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 105)

Label	Polynomial	Discriminant	Galois group	Class group
20.2.26332894319002837533243.1	x^20 - x^19 + 5x^18 - 6x^17 + 14x^16 - 20x^15 + 21x^14 - 38x^13 + 34x^12 - 41x^11 + 64x^10 - 51x^9 + 16x^8 - 51x^7 + 48x^6 - 5x^5 + 7x^4 - 14x^3 + 2x^2 - x - 1	\( -\,3^{5}\cdot 1609^{4}\cdot 4021^{2} \)	20T886	Trivial (GRH)
20.2.670930019119154175410176.1	x^20 - x^18 + x^14 + x^12 - x^10 - x^8 + x^6 - x^2 - 1	\( -\,2^{20}\cdot 7^{4}\cdot 41^{2}\cdot 631^{4} \)	20T886	Trivial (GRH)
20.0.6770156942057799680000000.3	x^20 - 6x^19 + 22x^18 - 68x^17 + 171x^16 - 330x^15 + 512x^14 - 722x^13 + 1083x^12 - 1772x^11 + 2736x^10 - 3544x^9 + 3679x^8 - 2974x^7 + 1804x^6 - 766x^5 + 178x^4 + 12x^3 - 16x^2 + 1	\( 2^{30}\cdot 5^{7}\cdot 13^{4}\cdot 41^{4} \)	20T886	Trivial (GRH)
20.0.6770156942057799680000000.4	x^20 - 6x^19 + 16x^18 - 14x^17 - 27x^16 + 80x^15 - 16x^14 - 232x^13 + 452x^12 - 256x^11 - 344x^10 + 702x^9 - 139x^8 - 1042x^7 + 1834x^6 - 1690x^5 + 999x^4 - 374x^3 + 88x^2 - 8x + 1	\( 2^{30}\cdot 5^{7}\cdot 13^{4}\cdot 41^{4} \)	20T886	Trivial (GRH)
20.0.30692828722191450251460608.1	x^20 + 6x^18 + 18x^16 + 41x^14 + 82x^12 + 133x^10 + 164x^8 + 164x^6 + 144x^4 + 96x^2 + 32	\( 2^{25}\cdot 13^{4}\cdot 47^{2}\cdot 347^{4} \)	20T886	Trivial (GRH)
20.0.30692828722191450251460608.2	x^20 - 6x^18 + 18x^16 - 41x^14 + 82x^12 - 133x^10 + 164x^8 - 164x^6 + 144x^4 - 96x^2 + 32	\( 2^{25}\cdot 13^{4}\cdot 47^{2}\cdot 347^{4} \)	20T886	Trivial (GRH)
20.6.249238158195972964709564416.1	x^20 - x^18 - 3x^16 + 5x^14 + x^12 - 7x^10 - x^8 + 5x^6 + 3x^4 - x^2 - 1	\( -\,2^{20}\cdot 461^{2}\cdot 5783^{4} \)	20T886	Trivial (GRH)
20.6.249238158195972964709564416.2	x^20 - 5x^18 + 6x^16 + 5x^14 - 14x^12 + 11x^10 - 3x^8 - 11x^6 + 11x^4 - x^2 - 1	\( -\,2^{20}\cdot 461^{2}\cdot 5783^{4} \)	20T886	Trivial (GRH)
20.0.819859666570846008320000000.1	x^20 - 5x^19 + 19x^18 - 47x^17 + 84x^16 - 121x^15 + 151x^14 - 265x^13 + 430x^12 - 361x^11 + 67x^10 + 163x^9 - 112x^8 - 29x^7 + 139x^6 - 205x^5 + 172x^4 - 61x^3 - 9x^2 + 7x + 1	\( 2^{16}\cdot 5^{7}\cdot 367^{4}\cdot 2971^{2} \)	20T886	Trivial (GRH)
20.0.976835052279288238333493248.1	x^20 - 2x^19 + 2x^18 + 14x^17 - 24x^16 + 46x^15 + 2x^14 - 64x^13 + 435x^12 - 718x^11 + 430x^10 + 1636x^9 - 3800x^8 + 3144x^7 + 1166x^6 - 5856x^5 + 6118x^4 - 3846x^3 + 1516x^2 - 338x + 169	\( 2^{30}\cdot 13^{7}\cdot 347^{4} \)	20T886	Trivial (GRH)
20.8.976835052279288238333493248.1	x^20 - 2x^19 - 2x^18 - 12x^17 + 17x^16 + 120x^15 - 180x^14 + 6x^13 - 431x^12 + 1204x^11 - 486x^10 - 648x^9 + 397x^8 + 276x^7 - 196x^6 - 232x^5 + 122x^4 - 46x^3 - 22x^2 + 12x - 1	\( 2^{30}\cdot 13^{7}\cdot 347^{4} \)	20T886	Trivial (GRH)
20.8.1939087758167060460339200000.1	x^20 - 6x^19 + 6x^18 + 38x^17 - 102x^16 - 26x^15 + 342x^14 - 200x^13 - 555x^12 + 864x^11 - 450x^10 - 732x^9 + 4753x^8 - 9582x^7 + 4798x^6 + 13520x^5 - 22979x^4 + 8184x^3 + 2886x^2 - 344x - 443	\( 2^{30}\cdot 5^{5}\cdot 4903^{4} \)	20T886	Trivial (GRH)
20.0.2888695059844566302720000000.1	x^20 + 5x^18 - 2x^16 - 35x^14 + 35x^12 + 70x^10 - 204x^8 + 203x^6 - 25x^4 - 150x^2 + 125	\( 2^{20}\cdot 5^{7}\cdot 13^{4}\cdot 41^{4}\cdot 661^{2} \)	20T886	$[2]$ (GRH)
20.4.13751385567564933204345703125.1	x^20 - 3x^19 + 3x^18 - 12x^17 + 7x^16 - 16x^15 + 71x^14 + 74x^13 - 182x^12 - 126x^11 - 75x^10 + 334x^9 - 33x^8 + 850x^7 - 1183x^6 + 615x^5 - 1430x^4 + 1760x^3 - 760x^2 - 80x + 160	\( 3^{4}\cdot 5^{13}\cdot 23^{4}\cdot 89^{6} \)	20T886	Trivial (GRH)
20.10.14358303430550460155146470400.1	x^20 - 2x^18 - 8x^16 + 14x^14 + 19x^12 - 25x^10 - 19x^8 + 14x^6 + 8x^4 - 2x^2 - 1	\( -\,2^{10}\cdot 5^{2}\cdot 61^{4}\cdot 397^{4}\cdot 1277^{2} \)	20T886	Trivial (GRH)
20.4.14881637754078591156501753125.2	x^20 - 2x^19 - 4x^18 + 11x^17 - 17x^16 + 40x^15 + 71x^14 - 383x^13 + 72x^12 + 1066x^11 - 770x^10 - 1286x^9 + 1454x^8 + 728x^7 - 1109x^6 - 879x^5 + 545x^4 + 800x^3 + 512x^2 - 366x - 425	\( 5^{5}\cdot 61^{8}\cdot 397^{4} \)	20T886	Trivial (GRH)
20.0.14881637754078591156501753125.2	x^20 - 9x^19 + 34x^18 - 61x^17 - 7x^16 + 326x^15 - 820x^14 + 888x^13 + 262x^12 - 2665x^11 + 5004x^10 - 6095x^9 + 6671x^8 - 7236x^7 + 6500x^6 - 3184x^5 - 904x^4 + 1267x^3 + 278x^2 - 16x + 1	\( 5^{5}\cdot 61^{8}\cdot 397^{4} \)	20T886	$[2]$ (GRH)
20.0.17546689939912502804480000000.1	x^20 - 10x^19 + 46x^18 - 114x^17 + 137x^16 + 6x^15 - 202x^14 + 178x^13 - 163x^12 + 584x^11 - 514x^10 - 574x^9 + 1003x^8 - 120x^7 - 204x^6 - 768x^5 + 1018x^4 - 476x^3 + 254x^2 + 12x + 13	\( 2^{30}\cdot 5^{7}\cdot 3803^{4} \)	20T886	Trivial (GRH)
20.0.17546689939912502804480000000.2	x^20 - 10x^19 + 54x^18 - 188x^17 + 477x^16 - 922x^15 + 1422x^14 - 1716x^13 + 1545x^12 - 1000x^11 + 660x^10 - 944x^9 + 1550x^8 - 1632x^7 + 1416x^6 - 570x^5 + 319x^4 - 92x^3 + 290x^2 - 204x + 101	\( 2^{30}\cdot 5^{7}\cdot 3803^{4} \)	20T886	Trivial (GRH)
20.4.17546689939912502804480000000.3	x^20 - 2x^19 + 8x^18 - 10x^17 + 71x^16 - 90x^15 + 112x^14 - 72x^13 + 75x^12 - 396x^11 + 14x^10 - 138x^9 - 303x^8 - 276x^7 - 160x^6 + 394x^5 + 400x^4 - 38x^3 - 108x^2 + 10x + 5	\( 2^{30}\cdot 5^{7}\cdot 3803^{4} \)	20T886	Trivial (GRH)
20.4.17546689939912502804480000000.4	x^20 - 2x^19 - 14x^18 + 30x^17 + 13x^16 - 8x^15 + 8x^14 - 100x^13 + 183x^12 - 182x^11 + 282x^10 - 336x^9 + 430x^8 - 294x^7 + 400x^6 - 232x^5 + 137x^4 - 130x^3 + 6x^2 - 24x + 1	\( 2^{30}\cdot 5^{7}\cdot 3803^{4} \)	20T886	Trivial (GRH)
20.0.18272005394296010009617128125.1	x^20 - x^19 + 8x^18 + 4x^17 + 21x^16 + 46x^15 + 70x^14 + 113x^13 + 239x^12 + 183x^11 + 477x^10 + 234x^9 + 582x^8 + 227x^7 + 403x^6 + 90x^5 + 135x^4 + 11x^3 + 23x^2 + 2x + 1	\( 5^{5}\cdot 13^{4}\cdot 331^{2}\cdot 347^{4}\cdot 359^{2} \)	20T886	$[2]$ (GRH)
20.4.37203326702151704132080078125.1	x^20 - 5x^19 + 2x^18 + 17x^17 + 3x^16 - 50x^15 - 38x^14 + 83x^13 + 108x^12 - 40x^11 - 167x^10 - 40x^9 + 108x^8 + 83x^7 - 38x^6 - 50x^5 + 3x^4 + 17x^3 + 2x^2 - 5x + 1	\( 3^{4}\cdot 5^{15}\cdot 67^{4}\cdot 27329^{2} \)	20T886	Trivial (GRH)
20.0.39791453062337649407082511117.1	x^20 - 2x^19 + 10x^18 - 23x^17 + 70x^16 - 161x^15 + 320x^14 - 478x^13 + 799x^12 - 734x^11 - 191x^10 + 1864x^9 - 2291x^8 + 343x^7 + 3691x^6 - 6541x^5 + 6432x^4 - 3710x^3 + 1335x^2 - 200x + 23	\( 43^{2}\cdot 61^{4}\cdot 397^{7} \)	20T886	Trivial (GRH)
20.0.39791453062337649407082511117.2	x^20 - 7x^19 + 32x^18 - 113x^17 + 340x^16 - 895x^15 + 2093x^14 - 4272x^13 + 7505x^12 - 11146x^11 + 14456x^10 - 18169x^9 + 25990x^8 - 43261x^7 + 72200x^6 - 102389x^5 + 116494x^4 - 101944x^3 + 65539x^2 - 29474x + 9391	\( 43^{2}\cdot 61^{4}\cdot 397^{7} \)	20T886	Trivial (GRH)
20.0.56366140167260768414380128125.1	x^20 - 5x^19 + 17x^18 - 39x^17 + 71x^16 - 97x^15 + 105x^14 + 10x^13 - 112x^12 + 230x^11 - 346x^10 + 391x^9 - 337x^8 + 129x^7 + 152x^6 - 330x^5 + 437x^4 - 408x^3 + 369x^2 - 162x + 81	\( 5^{5}\cdot 31^{2}\cdot 41^{2}\cdot 139^{2}\cdot 4903^{4} \)	20T886	$[2]$ (GRH)
20.0.123762470108084398839111328125.1	x^20 - x^19 + 9x^18 + 3x^17 + 23x^16 + 44x^15 + 67x^14 + 74x^13 + 196x^12 + 193x^11 + 212x^10 + 317x^9 + 246x^8 + 46x^7 + 104x^6 + 91x^5 + 36x^4 + 90x^3 + 105x^2 + 46x + 7	\( 3^{6}\cdot 5^{13}\cdot 23^{4}\cdot 89^{6} \)	20T886	$[2]$ (GRH)
20.4.138453609253168904356642578125.1	x^20 - 5x^19 + 6x^18 + 4x^17 - 32x^16 + 77x^15 - 45x^14 - 121x^13 - 13x^12 + 286x^11 + 15x^10 - 286x^9 - 13x^8 + 121x^7 - 45x^6 - 77x^5 - 32x^4 - 4x^3 + 6x^2 + 5x + 1	\( 5^{9}\cdot 11^{4}\cdot 131^{4}\cdot 128221^{2} \)	20T886	Trivial (GRH)
20.0.204805871732141549274867433472.1	x^20 - 8x^19 + 30x^18 - 76x^17 + 154x^16 - 268x^15 + 432x^14 - 696x^13 + 1126x^12 - 1752x^11 + 2432x^10 - 2840x^9 + 2904x^8 - 3080x^7 + 4224x^6 - 6528x^5 + 7900x^4 - 6048x^3 + 2392x^2 - 224x + 8	\( 2^{45}\cdot 359^{2}\cdot 461^{4} \)	20T886	Trivial (GRH)
20.4.343784639189123330108642578125.1	x^20 - x^19 - 13x^18 + 3x^17 + 66x^16 + 37x^15 - 155x^14 - 188x^13 + 158x^12 - 59x^11 - 628x^10 + 1261x^9 + 2853x^8 - 1301x^7 - 4675x^6 - 862x^5 + 2829x^4 + 1784x^3 + 145x^2 - 111x - 17	\( 3^{4}\cdot 5^{15}\cdot 23^{4}\cdot 89^{6} \)	20T886	$[2]$ (GRH)
20.0.343784639189123330108642578125.1	x^20 + 6x^18 + 53x^16 + 42x^14 + 14x^12 + 285x^10 + 555x^8 + 480x^6 + 230x^4 + 60x^2 + 5	\( 3^{4}\cdot 5^{15}\cdot 23^{4}\cdot 89^{6} \)	20T886	$[8]$ (GRH)
20.0.454096370963249429164851200000.1	x^20 + 18x^18 + 151x^16 + 916x^14 + 4375x^12 + 14216x^10 + 29335x^8 + 40150x^6 + 32250x^4 + 17500x^2 + 3125	\( 2^{30}\cdot 5^{5}\cdot 11^{2}\cdot 5783^{4} \)	20T886	Trivial (GRH)
20.4.454096370963249429164851200000.1	x^20 - 18x^18 + 151x^16 - 916x^14 + 4375x^12 - 14216x^10 + 29335x^8 - 40150x^6 + 32250x^4 - 17500x^2 + 3125	\( 2^{30}\cdot 5^{5}\cdot 11^{2}\cdot 5783^{4} \)	20T886	Trivial (GRH)
20.12.600185956979737536135275366437.1	x^20 - 3x^19 - 5x^18 + 25x^17 - 46x^16 - 13x^15 + 365x^14 - 472x^13 - 371x^12 + 1593x^11 - 2302x^10 + 766x^9 + 3059x^8 - 15045x^7 + 13322x^6 + 33357x^5 - 33574x^4 - 27881x^3 + 22946x^2 + 7006x - 2969	\( 61^{4}\cdot 167^{2}\cdot 397^{7} \)	20T886	Trivial (GRH)
20.8.600185956979737536135275366437.1	x^20 - 2x^19 + 12x^18 + 5x^17 - 6x^16 + 177x^15 - 33x^14 - 151x^13 + 561x^12 - 478x^11 - 1812x^10 + 96x^9 + 537x^8 - 1317x^7 + 1082x^6 + 3262x^5 + 354x^4 - 2274x^3 - 414x^2 + 610x - 61	\( 61^{4}\cdot 167^{2}\cdot 397^{7} \)	20T886	Trivial (GRH)
20.8.1154067626962609920750387200000.1	x^20 - 20x^18 + 190x^16 - 1178x^14 + 5407x^12 - 18472x^10 + 43415x^8 - 64600x^6 + 56375x^4 - 23750x^2 + 3125	\( 2^{30}\cdot 5^{5}\cdot 61^{4}\cdot 397^{4} \)	20T886	Trivial (GRH)
20.8.2041142339188397536405642340137.1	x^20 - 2x^19 - 9x^18 - 14x^17 - 38x^16 + 232x^15 + 513x^14 + 931x^13 + 803x^12 - 4877x^11 - 11819x^10 - 29224x^9 - 47959x^8 - 49550x^7 - 68486x^6 - 35730x^5 - 13642x^4 - 21829x^3 + 30757x^2 - 468x - 1733	\( 97^{5}\cdot 461^{2}\cdot 5783^{4} \)	20T886	Trivial (GRH)
20.0.2871772675093161595832481014077.1	x^20 - 5x^19 + 21x^18 - 53x^17 + 117x^16 - 186x^15 + 280x^14 - 333x^13 + 410x^12 - 357x^11 + 263x^10 + 16x^9 - 53x^8 + 134x^7 + 196x^6 + 35x^5 + 186x^4 + 54x^3 + 87x^2 + 7x + 1	\( 13^{7}\cdot 347^{4}\cdot 1776701^{2} \)	20T886	Trivial (GRH)
20.4.2918857922390691948807530253125.1	x^20 - 2x^19 - 20x^17 + 7x^16 + 39x^15 + 14x^14 + 149x^13 - 363x^12 + 123x^11 - 557x^10 - 878x^9 - 332x^8 - 740x^7 - 654x^6 - 63x^5 - 236x^4 - 77x^3 - 24x^2 - x + 1	\( 5^{5}\cdot 5519^{4}\cdot 1003369^{2} \)	20T886	Trivial (GRH)
20.4.3094061752702109970977783203125.1	x^20 - 10x^19 + 28x^18 + 33x^17 - 317x^16 + 496x^15 + 444x^14 - 2710x^13 + 4173x^12 - 2158x^11 - 2593x^10 + 5776x^9 - 5041x^8 + 2726x^7 - 1713x^6 + 1843x^5 - 794x^4 - 788x^3 - 186x^2 + 790x - 235	\( 3^{6}\cdot 5^{15}\cdot 23^{4}\cdot 89^{6} \)	20T886	$[8]$ (GRH)
20.0.4147457342145361888254380002693.1	x^20 - 3x^19 + 8x^18 + 9x^17 + 31x^16 - 48x^15 + 319x^14 - 72x^13 - 320x^12 + 1805x^11 + 769x^10 - 5642x^9 + 12508x^8 - 13426x^7 + 10745x^6 - 5290x^5 + 1922x^4 - 225x^3 - 4x^2 - 3x + 1	\( 61^{4}\cdot 397^{7}\cdot 439^{2} \)	20T886	Trivial (GRH)
20.0.4147457342145361888254380002693.2	x^20 - 3x^19 - 8x^18 + 34x^17 + 49x^16 - 314x^15 + 48x^14 + 1601x^13 - 1773x^12 - 5186x^11 + 12679x^10 + 1389x^9 - 32322x^8 + 25656x^7 + 54462x^6 - 161941x^5 + 210758x^4 - 170279x^3 + 92765x^2 - 31618x + 6295	\( 61^{4}\cdot 397^{7}\cdot 439^{2} \)	20T886	Trivial (GRH)
20.0.5886488028495486698036707508557.1	x^20 + 2x^18 - 7x^17 + 42x^16 + 29x^15 + 227x^14 - 720x^13 - 23x^12 + 435x^11 - 737x^10 + 3130x^9 + 194x^8 - 8170x^7 + 7368x^6 + 284x^5 - 6599x^4 + 4853x^3 + 1909x^2 - 2420x + 509	\( 61^{4}\cdot 397^{7}\cdot 523^{2} \)	20T886	Trivial (GRH)
20.0.5886488028495486698036707508557.2	x^20 - 6x^19 + 21x^18 - 54x^17 + 160x^16 - 544x^15 + 1464x^14 - 3516x^13 + 7215x^12 - 12712x^11 + 19585x^10 - 23990x^9 + 29238x^8 - 32441x^7 + 32064x^6 - 28847x^5 + 20422x^4 - 9705x^3 + 2781x^2 - 418x + 25	\( 61^{4}\cdot 397^{7}\cdot 523^{2} \)	20T886	Trivial (GRH)
20.8.6650335444120255587498908203125.1	x^20 - 7x^18 - 5x^16 + 75x^14 - 106x^12 + 777x^10 + 905x^8 - 10300x^6 + 8419x^4 - 1203x^2 + 5	\( 3^{4}\cdot 5^{9}\cdot 439^{2}\cdot 21611^{4} \)	20T886	Trivial (GRH)
20.4.7274482965241849665098876953125.1	x^20 - 5x^19 + 3x^18 - 6x^17 + 117x^16 - 247x^15 + 155x^14 - 783x^13 + 3106x^12 - 5565x^11 + 8493x^10 - 17260x^9 + 36573x^8 - 66315x^7 + 98679x^6 - 116489x^5 + 104460x^4 - 68033x^3 + 30405x^2 - 8441x + 1127	\( 3^{4}\cdot 5^{13}\cdot 23^{6}\cdot 89^{6} \)	20T886	$[2]$ (GRH)
20.10.8395788774631787308587848564736.1	x^20 - x^18 - 11x^16 + 7x^14 + 33x^12 - 11x^10 - 33x^8 + 7x^6 + 11x^4 - x^2 - 1	\( -\,2^{20}\cdot 3^{4}\cdot 43^{4}\cdot 109^{2}\cdot 1249^{4} \)	20T886	Trivial (GRH)
20.0.8594615979728083252716064453125.1	x^20 - 4x^19 + 13x^18 + 8x^17 + 71x^16 + 110x^15 + 364x^14 + 682x^13 + 1267x^12 + 2089x^11 + 2423x^10 + 2229x^9 + 1652x^8 + 1042x^7 + 1314x^6 + 220x^5 + 1556x^4 - 787x^3 + 428x^2 - 24x + 1	\( 3^{4}\cdot 5^{17}\cdot 23^{4}\cdot 89^{6} \)	20T886	$[2, 8]$ (GRH)
20.12.9964694368301019319239964622848.1	x^20 - 2x^19 - 18x^18 + 80x^17 - 8x^16 - 528x^15 + 650x^14 + 1288x^13 - 2362x^12 - 2020x^11 + 5100x^10 + 2818x^9 - 7673x^8 - 4766x^7 + 6906x^6 + 5736x^5 - 2650x^4 - 2290x^3 + 320x^2 + 124x - 17	\( 2^{30}\cdot 13^{7}\cdot 101^{2}\cdot 347^{4} \)	20T886	Trivial (GRH)
20.0.9964694368301019319239964622848.1	x^20 - 2x^19 - 2x^18 - 16x^17 + 89x^16 - 184x^15 + 590x^14 - 1944x^13 + 4371x^12 - 8374x^11 + 16186x^10 - 29220x^9 + 46110x^8 - 65880x^7 + 84452x^6 - 100670x^5 + 116483x^4 - 111656x^3 + 75518x^2 - 30558x + 8047	\( 2^{30}\cdot 13^{7}\cdot 101^{2}\cdot 347^{4} \)	20T886	$[3]$ (GRH)