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 100)

Label	Polynomial	Discriminant	Galois group	Class group
20.2.1816889967552059474944.1	x^20 - 6x^16 + 11x^12 + 3x^10 - 17x^8 + 6x^6 + 2x^2 - 1	\( -\,2^{10}\cdot 36497^{4} \)	20T992	Trivial
20.2.2265966431812150395904.1	x^20 + x^18 - 4x^16 - 7x^14 - x^12 + 21x^10 + 3x^8 - 13x^6 - 4x^4 + 3x^2 - 1	\( -\,2^{10}\cdot 38569^{4} \)	20T992	Trivial
20.2.4519908793361499099136.1	x^20 + x^18 - 2x^16 - x^14 + x^12 + x^10 - 7x^8 + 10x^6 - 4x^4 + 2x^2 - 1	\( -\,2^{12}\cdot 32411^{4} \)	20T992	Trivial
20.2.8085321984821794902016.1	x^20 - 2x^18 + x^16 - x^14 - 2x^12 + 4x^10 + x^6 + 2x^4 - 2x^2 - 1	\( -\,2^{12}\cdot 37483^{4} \)	20T992	Trivial (GRH)
20.0.10595546867344882662901.1	x^20 - x^19 + 3x^18 - 3x^17 + 8x^16 - 5x^15 + 12x^14 - 10x^13 + 16x^12 - 6x^11 + 8x^10 + x^8 - 5x^7 + 7x^6 + 2x^5 - 8x^4 + 6x^3 - 2x + 1	\( 11^{4}\cdot 19^{4}\cdot 199^{4}\cdot 3541 \)	20T992	Trivial
20.4.22905655334132142080000.1	x^20 - 4x^19 + x^18 + 20x^17 - 31x^16 - 18x^15 + 69x^14 - 3x^13 - 95x^12 + 43x^11 + 88x^10 - 135x^9 + 112x^8 - 40x^7 - 44x^6 + 37x^5 + 16x^4 - 9x^3 - 4x^2 - 2x - 1	\( 2^{15}\cdot 5^{4}\cdot 5783^{4} \)	20T992	Trivial (GRH)
20.2.45236940414786731232256.1	x^20 - 6x^19 + 15x^18 - 24x^17 + 42x^16 - 84x^15 + 132x^14 - 140x^13 + 82x^12 + 36x^11 - 198x^10 + 312x^9 - 230x^8 - 16x^7 + 157x^6 - 72x^5 - 58x^4 + 82x^3 - 41x^2 + 10x - 1	\( -\,2^{10}\cdot 17^{4}\cdot 19\cdot 2297^{4} \)	20T992	Trivial (GRH)
20.4.54760506817899727281152.1	x^20 - 8x^19 + 27x^18 - 51x^17 + 57x^16 - 26x^15 - 41x^14 + 134x^13 - 245x^12 + 349x^11 - 403x^10 + 378x^9 - 291x^8 + 195x^7 - 113x^6 + 42x^5 - x^4 - 12x^3 + 8x^2 - 1	\( 2^{10}\cdot 17^{4}\cdot 23\cdot 2297^{4} \)	20T992	Trivial (GRH)
20.2.61453477994727278116864.1	x^20 + 3x^18 + x^16 - 17x^14 - 36x^12 - 27x^10 + 2x^8 + 6x^6 + x^2 - 1	\( -\,2^{26}\cdot 5501^{4} \)	20T992	Trivial (GRH)
20.4.135285869682178618505573.1	x^20 - 2x^19 + 2x^18 + 7x^17 - 12x^16 + 8x^15 + 16x^14 - 33x^13 + 4x^12 + 7x^11 - 49x^10 + 7x^9 + 4x^8 - 33x^7 + 16x^6 + 8x^5 - 12x^4 + 7x^3 + 2x^2 - 2x + 1	\( 53^{5}\cdot 4241^{4} \)	20T992	Trivial (GRH)
20.0.140935348861746828910625.1	x^20 - x^19 - 7x^17 + 10x^16 + x^15 + 12x^14 - 19x^13 - 9x^12 + 3x^11 + 11x^10 - 7x^9 + 3x^8 + 2x^7 + 20x^6 - 19x^5 - 8x^4 - 8x^3 + 20x^2 - 5x + 1	\( 5^{4}\cdot 13^{2}\cdot 1193\cdot 5783^{4} \)	20T992	Trivial
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)
20.4.343697048162735885972621.1	x^20 - 3x^19 + 3x^18 + 3x^17 - 14x^16 + 21x^15 - 19x^14 - 3x^13 + 37x^12 - 50x^11 + 46x^10 - 32x^9 + 5x^8 + 2x^7 - 20x^6 + 10x^5 + 2x^4 + 8x^3 + 3x^2 + 1	\( 17^{4}\cdot 23\cdot 2297^{4}\cdot 6427 \)	20T992	Trivial (GRH)
20.4.753241319945149716516553.1	x^20 + x^16 - 3x^15 + x^14 - x^13 + 7x^12 - 10x^10 + 13x^9 + 17x^8 - 60x^7 - 17x^6 + 99x^5 - 17x^4 - 53x^3 + 19x^2 + 5x - 1	\( 38569^{4}\cdot 340393 \)	20T992	Trivial (GRH)
20.0.985146484173791435755549.1	x^20 - 10x^19 + 54x^18 - 201x^17 + 570x^16 - 1296x^15 + 2437x^14 - 3865x^13 + 5238x^12 - 6117x^11 + 6187x^10 - 5432x^9 + 4139x^8 - 2729x^7 + 1548x^6 - 748x^5 + 304x^4 - 102x^3 + 27x^2 - 5x + 1	\( 67\cdot 8287\cdot 36497^{4} \)	20T992	Trivial (GRH)
20.4.1272351014851188733590061.1	x^20 - 14x^18 - 3x^17 + 83x^16 + 37x^15 - 264x^14 - 185x^13 + 453x^12 + 441x^11 - 359x^10 - 416x^9 + 261x^8 + 316x^7 - 111x^6 - 168x^5 + 12x^4 + 54x^3 + 14x^2 - 2x - 1	\( 32411^{4}\cdot 1153021 \)	20T992	Trivial (GRH)
20.4.1399114076857325849673728.1	x^20 - 10x^19 + 55x^18 - 210x^17 + 615x^16 - 1452x^15 + 2850x^14 - 4740x^13 + 6763x^12 - 8338x^11 + 8911x^10 - 8250x^9 + 6582x^8 - 4476x^7 + 2538x^6 - 1152x^5 + 382x^4 - 70x^3 - 5x^2 + 6x - 1	\( 2^{20}\cdot 1193\cdot 5783^{4} \)	20T992	Trivial (GRH)
20.0.1873761689812481972620288.1	x^20 - 5x^19 + 14x^18 - 21x^17 + 28x^16 - 26x^15 + 32x^14 - 10x^13 + 53x^12 - 78x^11 + 185x^10 - 133x^9 + 237x^8 - 127x^7 + 262x^6 - 29x^5 + 84x^4 + 55x^3 + 36x^2 + 10x + 1	\( 2^{10}\cdot 17^{4}\cdot 787\cdot 2297^{4} \)	20T992	Trivial (GRH)
20.2.2060764600365471574508544.1	x^20 - 3x^19 + 6x^17 + 8x^15 - 30x^14 - 36x^13 + 64x^12 + 106x^11 - 96x^10 - 95x^9 + 39x^8 + x^7 - 36x^6 + 72x^5 + 82x^4 - 9x^3 - 30x^2 - 18x - 9	\( -\,2^{10}\cdot 3^{4}\cdot 17^{4}\cdot 4153^{4} \)	20T992	Trivial
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)
20.0.2281304769909875422527488.1	x^20 - 4x^19 + 8x^18 - 20x^17 + 44x^16 - 64x^15 + 88x^14 - 138x^13 + 223x^12 - 366x^11 + 624x^10 - 1026x^9 + 1404x^8 - 1654x^7 + 1818x^6 - 1776x^5 + 1450x^4 - 1010x^3 + 774x^2 - 598x + 223	\( 2^{30}\cdot 317\cdot 1609^{4} \)	20T992	Trivial (GRH)
20.4.5552552362447981947401101.1	x^20 - x^19 + x^18 + x^17 + 3x^16 + 18x^14 + 11x^13 - 8x^12 + 117x^11 + 303x^10 + 327x^9 + 193x^8 + 45x^7 - 46x^6 - 76x^5 - 39x^4 + 36x^3 + 40x^2 + 4x - 1	\( 36497^{4}\cdot 3129421 \)	20T992	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)
20.0.10024198901653010587170469.1	x^20 - x^19 + 5x^18 - 2x^17 + 11x^16 - 3x^15 + 17x^14 - 4x^13 + 21x^12 - 5x^11 + 23x^10 - 5x^9 + 21x^8 - 4x^7 + 17x^6 - 3x^5 + 11x^4 - 2x^3 + 5x^2 - x + 1	\( 7^{4}\cdot 103\cdot 137^{4}\cdot 163^{5} \)	20T992	Trivial (GRH)
20.10.18546881403289244170576896.1	x^20 - 7x^18 + 18x^16 - 38x^14 + 84x^12 - 60x^10 - 128x^8 + 261x^6 - 186x^4 + 63x^2 - 9	\( -\,2^{10}\cdot 3^{6}\cdot 17^{4}\cdot 4153^{4} \)	20T992	Trivial (GRH)
20.2.18546881403289244170576896.1	x^20 - 3x^19 + 5x^18 - x^17 - 2x^16 + 8x^15 - 25x^14 + 58x^13 - 111x^12 + 153x^11 - 102x^10 + 258x^9 - 149x^8 + 191x^7 - 118x^6 + 70x^5 - 37x^4 + 16x^3 - 9x^2 + 7x + 1	\( -\,2^{10}\cdot 3^{6}\cdot 17^{4}\cdot 4153^{4} \)	20T992	Trivial (GRH)
20.4.22958799056697995850416128.1	x^20 - 2x^19 - 4x^18 + 14x^16 + 2x^15 - 24x^14 + 131x^12 + 164x^11 + 34x^10 + 4x^9 + 205x^8 + 444x^7 + 262x^6 - 104x^5 - 389x^4 - 480x^3 - 306x^2 - 142x - 37	\( 2^{30}\cdot 37\cdot 4903^{4} \)	20T992	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)
20.0.29082655566181219410952789.1	x^20 - 3x^19 + 7x^18 - 14x^17 + 22x^16 - 33x^15 + 48x^14 - 52x^13 + 76x^12 - 63x^11 + 89x^10 - 63x^9 + 76x^8 - 52x^7 + 48x^6 - 33x^5 + 22x^4 - 14x^3 + 7x^2 - 3x + 1	\( 7^{4}\cdot 67\cdot 137^{4}\cdot 163^{4}\cdot 727 \)	20T992	Trivial (GRH)
20.10.35032998206213016766645248.1	x^20 - 10x^18 + 42x^16 - 113x^14 + 236x^12 - 329x^10 + 191x^8 + 128x^6 - 249x^4 + 119x^2 - 17	\( -\,2^{10}\cdot 3^{4}\cdot 17^{5}\cdot 4153^{4} \)	20T992	Trivial (GRH)
20.4.35032998206213016766645248.1	x^20 - 3x^19 + 5x^18 + x^17 - 24x^16 + 49x^15 - 24x^14 - 72x^13 + 138x^12 - 116x^11 - 27x^10 + 194x^9 - 280x^8 + 229x^7 - 8x^6 - 194x^5 + 253x^4 - 165x^3 + 51x^2 - 9	\( 2^{10}\cdot 3^{4}\cdot 17^{5}\cdot 4153^{4} \)	20T992	Trivial (GRH)
20.8.35032998206213016766645248.1	x^20 - 7x^18 + 16x^16 - 13x^14 - 6x^12 + 54x^10 - 80x^8 - 34x^6 + 54x^4 + 51x^2 + 17	\( 2^{10}\cdot 3^{4}\cdot 17^{5}\cdot 4153^{4} \)	20T992	Trivial (GRH)
20.4.35032998206213016766645248.2	x^20 - 4x^19 + x^18 + 8x^17 + 4x^16 - 22x^15 - 11x^14 + 38x^13 + 76x^12 - 161x^11 - 48x^10 + 255x^9 - 50x^8 - 237x^7 + 154x^6 + 27x^5 + 28x^4 - 126x^3 + 84x^2 - 9x - 9	\( 2^{10}\cdot 3^{4}\cdot 17^{5}\cdot 4153^{4} \)	20T992	Trivial (GRH)
20.8.35032998206213016766645248.2	x^20 - 15x^16 + 6x^14 + 65x^12 - 16x^10 - 195x^8 + 194x^6 + 10x^4 - 68x^2 + 17	\( 2^{10}\cdot 3^{4}\cdot 17^{5}\cdot 4153^{4} \)	20T992	Trivial (GRH)
20.8.35032998206213016766645248.3	x^20 - x^18 - 14x^16 + 6x^14 + 86x^12 - 18x^10 - 374x^8 + 465x^6 - 82x^4 - 85x^2 + 17	\( 2^{10}\cdot 3^{4}\cdot 17^{5}\cdot 4153^{4} \)	20T992	Trivial (GRH)
20.10.37939607261791361436851947.1	x^20 - x^19 - 7x^18 + 17x^17 + 5x^16 - 57x^15 + 55x^14 + 38x^13 - 176x^12 + 108x^11 + 241x^10 - 244x^9 - 92x^8 + 195x^7 - 120x^6 - 73x^5 + 130x^4 + 16x^3 - 34x^2 - 2x + 1	\( -\,7^{6}\cdot 43^{5}\cdot 1217^{4} \)	20T992	Trivial (GRH)
20.6.37939607261791361436851947.1	x^20 - 4x^19 + 10x^18 - 14x^17 + 16x^16 - 27x^15 + 19x^14 + 4x^13 + 5x^12 + 67x^11 - 178x^10 - 69x^9 - 69x^8 - 44x^7 + 271x^6 + 97x^5 - 98x^4 - 15x^3 + 20x^2 + 2x - 1	\( -\,7^{6}\cdot 43^{5}\cdot 1217^{4} \)	20T992	Trivial (GRH)
20.10.46465044146768981515042816.1	x^20 - 10x^19 + 37x^18 - 46x^17 - 81x^16 + 358x^15 - 434x^14 - 60x^13 + 775x^12 - 1046x^11 + 945x^10 - 638x^9 - 310x^8 + 1564x^7 - 1908x^6 + 1168x^5 - 339x^4 - 2x^3 + 34x^2 - 10x + 1	\( -\,2^{20}\cdot 83^{4}\cdot 983^{4} \)	20T992	Trivial (GRH)
20.10.46465044146768981515042816.2	x^20 - 6x^19 + 8x^18 + 26x^17 - 98x^16 + 82x^15 + 111x^14 - 194x^13 - 100x^12 + 70x^11 + 1277x^10 - 2956x^9 + 2439x^8 + 390x^7 - 2506x^6 + 2138x^5 - 732x^4 - 12x^3 + 74x^2 - 12x - 1	\( -\,2^{20}\cdot 83^{4}\cdot 983^{4} \)	20T992	Trivial (GRH)
20.2.88479824944732981077999616.1	x^20 - 2x^19 + 4x^18 - 8x^17 + 2x^16 - 8x^14 + 72x^13 + 28x^12 + 136x^11 + 8x^10 - 160x^9 - 232x^8 - 720x^7 - 848x^6 - 992x^5 - 960x^4 - 864x^3 - 512x^2 - 192x - 32	\( -\,2^{30}\cdot 13^{4}\cdot 199\cdot 347^{4} \)	20T992	Trivial (GRH)
20.10.123694350305361166820442112.1	x^20 - 8x^19 + 24x^18 - 30x^17 - 18x^16 + 200x^15 - 584x^14 + 960x^13 - 937x^12 + 480x^11 + 328x^10 - 1274x^9 + 1384x^8 - 422x^7 - 322x^6 + 272x^5 - 60x^4 + 18x^3 - 20x^2 + 8x - 1	\( -\,2^{30}\cdot 103\cdot 5783^{4} \)	20T992	Trivial (GRH)
20.2.123694350305361166820442112.1	x^20 - 8x^19 + 32x^18 - 86x^17 + 184x^16 - 346x^15 + 570x^14 - 744x^13 + 617x^12 + 60x^11 - 1438x^10 + 3750x^9 - 7269x^8 + 11538x^7 - 14898x^6 + 15532x^5 - 13107x^4 + 8930x^3 - 4740x^2 + 1768x - 347	\( -\,2^{30}\cdot 103\cdot 5783^{4} \)	20T992	Trivial (GRH)
20.0.241037416511364091609284608.1	x^20 - 9x^18 + 33x^16 - 55x^14 - 14x^12 - 37x^10 + 525x^8 + 379x^6 - 229x^4 + 83	\( 2^{16}\cdot 83^{5}\cdot 983^{4} \)	20T992	Trivial (GRH)
20.4.315296983855917150899807232.1	x^20 + 6x^18 - 4x^16 - 44x^14 - 3x^12 - 31x^10 - 671x^8 - 1368x^6 - 912x^4 + 153	\( 2^{10}\cdot 3^{6}\cdot 17^{5}\cdot 4153^{4} \)	20T992	Trivial (GRH)
20.8.315296983855917150899807232.1	x^20 - 6x^19 + 5x^18 + 39x^17 - 109x^16 + 99x^15 - 60x^14 + 102x^13 + 43x^12 - 426x^11 + 499x^10 - 258x^9 + 172x^8 - 111x^7 - 45x^6 + 63x^5 + 11x^4 - 15x^3 - 7x^2 + 3x + 1	\( 2^{10}\cdot 3^{6}\cdot 17^{5}\cdot 4153^{4} \)	20T992	Trivial (GRH)
20.12.333344467865374796821005421.1	x^20 - 2x^19 - 16x^18 + 24x^17 + 96x^16 - 30x^15 - 360x^14 - 336x^13 + 617x^12 + 1473x^11 + 174x^10 - 2098x^9 - 1732x^8 + 763x^7 + 1463x^6 + 152x^5 - 412x^4 - 67x^3 + 49x^2 + x - 1	\( 7^{4}\cdot 137^{4}\cdot 163^{4}\cdot 179\cdot 3119 \)	20T992	Trivial (GRH)