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 54)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.247762589365422180532224.1	x^20 + 2x^18 + x^16 + 4x^14 + 2x^12 + 8x^10 + 2x^8 + 4x^6 + x^4 + 2x^2 + 1	\( 2^{26}\cdot 3^{22}\cdot 7^{6} \)	20T664	Trivial (GRH)
20.0.425045144526358050832384.1	x^20 - 5x^19 + 12x^18 - 13x^17 + 2x^16 + 9x^15 - 10x^14 + 7x^13 - 3x^12 - 10x^11 + 12x^10 + 10x^9 - 3x^8 - 7x^7 - 10x^6 - 9x^5 + 2x^4 + 13x^3 + 12x^2 + 5x + 1	\( 2^{16}\cdot 13^{10}\cdot 19^{6} \)	20T664	Trivial
20.0.1940164150557599013535744.3	x^20 + x^18 - 11x^16 + 32x^14 - 59x^12 + 73x^10 - 59x^8 + 32x^6 - 11x^4 + x^2 + 1	\( 2^{32}\cdot 277^{6} \)	20T664	Trivial (GRH)
20.4.3964201429846754888515584.1	x^20 - 2x^18 + x^16 - 4x^14 + 2x^12 - 8x^10 + 2x^8 - 4x^6 + x^4 - 2x^2 + 1	\( 2^{30}\cdot 3^{22}\cdot 7^{6} \)	20T664	Trivial (GRH)
20.4.4456788206200304960536576.1	x^20 - 2x^19 - x^18 + 9x^16 + 18x^15 - 18x^14 + 12x^13 - 77x^12 + 54x^11 - 45x^10 + 106x^9 - 53x^8 + 48x^7 - 84x^6 + 40x^5 - 33x^4 + 34x^3 - 3x^2 - 6x + 1	\( 2^{20}\cdot 97^{2}\cdot 277^{6} \)	20T664	Trivial (GRH)
20.0.7348979425488170687017441.1	x^20 - 3x^19 + x^18 + 4x^17 - 10x^16 + 8x^15 + 28x^14 - 43x^13 + x^12 + 40x^11 - 104x^10 + 90x^9 + 118x^8 - 35x^7 - 16x^6 - 301x^5 - 173x^4 + 220x^3 + 425x^2 + 500x + 625	\( 23^{2}\cdot 4903^{6} \)	20T664	Trivial (GRH)
20.0.7833215942848814041519681.1	x^20 - 9x^18 + 12x^16 + 96x^14 - 94x^12 + 144x^10 + 416x^8 - 153x^6 + 130x^4 + 135x^2 + 49	\( 7^{2}\cdot 53^{6}\cdot 139^{6} \)	20T664	$[2]$ (GRH)
20.0.7833215942848814041519681.2	x^20 - 4x^19 + x^18 + 25x^17 - 54x^16 - 2x^15 + 213x^14 - 444x^13 + 198x^12 + 1046x^11 - 2272x^10 + 459x^9 + 4701x^8 - 6376x^7 - 976x^6 + 9517x^5 - 6777x^4 - 4418x^3 + 10196x^2 - 6683x + 1681	\( 7^{2}\cdot 53^{6}\cdot 139^{6} \)	20T664	Trivial (GRH)
20.4.10301685869703920569286656.1	x^20 - 9x^18 + 15x^16 + 42x^14 - 51x^12 - 15x^10 - 51x^8 + 42x^6 + 15x^4 - 9x^2 + 1	\( 2^{28}\cdot 13^{8}\cdot 19^{6} \)	20T664	Trivial (GRH)
20.0.16907520178290136214142976.1	x^20 - 4x^18 + 7x^16 - 6x^14 - 12x^12 + 69x^10 + 152x^8 + 132x^6 + 59x^4 + 13x^2 + 1	\( 2^{32}\cdot 89^{8} \)	20T664	$[2]$
20.0.16907520178290136214142976.2	x^20 + x^18 - 3x^16 + 17x^14 - 26x^12 + 36x^10 - 26x^8 + 17x^6 - 3x^4 + x^2 + 1	\( 2^{32}\cdot 89^{8} \)	20T664	$[2]$ (GRH)
20.4.16907520178290136214142976.2	x^20 - 4x^18 + x^16 + 12x^14 + 12x^12 - 54x^10 + 2x^8 + 54x^6 - 16x^4 - 8x^2 + 1	\( 2^{32}\cdot 89^{8} \)	20T664	Trivial (GRH)
20.8.164826973915262729108586496.1	x^20 - 7x^18 + 21x^16 - 32x^14 + 21x^12 - 7x^10 + 21x^8 - 32x^6 + 21x^4 - 7x^2 + 1	\( 2^{32}\cdot 13^{8}\cdot 19^{6} \)	20T664	Trivial (GRH)
20.0.201707501835641831643973969.1	x^20 - 4x^19 + 8x^18 - 11x^17 + 27x^16 - 64x^15 + 67x^14 - 41x^13 + 185x^12 - 419x^11 + 436x^10 - 249x^9 + 491x^8 - 976x^7 + 1931x^6 - 2345x^5 + 1655x^4 - 708x^3 + 1268x^2 - 1378x + 547	\( 61^{6}\cdot 397^{6} \)	20T664	Trivial (GRH)
20.4.201707501835641831643973969.1	x^20 - 2x^19 + 4x^18 + 5x^17 - 23x^16 + 20x^15 + 14x^14 - 14x^13 - 16x^12 - 88x^11 + 129x^10 + 69x^9 - 112x^8 - 175x^7 + 169x^6 + 381x^5 - 348x^4 - 375x^3 - 62x^2 + 45x + 25	\( 61^{6}\cdot 397^{6} \)	20T664	Trivial (GRH)
20.8.201707501835641831643973969.1	x^20 - 2x^19 - 7x^18 + 5x^17 + 22x^16 + 44x^15 - 18x^14 - 219x^13 - 162x^12 + 264x^11 + 541x^10 + 401x^9 - 461x^8 - 1172x^7 - 320x^6 + 485x^5 + 879x^4 + 61x^3 - 465x^2 - 3x + 53	\( 61^{6}\cdot 397^{6} \)	20T664	Trivial (GRH)
20.0.201707501835641831643973969.2	x^20 - 3x^19 + 9x^18 - 14x^17 + 25x^16 - 34x^15 + 31x^14 + 54x^13 - 181x^12 + 317x^11 - 216x^10 + 4x^9 + 233x^8 - 295x^7 + 402x^6 - 270x^5 + 267x^4 - 98x^3 + 58x^2 + 4x + 1	\( 61^{6}\cdot 397^{6} \)	20T664	Trivial (GRH)
20.8.706754562236775450201184969.1	x^20 - 2x^19 - 2x^18 + 2x^17 - 14x^16 + 76x^15 - 20x^14 - 70x^13 - 236x^12 - 599x^11 + 1411x^10 + 1710x^9 - 54x^8 - 2853x^7 - 6351x^6 + 5389x^5 + 9749x^4 - 7353x^3 - 7185x^2 + 2405x + 1369	\( 7^{6}\cdot 43^{2}\cdot 1217^{6} \)	20T664	Trivial (GRH)
20.0.5042687545891045791099349225.1	x^20 - x^19 + 3x^18 + 3x^17 + 20x^16 - 28x^15 + 191x^14 - 111x^13 + 453x^12 - 673x^11 + 3780x^10 - 6271x^9 + 12461x^8 - 9852x^7 + 16545x^6 - 17963x^5 + 24120x^4 - 16890x^3 + 11544x^2 - 5728x + 1229	\( 5^{2}\cdot 61^{6}\cdot 397^{6} \)	20T664	$[2]$ (GRH)
20.4.5042687545891045791099349225.1	x^20 - 3x^19 - 10x^18 + 33x^17 + 79x^16 - 383x^15 + 149x^14 + 1322x^13 - 1835x^12 - 1687x^11 + 5259x^10 - 1067x^9 - 8728x^8 + 14083x^7 - 7182x^6 - 10093x^5 + 17023x^4 - 2485x^3 - 3185x^2 - 8827x + 9409	\( 5^{2}\cdot 61^{6}\cdot 397^{6} \)	20T664	$[2]$ (GRH)
20.0.5042687545891045791099349225.2	x^20 - 2x^19 + 12x^18 - 8x^17 + 38x^16 + 39x^15 + 88x^14 + 156x^13 + 288x^12 + 521x^11 + 805x^10 + 1064x^9 + 2032x^8 + 2084x^7 + 4408x^6 + 5077x^5 + 5680x^4 + 5076x^3 + 8356x^2 + 2295x + 7225	\( 5^{2}\cdot 61^{6}\cdot 397^{6} \)	20T664	$[2]$ (GRH)
20.0.8077201199519837905907996049.1	x^20 - 5x^19 + 20x^18 - 53x^17 + 135x^16 - 359x^15 + 888x^14 - 1964x^13 + 4087x^12 - 6699x^11 + 11320x^10 - 14375x^9 + 18116x^8 - 16578x^7 + 13361x^6 - 7273x^5 + 3010x^4 - 396x^3 + 126x^2 + 54x + 9	\( 3^{24}\cdot 7^{6}\cdot 79^{6} \)	20T664	Trivial (GRH)
20.4.72694810795678541153171964441.1	x^20 - 2x^19 - 4x^18 + 18x^17 - 9x^16 - 24x^15 - x^14 + 62x^13 + x^12 - 160x^11 + 128x^10 - 56x^9 - 94x^8 + 287x^7 - 44x^6 - 747x^5 + 711x^4 + 45x^3 - 81x^2 - 81x + 81	\( 3^{26}\cdot 7^{6}\cdot 79^{6} \)	20T664	Trivial (GRH)
20.4.72694810795678541153171964441.2	x^20 - 8x^19 + 29x^18 - 55x^17 + 80x^16 - 26x^15 - 121x^14 + 500x^13 - 1058x^12 + 1728x^11 - 1947x^10 + 1311x^9 + 238x^8 - 1124x^7 - 286x^6 - 40x^5 + 3317x^4 - 3665x^3 + 1100x^2 + 80x - 29	\( 3^{26}\cdot 7^{6}\cdot 79^{6} \)	20T664	Trivial (GRH)
20.8.169636009043774780412582107929.1	x^20 - 7x^18 - x^17 - 3x^16 - 16x^15 - 367x^14 + 1220x^13 - 645x^12 + 2504x^11 - 3687x^10 - 17015x^9 + 38818x^8 - 3507x^7 - 49759x^6 + 37703x^5 - 126x^4 - 644x^3 - 5506x^2 - 1071x + 2161	\( 29^{2}\cdot 61^{6}\cdot 397^{6} \)	20T664	Trivial (GRH)
20.4.372957170894101746709707868681.1	x^20 - 10x^19 + 35x^18 - 30x^17 - 93x^16 + 132x^15 + 448x^14 - 1366x^13 + 1236x^12 - 6x^11 - 373x^10 - 693x^9 + 5066x^8 - 15386x^7 + 18856x^6 - 5521x^5 - 35907x^4 + 64294x^3 - 15860x^2 - 14823x + 6893	\( 43^{2}\cdot 61^{6}\cdot 397^{6} \)	20T664	$[2]$ (GRH)
20.4.372957170894101746709707868681.2	x^20 + 22x^18 + 187x^16 + 802x^14 + 1857x^12 + 1505x^10 - 3582x^8 - 6574x^6 - 1512x^4 + 188x^2 + 25	\( 43^{2}\cdot 61^{6}\cdot 397^{6} \)	20T664	Trivial (GRH)
20.4.372957170894101746709707868681.3	x^20 - 6x^19 - x^18 + 71x^17 - 92x^16 - 440x^15 + 1356x^14 - 39x^13 - 4772x^12 + 4446x^11 + 12103x^10 - 31859x^9 + 29097x^8 - 8504x^7 - 2704x^6 + 7209x^5 - 12317x^4 + 30117x^3 - 40187x^2 + 23241x + 9311	\( 43^{2}\cdot 61^{6}\cdot 397^{6} \)	20T664	$[2]$ (GRH)
20.0.720989134450436684961004342041.1	x^20 - x^19 + 8x^18 + 4x^17 + 22x^16 + 86x^15 - 7x^14 + 353x^13 + 1368x^12 + 295x^11 + 5903x^10 + 9139x^9 + 5706x^8 + 27869x^7 + 20349x^6 + 39353x^5 + 67346x^4 + 50508x^3 + 82588x^2 + 28758x + 23577	\( 3^{2}\cdot 65657^{6} \)	20T664	Trivial (GRH)
20.12.750553614330423255547227138649.2	x^20 - 4x^19 - 139x^16 + 262x^15 + 245x^14 - 1012x^13 + 2727x^12 - 1350x^11 - 5828x^10 + 9782x^9 - 9436x^8 - 5429x^7 + 20598x^6 - 8915x^5 - 6469x^4 + 9635x^3 - 2343x^2 - 2773x + 691	\( 61^{8}\cdot 397^{6} \)	20T664	Trivial (GRH)
20.4.750553614330423255547227138649.2	x^20 - 4x^19 + 31x^18 - 95x^17 + 380x^16 - 917x^15 + 2195x^14 - 3864x^13 + 4845x^12 - 4682x^11 - 975x^10 + 7563x^9 - 4626x^8 - 84x^7 + 1252x^6 - 5488x^5 + 6505x^4 + 1055x^3 - 4816x^2 + 922x + 701	\( 61^{8}\cdot 397^{6} \)	20T664	Trivial (GRH)
20.4.1897865884771553993938151074321.1	x^20 - 6x^19 + 20x^18 - 43x^17 + 69x^16 + 20x^15 - 412x^14 + 944x^13 - 1323x^12 + 777x^11 + 4726x^10 - 14558x^9 + 13369x^8 + 6119x^7 - 26308x^6 + 25264x^5 - 7173x^4 - 3960x^3 + 1458x^2 + 810x + 243	\( 61^{6}\cdot 97^{2}\cdot 397^{6} \)	20T664	Trivial (GRH)
20.4.1897865884771553993938151074321.2	x^20 - 15x^18 - x^17 + 85x^16 - 15x^15 - 274x^14 + 86x^13 + 454x^12 - 1160x^11 - 1897x^10 + 3810x^9 + 456x^8 - 4631x^7 + 1573x^6 + 1490x^5 - 1257x^4 + 395x^3 + 204x^2 - 392x - 101	\( 61^{6}\cdot 97^{2}\cdot 397^{6} \)	20T664	Trivial (GRH)
20.8.5625420518694215042718790021441.1	x^20 - 19x^18 + 151x^16 - 820x^14 + 3187x^12 - 7771x^10 + 14792x^8 - 4511x^6 - 11460x^4 - 7296x^2 + 6889	\( 61^{6}\cdot 167^{2}\cdot 397^{6} \)	20T664	Trivial (GRH)
20.0.38873271461266729436258307279649.1	x^20 + 25x^18 - 8x^17 + 251x^16 - 195x^15 + 1387x^14 - 1559x^13 + 5728x^12 - 4324x^11 + 20625x^10 - 1757x^9 + 45739x^8 - 6027x^7 + 43006x^6 + 3115x^5 + 5272x^4 + 9596x^3 + 565x^2 + 738x + 743	\( 61^{6}\cdot 397^{6}\cdot 439^{2} \)	20T664	$[2]$ (GRH)
20.0.38873271461266729436258307279649.2	x^20 + 2x^18 + 99x^16 + 345x^14 + 609x^12 + 6808x^10 + 17406x^8 + 72977x^6 + 356580x^4 + 541996x^2 + 212521	\( 61^{6}\cdot 397^{6}\cdot 439^{2} \)	20T664	$[2]$ (GRH)
20.0.38873271461266729436258307279649.3	x^20 - 6x^18 - 3x^17 + 61x^16 + 196x^15 + 270x^14 - 1345x^13 - 2216x^12 - 4079x^11 + 18278x^10 + 65312x^9 + 166118x^8 + 262247x^7 + 347755x^6 + 337297x^5 + 278532x^4 + 157724x^3 + 66967x^2 + 16411x + 3655	\( 61^{6}\cdot 397^{6}\cdot 439^{2} \)	20T664	$[2]$ (GRH)
20.0.55172851269601274567744555766601.1	x^20 + 32x^18 + 392x^16 + 2316x^14 + 7038x^12 + 12193x^10 + 15182x^8 + 12211x^6 + 3337x^4 + 146x^2 + 1	\( 61^{6}\cdot 397^{6}\cdot 523^{2} \)	20T664	$[2]$ (GRH)
20.8.97182738115842943341316071817216.1	x^20 + 22x^18 + 90x^16 - 759x^14 - 4205x^12 + 8223x^10 + 43347x^8 - 29843x^6 - 138146x^4 + 29386x^2 + 78961	\( 2^{16}\cdot 33769^{6} \)	20T664	Trivial (GRH)
20.8.97182738115842943341316071817216.2	x^20 - 8x^19 - 3x^18 + 172x^17 - 249x^16 - 1482x^15 + 3491x^14 + 6297x^13 - 21316x^12 - 12843x^11 + 74021x^10 + 3050x^9 - 157164x^8 + 43731x^7 + 203596x^6 - 96962x^5 - 151522x^4 + 97327x^3 + 35892x^2 - 20943x - 5087	\( 2^{16}\cdot 33769^{6} \)	20T664	Trivial (GRH)
20.12.211505645444809969257911648518144.2	x^20 - 10x^18 + 121x^16 - 904x^14 + 3534x^12 - 7860x^10 + 10421x^8 - 8052x^6 + 3253x^4 - 506x^2 + 1	\( 2^{20}\cdot 61^{6}\cdot 397^{6} \)	20T664	Trivial (GRH)
20.12.211505645444809969257911648518144.3	x^20 - 44x^18 + 689x^16 - 5121x^14 + 19298x^12 - 35636x^10 + 44850x^8 - 175221x^6 + 543009x^4 - 614953x^2 + 157609	\( 2^{20}\cdot 61^{6}\cdot 397^{6} \)	20T664	Trivial (GRH)
20.12.211505645444809969257911648518144.4	x^20 - 16x^18 + 62x^16 + 96x^14 - 849x^12 + 26x^10 + 5566x^8 - 8046x^6 + 2504x^4 - 130x^2 + 1	\( 2^{20}\cdot 61^{6}\cdot 397^{6} \)	20T664	Trivial (GRH)
20.8.211505645444809969257911648518144.4	x^20 - 31x^18 + 341x^16 - 1661x^14 + 3815x^12 - 2872x^10 - 4057x^8 + 9199x^6 - 5591x^4 + 740x^2 + 1	\( 2^{20}\cdot 61^{6}\cdot 397^{6} \)	20T664	Trivial (GRH)
20.16.1554923809853487093461057149075456.1	x^20 - 4x^19 - 33x^18 + 154x^17 + 359x^16 - 2072x^15 - 1485x^14 + 12257x^13 + 1054x^12 - 31939x^11 + 14181x^10 + 19760x^9 - 71590x^8 + 47927x^7 + 152984x^6 - 48488x^5 - 128668x^4 - 21189x^3 + 14432x^2 + 1661x - 461	\( 2^{20}\cdot 33769^{6} \)	20T664	Trivial (GRH)
20.12.2792809998923504933891232182912929.1	x^20 - 4x^19 - 30x^18 + 182x^17 - 202x^16 - 1326x^15 + 10399x^14 - 28727x^13 - 6538x^12 + 251568x^11 - 889350x^10 + 1520072x^9 + 414154x^8 - 8323211x^7 + 23192597x^6 - 39663666x^5 + 40839719x^4 - 21427354x^3 - 6622819x^2 + 27086759x - 14942897	\( 61^{10}\cdot 397^{6} \)	20T664	Trivial (GRH)
20.12.3571845245827993179290792655188224.1	x^20 - 6x^19 - 29x^18 + 230x^17 + 214x^16 - 3572x^15 + 1593x^14 + 29365x^13 - 39183x^12 - 129941x^11 + 299333x^10 + 225757x^9 - 1139860x^8 + 451847x^7 + 1967643x^6 - 2586704x^5 - 189728x^4 + 2856756x^3 - 2626396x^2 + 1042316x - 159652	\( 2^{8}\cdot 97^{2}\cdot 33769^{6} \)	20T664	Trivial (GRH)
20.4.23080384986117811607720055947265625.1	x^20 - 2x^19 - 7x^18 + 21x^17 - 77x^16 + 533x^15 - 1933x^14 + 4400x^13 - 6397x^12 + 26183x^11 - 73376x^10 + 113455x^9 - 99454x^8 + 119205x^7 - 194297x^6 + 120457x^5 - 30647x^4 + 37878x^3 - 13189x^2 - 3276x + 1521	\( 5^{10}\cdot 36497^{6} \)	20T664	$[6]$ (GRH)
20.16.24878780957655793495376914385207296.1	x^20 - 48x^18 + 882x^16 - 7657x^14 + 30875x^12 - 45197x^10 - 6581x^8 + 40523x^6 - 10226x^4 - 852x^2 + 1	\( 2^{24}\cdot 33769^{6} \)	20T664	Trivial (GRH)
20.4.57149523933247890868652682483011584.1	x^20 - 2x^19 - 25x^18 + 22x^17 + 340x^16 + 18x^15 - 2154x^14 - 846x^13 + 7834x^12 + 1924x^11 - 22488x^10 - 23996x^9 - 33136x^8 - 68098x^7 - 95903x^6 - 115590x^5 + 27465x^4 + 228482x^3 + 124442x^2 + 74898x - 1297	\( 2^{12}\cdot 97^{2}\cdot 33769^{6} \)	20T664	$[7]$ (GRH)