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 42 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.2.13934496372519102386176.1	x^20 - 9x^18 + 37x^16 - 91x^14 + 148x^12 - 166x^10 + 129x^8 - 65x^6 + 15x^4 + 3x^2 - 1	\( -\,2^{12}\cdot 67^{4}\cdot 641^{4} \)	20T1106	Trivial (GRH)
20.2.13934496372519102386176.2	x^20 - 2x^18 - 2x^16 + 8x^14 + 3x^12 - 12x^10 - 2x^8 + 9x^6 + 2x^4 - 3x^2 - 1	\( -\,2^{12}\cdot 67^{4}\cdot 641^{4} \)	20T1106	Trivial (GRH)
20.4.58350703559923741242112.1	x^20 - 6x^19 + 14x^18 - 12x^17 - 16x^16 + 82x^15 - 189x^14 + 278x^13 - 236x^12 + 82x^11 - 7x^10 + 76x^9 - 107x^8 + 24x^7 + 7x^6 + 76x^5 - 118x^4 + 60x^3 - 3x^2 - 6x + 1	\( 2^{8}\cdot 67^{5}\cdot 641^{4} \)	20T1106	Trivial (GRH)
20.2.169555245289201560361024.1	x^20 - 4x^19 + 9x^18 - 10x^17 + 5x^16 + 5x^15 - 11x^14 + 14x^13 - 8x^12 - x^11 + 8x^10 - x^9 - 8x^8 + 14x^7 - 11x^6 + 5x^5 + 5x^4 - 10x^3 + 9x^2 - 4x + 1	\( -\,2^{6}\cdot 307^{4}\cdot 739^{4} \)	20T1106	Trivial (GRH)
20.0.558250760924046539346176.1	x^20 - x^19 + 4x^18 + 4x^17 + 13x^16 + 26x^15 + 29x^14 + 7x^13 + 63x^12 + 33x^11 - 40x^10 - 6x^9 + 67x^8 - 62x^7 - 64x^6 + 46x^5 + 53x^4 - 10x^2 - x + 1	\( 2^{8}\cdot 67^{4}\cdot 641^{5} \)	20T1106	Trivial (GRH)
20.4.558250760924046539346176.1	x^20 - 4x^19 - 3x^18 + 27x^17 - 4x^16 - 71x^15 + 12x^14 + 112x^13 - 12x^12 - 133x^11 + 23x^10 + 184x^9 + 39x^8 - 186x^7 - 175x^6 - 12x^5 + 73x^4 + 49x^3 + 10x^2 - 2x - 1	\( 2^{8}\cdot 67^{4}\cdot 641^{5} \)	20T1106	Trivial (GRH)
20.0.655711672286612839497728.1	x^20 - 4x^19 + 12x^18 - 23x^17 + 30x^16 - 37x^15 + 29x^14 - 51x^13 + 60x^12 - 45x^11 + 83x^10 + 24x^9 + 156x^8 + 42x^7 + 57x^6 - 22x^5 + x^4 - 8x^3 + 4x^2 + x + 1	\( 2^{15}\cdot 66883^{4} \)	20T1106	Trivial (GRH)
20.10.43406142794035599452422144.1	x^20 - 8x^18 + 23x^16 - 33x^14 + 25x^12 + 10x^10 - 40x^8 + 21x^6 + x^4 - 1	\( -\,2^{14}\cdot 307^{4}\cdot 739^{4} \)	20T1106	Trivial (GRH)
20.2.43406142794035599452422144.1	x^20 + 11x^18 + 51x^16 + 134x^14 + 226x^12 + 258x^10 + 200x^8 + 104x^6 + 34x^4 + 3x^2 - 1	\( -\,2^{14}\cdot 307^{4}\cdot 739^{4} \)	20T1106	Trivial (GRH)
20.6.43406142794035599452422144.1	x^20 - 2x^18 - 13x^16 + 3x^14 + 36x^12 + x^10 - 43x^8 - 11x^6 + 15x^4 + 3x^2 - 1	\( -\,2^{14}\cdot 307^{4}\cdot 739^{4} \)	20T1106	Trivial (GRH)
20.6.43406142794035599452422144.2	x^20 + x^18 + 2x^16 + 4x^14 - 10x^12 - 8x^10 - 10x^8 - 22x^6 + 8x^4 + 4x^2 - 1	\( -\,2^{14}\cdot 307^{4}\cdot 739^{4} \)	20T1106	Trivial (GRH)
20.4.52053460303784879030834368.1	x^20 - 9x^19 + 29x^18 - 16x^17 - 142x^16 + 364x^15 - 75x^14 - 1050x^13 + 1679x^12 + 65x^11 - 3046x^10 + 3552x^9 - 721x^8 - 2254x^7 + 3032x^6 - 2234x^5 + 1125x^4 - 313x^3 - 26x^2 + 49x - 11	\( 2^{6}\cdot 307^{5}\cdot 739^{4} \)	20T1106	Trivial (GRH)
20.8.52053460303784879030834368.1	x^20 - x^19 - 5x^18 - x^17 + 4x^16 + 12x^15 + x^14 + 31x^13 + 3x^12 - 55x^11 - 38x^10 - 41x^9 + 86x^8 + 175x^7 + 88x^6 - 170x^5 - 112x^4 + 62x^3 + 9x^2 + 5x - 1	\( 2^{6}\cdot 307^{5}\cdot 739^{4} \)	20T1106	Trivial (GRH)
20.8.52053460303784879030834368.2	x^20 - 6x^19 + 15x^18 - 28x^17 + 57x^16 - 92x^15 + 118x^14 - 194x^13 + 192x^12 + 224x^11 - 651x^10 + 414x^9 - 472x^8 + 1340x^7 - 767x^6 - 1308x^5 + 1540x^4 - 84x^3 - 412x^2 + 120x - 8	\( 2^{6}\cdot 307^{5}\cdot 739^{4} \)	20T1106	Trivial (GRH)
20.12.601054799445266025059165593.1	x^20 - 15x^18 - 7x^17 + 90x^16 + 70x^15 - 283x^14 - 261x^13 + 470x^12 + 366x^11 - 373x^10 + 42x^9 + 178x^8 - 404x^7 - 116x^6 + 100x^5 - 55x^4 + 8x^3 + 18x^2 - x - 1	\( 307^{5}\cdot 739^{5} \)	20T1106	Trivial (GRH)
20.10.1991862385339271699798949888.1	x^20 - 4x^18 - 6x^16 - 86x^14 + 107x^12 + 380x^10 - 117x^8 - 436x^6 + 23x^4 + 66x^2 - 7	\( -\,2^{30}\cdot 3^{8}\cdot 7\cdot 2521^{4} \)	20T1106	Trivial (GRH)
20.0.5555986277636556729910034432.1	x^20 + 19x^18 + 138x^16 + 475x^14 + 764x^12 + 420x^10 - 112x^8 + 48x^6 + 448x^4 + 448x^2 + 128	\( 2^{21}\cdot 307^{4}\cdot 739^{4} \)	20T1106	Trivial (GRH)
20.12.8559657447934762371705574592.1	x^20 - 4x^19 - x^18 + 14x^17 - 19x^16 + 112x^15 - 137x^14 - 422x^13 + 655x^12 + 525x^11 - 1159x^10 - 282x^9 + 1997x^8 - 958x^7 - 1929x^6 + 1972x^5 + 59x^4 - 575x^3 + 124x^2 + 37x - 11	\( 2^{6}\cdot 19\cdot 307^{4}\cdot 739^{4}\cdot 2657 \)	20T1106	Trivial (GRH)
20.0.13325685837768929031893598208.1	x^20 + 12x^18 + 54x^16 + 233x^14 + 818x^12 + 1985x^10 + 3832x^8 + 5370x^6 + 4475x^4 + 1886x^2 + 307	\( 2^{14}\cdot 307^{5}\cdot 739^{4} \)	20T1106	Trivial (GRH)
20.4.13325685837768929031893598208.1	x^20 + 5x^18 - 21x^16 - 78x^14 + 82x^12 + 312x^10 - 250x^8 - 1060x^6 - 614x^4 + 307x^2 + 307	\( 2^{14}\cdot 307^{5}\cdot 739^{4} \)	20T1106	Trivial (GRH)
20.8.220780185453929919617462158203125.1	x^20 - 2x^19 - 12x^18 + 41x^17 - 34x^16 - 158x^15 + 469x^14 - 273x^13 - 683x^12 + 2098x^11 - 2036x^10 - 840x^9 + 3590x^8 - 4585x^7 + 3615x^6 - 1870x^5 - 565x^4 + 1455x^3 - 545x^2 - 130x + 85	\( 5^{17}\cdot 11^{4}\cdot 71^{4}\cdot 167^{4} \)	20T1106	Trivial (GRH)
20.6.706496593452575742775878906250000.1	x^20 + 6x^18 - 28x^16 - 256x^14 - 480x^12 - 10x^10 + 511x^8 + 142x^6 - 141x^4 - 25x^2 - 1	\( -\,2^{4}\cdot 5^{16}\cdot 11^{4}\cdot 71^{4}\cdot 167^{4} \)	20T1106	Trivial (GRH)
20.6.706496593452575742775878906250000.2	x^20 - 8x^18 - 12x^17 + 21x^16 + 113x^15 + 39x^14 - 616x^13 - 580x^12 - 49x^11 + 4488x^10 + 8822x^9 - 13873x^8 - 27185x^7 + 64308x^6 + 27027x^5 - 168694x^4 - 22583x^3 + 125829x^2 - 48793x + 4541	\( -\,2^{4}\cdot 5^{16}\cdot 11^{4}\cdot 71^{4}\cdot 167^{4} \)	20T1106	Trivial (GRH)
20.10.3532482967262878713879394531250000.1	x^20 - x^18 - 58x^16 - 37x^14 + 740x^12 + 918x^10 - 1600x^8 - 1545x^6 + 1145x^4 + 500x^2 - 80	\( -\,2^{4}\cdot 5^{17}\cdot 11^{4}\cdot 71^{4}\cdot 167^{4} \)	20T1106	Trivial (GRH)
20.14.3532482967262878713879394531250000.1	x^20 - 6x^19 - 14x^18 + 138x^17 - 30x^16 - 1030x^15 + 707x^14 + 3410x^13 + 2091x^12 - 16890x^11 - 23697x^10 + 103685x^9 - 13247x^8 - 225987x^7 + 206875x^6 + 64934x^5 - 125856x^4 + 1829x^3 + 20366x^2 + 495x - 575	\( -\,2^{4}\cdot 5^{17}\cdot 11^{4}\cdot 71^{4}\cdot 167^{4} \)	20T1106	Trivial (GRH)
20.8.3532482967262878713879394531250000.1	x^20 - 8x^19 + 36x^18 - 99x^17 + 178x^16 - 52x^15 - 789x^14 + 1554x^13 + 1331x^12 - 10275x^11 + 18084x^10 - 13855x^9 + 4749x^8 - 6003x^7 + 9274x^6 - 2853x^5 - 2318x^4 + 1020x^3 + 153x^2 - 53x + 1	\( 2^{4}\cdot 5^{17}\cdot 11^{4}\cdot 71^{4}\cdot 167^{4} \)	20T1106	Trivial (GRH)
20.4.5519504636348247990436553955078125.1	x^20 - 6x^19 + 4x^18 + 4x^17 + 56x^16 - 392x^15 + 2527x^14 - 8793x^13 + 21562x^12 - 44709x^11 + 71626x^10 - 100897x^9 + 115538x^8 - 104897x^7 + 83844x^6 - 36305x^5 + 12251x^4 + 9896x^3 - 12979x^2 + 10552x - 8996	\( 5^{19}\cdot 11^{4}\cdot 71^{4}\cdot 167^{4} \)	20T1106	Trivial (GRH)
20.4.5519504636348247990436553955078125.2	x^20 - 2x^19 + 14x^18 + 13x^17 + 118x^16 + 196x^15 + 847x^14 + 623x^13 + 2076x^12 - 260x^11 - 1453x^10 - 15930x^9 - 31480x^8 - 60930x^7 - 109455x^6 - 148985x^5 - 161345x^4 - 131605x^3 - 69635x^2 - 20100x - 2320	\( 5^{19}\cdot 11^{4}\cdot 71^{4}\cdot 167^{4} \)	20T1106	Trivial (GRH)
20.10.7374058194161259315223236083984375.1	x^20 - 3x^19 - 24x^18 + 78x^17 + 290x^16 - 820x^15 - 2974x^14 + 6009x^13 + 21932x^12 - 32823x^11 - 104821x^10 + 121669x^9 + 335205x^8 - 328575x^7 - 654684x^6 + 612777x^5 + 629360x^4 - 580653x^3 - 222619x^2 + 192249x + 4057	\( -\,5^{16}\cdot 11^{4}\cdot 71^{4}\cdot 167^{5} \)	20T1106	Trivial (GRH)
20.14.88312074181571967846984863281250000.1	x^20 - 2x^19 - 34x^18 - 29x^17 + 449x^16 + 1262x^15 - 1876x^14 - 11657x^13 - 3673x^12 + 46757x^11 + 53245x^10 - 87641x^9 - 184832x^8 + 8386x^7 + 229497x^6 + 129613x^5 - 72992x^4 - 88509x^3 - 18040x^2 + 5264x + 1679	\( -\,2^{4}\cdot 5^{19}\cdot 11^{4}\cdot 71^{4}\cdot 167^{4} \)	20T1106	Trivial (GRH)
20.12.88312074181571967846984863281250000.1	x^20 - 6x^19 - x^18 + 62x^17 - 72x^16 - 619x^15 + 1808x^14 + 2586x^13 - 17551x^12 + 18084x^11 + 51190x^10 - 138959x^9 + 17681x^8 + 250533x^7 - 232783x^6 - 82051x^5 + 268062x^4 - 129551x^3 - 69134x^2 + 78266x - 18031	\( 2^{4}\cdot 5^{19}\cdot 11^{4}\cdot 71^{4}\cdot 167^{4} \)	20T1106	Trivial (GRH)
20.12.88312074181571967846984863281250000.2	x^20 - 31x^18 - 25x^17 + 252x^16 + 416x^15 - 873x^14 - 3125x^13 + 3762x^12 + 5681x^11 - 6849x^10 + 18043x^9 - 72863x^8 + 76373x^7 + 49800x^6 - 151726x^5 + 98093x^4 - 4x^3 - 26737x^2 + 11247x - 1439	\( 2^{4}\cdot 5^{19}\cdot 11^{4}\cdot 71^{4}\cdot 167^{4} \)	20T1106	Trivial (GRH)
20.16.117984931106580149043571777343750000.1	x^20 - 7x^19 - 10x^18 + 177x^17 - 241x^16 - 1276x^15 + 3869x^14 + 420x^13 - 18915x^12 + 33978x^11 + 35140x^10 - 212941x^9 + 51215x^8 + 715516x^7 - 536463x^6 - 1270173x^5 + 1304402x^4 + 1073265x^3 - 1303520x^2 - 336331x + 463261	\( 2^{4}\cdot 5^{16}\cdot 11^{4}\cdot 71^{4}\cdot 167^{5} \)	20T1106	Trivial (GRH)
20.2.2893810046781750242410000000000000000.1	x^20 + 31x^18 + 392x^16 + 2630x^14 + 10281x^12 + 24396x^10 + 35275x^8 + 29900x^6 + 13275x^4 + 2225x^2 - 25	\( -\,2^{16}\cdot 5^{16}\cdot 11^{4}\cdot 71^{4}\cdot 167^{4} \)	20T1106	$[3]$ (GRH)
20.16.6157338592124651528211402130126953125.1	x^20 - 8x^19 + 14x^18 - 4x^17 + 71x^16 + 597x^15 - 3849x^14 + 101x^13 + 25824x^12 - 25565x^11 - 62207x^10 + 105347x^9 + 33338x^8 - 147473x^7 + 57538x^6 + 51577x^5 - 40639x^4 + 808x^3 + 5882x^2 - 1369x + 17	\( 5^{17}\cdot 11^{4}\cdot 71^{4}\cdot 167^{6} \)	20T1106	Trivial (GRH)
20.18.10685760975970208109485168457031250000.1	x^20 - 6x^19 - 37x^18 + 252x^17 + 338x^16 - 3357x^15 + 897x^14 + 12338x^13 - 11561x^12 + 30017x^11 - 72928x^10 - 65045x^9 + 243819x^8 - 72772x^7 - 156917x^6 + 98528x^5 + 12244x^4 - 18975x^3 + 3271x^2 - 113x + 1	\( -\,2^{4}\cdot 5^{19}\cdot 11^{6}\cdot 71^{4}\cdot 167^{4} \)	20T1106	Trivial (GRH)
20.18.10685760975970208109485168457031250000.2	x^20 - 60x^18 - 92x^17 + 1149x^16 + 2729x^15 - 9680x^14 - 31471x^13 + 37687x^12 + 186305x^11 - 47867x^10 - 623685x^9 - 110356x^8 + 1208701x^7 + 469677x^6 - 1316497x^5 - 663935x^4 + 733746x^3 + 423836x^2 - 158296x - 99181	\( -\,2^{4}\cdot 5^{19}\cdot 11^{6}\cdot 71^{4}\cdot 167^{4} \)	20T1106	Trivial (GRH)
20.2.14469050233908751212050000000000000000.1	x^20 - x^18 - 385x^16 - 5023x^14 - 29810x^12 - 98407x^10 - 191950x^8 - 223625x^6 - 152045x^4 - 55525x^2 - 8405	\( -\,2^{16}\cdot 5^{17}\cdot 11^{4}\cdot 71^{4}\cdot 167^{4} \)	20T1106	$[8]$ (GRH)
20.20.691620601180838307935990000000000000000.1	x^20 - 25x^18 + 268x^16 - 1610x^14 + 5944x^12 - 13915x^10 + 20585x^8 - 18633x^6 + 9660x^4 - 2519x^2 + 239	\( 2^{16}\cdot 5^{16}\cdot 11^{4}\cdot 71^{4}\cdot 167^{4}\cdot 239 \)	20T1106	Trivial (GRH)
20.0.879718254221652073692640000000000000000.1	x^20 + 25x^18 + 268x^16 + 1610x^14 + 5944x^12 + 13905x^10 + 20460x^8 + 18067x^6 + 8540x^4 + 1606x^2 + 19	\( 2^{20}\cdot 5^{16}\cdot 11^{4}\cdot 19\cdot 71^{4}\cdot 167^{4} \)	20T1106	$[2, 5348]$ (GRH)
20.20.879718254221652073692640000000000000000.1	x^20 - 25x^18 + 268x^16 - 1610x^14 + 5944x^12 - 13905x^10 + 20460x^8 - 18067x^6 + 8540x^4 - 1606x^2 + 19	\( 2^{20}\cdot 5^{16}\cdot 11^{4}\cdot 19\cdot 71^{4}\cdot 167^{4} \)	20T1106	Trivial (GRH)
20.0.11065929618893412926975840000000000000000.1	x^20 + 25x^18 + 268x^16 + 1610x^14 + 5944x^12 + 13915x^10 + 20585x^8 + 18633x^6 + 9660x^4 + 2519x^2 + 239	\( 2^{20}\cdot 5^{16}\cdot 11^{4}\cdot 71^{4}\cdot 167^{4}\cdot 239 \)	20T1106	$[2, 17902]$ (GRH)