 33x^18 - 12x^17 - 160x^16 + 260x^15 + 251x^14 - 799x^13 - 123x^12 + 1297x^11 - 52x^10 - 1396x^9 + 42x^8 + 1031x^7 + 58x^6 - 475x^5 - 69x^4 + 110x^3 + 20x^2 - 7x - 1	\( 3^{6}\cdot 61\cdot 11119^{4}\cdot 33829 \)	20T1015	Trivial (GRH)
20.8.24868623129665465017517056.1	x^20 - 7x^16 + 11x^14 + 2x^12 - 33x^10 + 28x^8 + 11x^6 - 13x^4 + 1	\( 2^{10}\cdot 11^{16}\cdot 727^{2} \)	20T751	Trivial (GRH)