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
20.0.121340256145132297570901.1	x^20 - x^19 + 6x^18 - 3x^17 + 20x^16 - 10x^15 + 40x^14 - 7x^13 + 73x^12 + 20x^11 + 98x^10 + 32x^9 + 72x^8 + 32x^7 + 82x^6 + 64x^5 + 64x^4 + 35x^3 + 17x^2 + 5x + 1	\( 41381^{5} \)	20T965	Trivial (GRH)
20.2.264180002785783378345984.1	x^20 + 6x^18 + 13x^16 + 7x^14 - 21x^12 - 41x^10 - 38x^8 - 35x^6 - 14x^4 + 7x^2 - 1	\( -\,2^{26}\cdot 89^{8} \)	20T965	Trivial (GRH)
20.2.264180002785783378345984.2	x^20 - 6x^18 + 13x^16 - 7x^14 - 21x^12 + 41x^10 - 38x^8 + 35x^6 - 14x^4 - 7x^2 - 1	\( -\,2^{26}\cdot 89^{8} \)	20T965	Trivial (GRH)
20.0.950930896615524819533824.1	x^20 - 4x^19 + 8x^18 - 7x^17 + 3x^16 - 8x^15 + 16x^14 + 4x^13 + 2x^12 - 64x^11 + 24x^10 + 78x^9 - 6x^8 - 80x^7 + 8x^6 + 40x^5 - 9x^4 - 4x^3 - x + 1	\( 2^{50}\cdot 61^{5} \)	20T965	Trivial
20.4.1793075893656120387960832.1	x^20 - 4x^19 + 28x^17 - 56x^16 + 16x^15 + 96x^14 - 212x^13 + 226x^12 + 76x^11 - 536x^10 + 400x^9 + 274x^8 - 436x^7 + 20x^6 + 160x^5 - 34x^4 - 32x^3 + 12x^2 + 4x - 2	\( 2^{40}\cdot 277^{5} \)	20T965	Trivial (GRH)
20.4.15214894345848397112541184.1	x^20 + x^18 + x^16 + 4x^14 - 34x^12 - 54x^10 + 102x^8 + 28x^6 + 69x^4 - 183x^2 + 61	\( 2^{54}\cdot 61^{5} \)	20T965	Trivial (GRH)
20.0.66311033145747514657031168.1	x^20 - 4x^19 + 15x^18 - 50x^17 + 134x^16 - 285x^15 + 533x^14 - 860x^13 + 1089x^12 - 1054x^11 + 1227x^10 - 2545x^9 + 5545x^8 - 9396x^7 + 12677x^6 - 13646x^5 + 11664x^4 - 7435x^3 + 3423x^2 - 1021x + 229	\( 2^{10}\cdot 36497^{5} \)	20T965	Trivial (GRH)
20.4.66311033145747514657031168.1	x^20 - 5x^19 + 19x^18 - 58x^17 + 148x^16 - 318x^15 + 647x^14 - 1126x^13 + 1809x^12 - 2856x^11 + 3545x^10 - 4617x^9 + 5447x^8 - 4421x^7 + 4166x^6 - 3071x^5 + 1627x^4 - 495x^3 + 144x^2 + 192x + 23	\( 2^{10}\cdot 36497^{5} \)	20T965	Trivial (GRH)
20.0.66311033145747514657031168.2	x^20 - 7x^19 + 36x^18 - 143x^17 + 460x^16 - 1243x^15 + 2873x^14 - 5714x^13 + 9802x^12 - 14545x^11 + 18690x^10 - 20784x^9 + 20007x^8 - 16441x^7 + 11349x^6 - 6414x^5 + 2707x^4 - 756x^3 + 76x^2 + 31x + 47	\( 2^{10}\cdot 36497^{5} \)	20T965	Trivial (GRH)
20.4.66311033145747514657031168.2	x^20 - 3x^19 + 2x^18 + x^17 - 13x^16 - 50x^15 + 172x^14 - 113x^13 - 56x^12 + 664x^11 - 317x^10 + 283x^9 + 1070x^8 - 157x^7 + 629x^6 + 205x^5 - 288x^4 + 907x^3 - 103x^2 - 216x + 423	\( 2^{10}\cdot 36497^{5} \)	20T965	Trivial (GRH)
20.10.1082081291410568717705150464.1	x^20 - 10x^18 + 36x^16 - 48x^14 - 13x^12 + 78x^10 - 21x^8 - 52x^6 + 24x^4 + 8x^2 - 4	\( -\,2^{38}\cdot 89^{8} \)	20T965	Trivial (GRH)
20.2.1082081291410568717705150464.1	x^20 + 10x^18 + 36x^16 + 48x^14 - 13x^12 - 78x^10 - 21x^8 + 52x^6 + 24x^4 - 8x^2 - 4	\( -\,2^{38}\cdot 89^{8} \)	20T965	$[2]$ (GRH)
20.6.1082081291410568717705150464.1	x^20 - 8x^18 + 15x^16 + 12x^14 - 81x^12 + 208x^10 - 512x^8 + 312x^6 + 170x^4 + 12x^2 - 1	\( -\,2^{38}\cdot 89^{8} \)	20T965	Trivial (GRH)
20.6.1082081291410568717705150464.2	x^20 + 8x^18 + 15x^16 - 12x^14 - 81x^12 - 208x^10 - 512x^8 - 312x^6 + 170x^4 - 12x^2 - 1	\( -\,2^{38}\cdot 89^{8} \)	20T965	Trivial (GRH)
20.4.1278738646439085866881737729.1	x^20 - 7x^19 + 21x^18 - 34x^17 + 16x^16 + 90x^15 - 371x^14 + 720x^13 - 1016x^12 + 794x^11 + 321x^10 - 2526x^9 + 5329x^8 - 7939x^7 + 9365x^6 - 8839x^5 + 6866x^4 - 4198x^3 + 1920x^2 - 493x + 53	\( 3^{6}\cdot 17^{5}\cdot 4153^{5} \)	20T965	Trivial (GRH)
20.8.1278738646439085866881737729.1	x^20 - 7x^19 + 19x^18 - 25x^17 + x^16 + 106x^15 - 414x^14 + 940x^13 - 1221x^12 + 533x^11 + 981x^10 - 1779x^9 + 785x^8 + 800x^7 - 1103x^6 + 231x^5 + 338x^4 - 211x^3 - 6x^2 + 15x - 1	\( 3^{6}\cdot 17^{5}\cdot 4153^{5} \)	20T965	Trivial (GRH)
20.6.3042351129053791179853791232.2	x^20 - 2x^19 - 10x^18 + 18x^17 + 18x^16 + 74x^15 - 338x^14 + 252x^13 - 95x^12 + 184x^11 + 1156x^10 - 3512x^9 + 4896x^8 - 6534x^7 + 7762x^6 - 6956x^5 + 5508x^4 - 3418x^3 + 1830x^2 - 1156x + 191	\( -\,2^{30}\cdot 4903^{5} \)	20T965	Trivial (GRH)
20.6.3042351129053791179853791232.3	x^20 - 12x^18 - 22x^17 + 10x^16 + 134x^15 + 102x^14 + 16x^13 - 213x^12 - 140x^11 - 720x^10 - 598x^9 - 207x^8 + 922x^7 + 1176x^6 + 1060x^5 + 195x^4 - 446x^3 - 292x^2 - 36x - 1	\( -\,2^{30}\cdot 4903^{5} \)	20T965	Trivial (GRH)
20.10.4489512207214609404507717632.1	x^20 - 6x^19 + 3x^18 + 48x^17 - 130x^16 + 82x^15 + 170x^14 - 320x^13 + 72x^12 + 138x^11 + 81x^10 + 18x^9 + 137x^8 - 454x^7 - 217x^6 + 894x^5 + 363x^4 - 238x^3 - 60x^2 + 18x - 1	\( -\,2^{26}\cdot 19^{8}\cdot 83^{5} \)	20T965	Trivial (GRH)
20.2.4489512207214609404507717632.1	x^20 - 2x^19 + 9x^18 - 12x^17 + 37x^16 - 86x^15 - 14x^14 - 46x^13 - 40x^12 + 58x^11 + 180x^10 - 130x^9 + 364x^8 - 258x^7 - 90x^6 - 42x^5 - 425x^4 + 128x^3 - 197x^2 + 70x - 17	\( -\,2^{26}\cdot 19^{8}\cdot 83^{5} \)	20T965	Trivial (GRH)
20.4.8733767413172976390878789632.1	x^20 - 6x^19 + 13x^18 - 44x^16 + 78x^15 + 9x^14 - 176x^13 - 220x^12 + 146x^11 + 1380x^10 + 1140x^9 + 342x^8 + 456x^7 - 210x^6 - 490x^5 - 280x^4 + 34x^3 + 45x^2 + 4x - 1	\( 2^{20}\cdot 61^{5}\cdot 397^{5} \)	20T965	Trivial (GRH)
20.8.8733767413172976390878789632.1	x^20 - 4x^19 - 2x^18 + 18x^17 + 15x^16 - 24x^15 - 72x^14 - 36x^13 - 21x^12 - 52x^11 + 321x^10 + 778x^9 + 475x^8 - 370x^7 - 960x^6 - 1132x^5 - 1154x^4 - 990x^3 - 579x^2 - 190x - 25	\( 2^{20}\cdot 61^{5}\cdot 397^{5} \)	20T965	Trivial (GRH)
20.8.46045894455076759556429185024.1	x^20 - 6x^19 + 21x^18 - 50x^17 + 71x^16 - 74x^15 - 72x^14 + 476x^13 - 939x^12 + 1552x^11 - 1443x^10 + 1964x^9 - 981x^8 - 502x^7 - 1284x^6 - 1218x^5 + 137x^4 + 298x^3 + 57x^2 - 4x - 1	\( 2^{20}\cdot 33769^{5} \)	20T965	Trivial (GRH)
20.8.46045894455076759556429185024.2	x^20 - 9x^19 + 25x^18 + 31x^17 - 407x^16 + 1186x^15 - 1145x^14 - 2608x^13 + 10648x^12 - 15324x^11 + 5219x^10 + 18865x^9 - 39562x^8 + 41696x^7 - 28185x^6 + 12502x^5 - 3251x^4 + 263x^3 + 66x^2 - 6x - 1	\( 2^{20}\cdot 33769^{5} \)	20T965	Trivial (GRH)
20.0.145492041550402658631877714944.1	x^20 + 11x^18 - 13x^17 + 41x^16 - 35x^15 + 98x^14 - 82x^13 + 391x^12 - 1782x^11 + 5861x^10 - 14623x^9 + 30214x^8 - 49737x^7 + 62776x^6 - 59352x^5 + 41464x^4 - 20953x^3 + 7352x^2 - 1632x + 179	\( 2^{10}\cdot 3^{4}\cdot 17^{5}\cdot 4153^{5} \)	20T965	Trivial (GRH)
20.12.145492041550402658631877714944.1	x^20 - 10x^19 + 29x^18 + 10x^17 - 186x^16 + 296x^15 - 45x^14 - 456x^13 + 629x^12 - 538x^11 + 2277x^10 - 2736x^9 - 2655x^8 + 5090x^7 - 767x^6 - 1130x^5 + 366x^4 - 578x^3 + 487x^2 - 68x - 17	\( 2^{10}\cdot 3^{4}\cdot 17^{5}\cdot 4153^{5} \)	20T965	Trivial (GRH)
20.4.145492041550402658631877714944.1	x^20 - x^19 - 2x^18 - x^17 - 8x^16 - 55x^15 - 142x^14 + 35x^13 - 7x^12 - 895x^11 + 915x^10 + 993x^9 - 851x^8 + 1056x^7 - 2540x^6 + 3371x^5 + 1144x^4 + 4138x^3 + 2012x^2 + 245x - 49	\( 2^{10}\cdot 3^{4}\cdot 17^{5}\cdot 4153^{5} \)	20T965	Trivial (GRH)
20.4.1309428373953623927686899434496.1	x^20 - 4x^19 + 10x^18 - 37x^17 + 138x^16 - 312x^15 + 458x^14 - 751x^13 + 1876x^12 - 4291x^11 + 4771x^10 + 1076x^9 - 14353x^8 + 22186x^7 - 19348x^6 + 9111x^5 - 7621x^4 + 3787x^3 + 3137x^2 - 7870x + 2689	\( 2^{10}\cdot 3^{6}\cdot 17^{5}\cdot 4153^{5} \)	20T965	Trivial (GRH)
20.12.1697562448531136375219997900800.1	x^20 - 6x^19 - 8x^18 + 126x^17 - 178x^16 - 736x^15 + 2257x^14 + 514x^13 - 8865x^12 + 6504x^11 + 16536x^10 - 23970x^9 - 16173x^8 + 53162x^7 - 28956x^6 - 16132x^5 + 21457x^4 - 2988x^3 - 3477x^2 + 712x + 211	\( 2^{20}\cdot 5^{2}\cdot 36497^{5} \)	20T965	Trivial (GRH)
20.0.5993774335551541600171439685632.1	x^20 - 8x^19 + 24x^18 - 18x^17 - 42x^16 - 168x^15 + 2166x^14 - 9680x^13 + 28906x^12 - 66286x^11 + 123592x^10 - 193668x^9 + 260217x^8 - 302858x^7 + 307800x^6 - 274640x^5 + 211730x^4 - 133196x^3 + 61838x^2 - 17836x + 2401	\( 2^{20}\cdot 89417^{5} \)	20T965	$[2]$ (GRH)
20.12.60656583790251750925293253033984.1	x^20 - x^19 - 4x^18 + 53x^17 - 180x^16 + x^15 + 932x^14 - 3739x^13 + 4578x^12 + 5437x^11 - 12484x^10 + 13485x^9 - 5616x^8 - 19515x^7 + 17168x^6 + 6963x^5 - 6524x^4 - 1563x^3 + 924x^2 + 133x - 53	\( 2^{24}\cdot 83^{5}\cdot 983^{5} \)	20T965	Trivial (GRH)
20.16.60656583790251750925293253033984.1	x^20 - 5x^19 - 12x^18 + 129x^17 - 308x^16 - 69x^15 + 2418x^14 - 5821x^13 + 1666x^12 + 13619x^11 - 18006x^10 - 3623x^9 + 21094x^8 - 10043x^7 - 6064x^6 + 6211x^5 - 600x^4 - 847x^3 + 286x^2 - 31x + 1	\( 2^{24}\cdot 83^{5}\cdot 983^{5} \)	20T965	Trivial (GRH)
20.4.60656583790251750925293253033984.1	x^20 - 5x^19 + 15x^18 + 18x^17 - 185x^16 + 479x^15 + 161x^14 - 3084x^13 + 6079x^12 - 59x^11 - 23353x^10 + 49692x^9 - 41581x^8 - 23137x^7 + 109909x^6 - 157510x^5 + 139437x^4 - 84541x^3 + 35201x^2 - 9466x + 1532	\( 2^{24}\cdot 83^{5}\cdot 983^{5} \)	20T965	Trivial (GRH)
20.8.60656583790251750925293253033984.1	x^20 + 7x^18 - 38x^17 - x^16 - 96x^15 + 594x^14 + 60x^13 + 591x^12 - 9764x^11 + 7103x^10 - 2574x^9 + 50897x^8 - 53828x^7 + 16940x^6 - 33280x^5 - 1281x^4 + 49772x^3 - 27551x^2 + 534x + 1483	\( 2^{24}\cdot 83^{5}\cdot 983^{5} \)	20T965	Trivial (GRH)
20.12.60656583790251750925293253033984.2	x^20 - 5x^19 - 12x^18 + 53x^17 + 143x^16 - 438x^15 - 522x^14 + 2262x^13 + 334x^12 - 6620x^11 + 1056x^10 + 10400x^9 - 2344x^8 - 9000x^7 + 3520x^6 + 7696x^5 + 240x^4 - 3616x^3 - 2032x^2 - 336x + 16	\( 2^{24}\cdot 83^{5}\cdot 983^{5} \)	20T965	Trivial (GRH)
20.16.60656583790251750925293253033984.2	x^20 - 5x^19 - 19x^18 + 131x^17 + 82x^16 - 1391x^15 + 655x^14 + 7617x^13 - 8202x^12 - 22465x^11 + 35119x^10 + 32681x^9 - 74266x^8 - 11839x^7 + 78011x^6 - 25049x^5 - 29654x^4 + 26449x^3 - 8713x^2 + 1333x - 79	\( 2^{24}\cdot 83^{5}\cdot 983^{5} \)	20T965	Trivial (GRH)
20.4.60656583790251750925293253033984.2	x^20 - 10x^19 + 54x^18 - 173x^17 + 372x^16 - 564x^15 + 576x^14 - 589x^13 + 486x^12 - 326x^11 + 1828x^10 - 2917x^9 - 2730x^8 - 2860x^7 + 9332x^6 + 21581x^5 + 12684x^4 - 2140x^3 - 13884x^2 - 9209x - 3659	\( 2^{24}\cdot 83^{5}\cdot 983^{5} \)	20T965	$[2]$ (GRH)
20.8.60656583790251750925293253033984.2	x^20 - 6x^19 + 8x^18 + 21x^17 - 130x^16 + 56x^15 + 632x^14 - 2013x^13 + 1535x^12 + 3162x^11 - 7188x^10 + 2022x^9 + 12612x^8 - 9338x^7 - 9668x^6 + 12710x^5 - 6487x^4 - 8092x^3 + 8246x^2 + 2381x - 811	\( 2^{24}\cdot 83^{5}\cdot 983^{5} \)	20T965	Trivial (GRH)
20.12.60656583790251750925293253033984.3	x^20 - 10x^19 + 26x^18 + 37x^17 - 277x^16 + 408x^15 + 62x^14 - 1434x^13 + 3782x^12 - 2848x^11 - 8988x^10 + 25740x^9 - 27084x^8 - 416x^7 + 45560x^6 - 58280x^5 + 9864x^4 + 35584x^3 - 24480x^2 - 432x + 3184	\( 2^{24}\cdot 83^{5}\cdot 983^{5} \)	20T965	Trivial (GRH)
20.8.60656583790251750925293253033984.3	x^20 - 5x^19 + 21x^18 - 6x^17 - 133x^16 + 691x^15 - 2067x^14 + 4200x^13 - 6887x^12 + 7539x^11 - 4791x^10 - 3064x^9 + 13209x^8 - 18369x^7 + 15399x^6 - 2356x^5 - 7759x^4 + 11773x^3 - 5869x^2 + 778x + 4	\( 2^{24}\cdot 83^{5}\cdot 983^{5} \)	20T965	Trivial (GRH)
20.12.60656583790251750925293253033984.4	x^20 - x^19 - 2x^18 - 61x^17 + 82x^16 + 185x^15 - 574x^14 + 2781x^13 - 6545x^12 + 11008x^11 - 14888x^10 + 11974x^9 - 4938x^8 - 7732x^7 + 20916x^6 - 11456x^5 - 6359x^4 + 6493x^3 - 302x^2 - 699x + 113	\( 2^{24}\cdot 83^{5}\cdot 983^{5} \)	20T965	Trivial (GRH)
20.8.60656583790251750925293253033984.4	x^20 - 6x^19 + 2x^18 + 41x^17 - 78x^16 - 62x^15 + 154x^14 + 111x^13 - 615x^12 + 1334x^11 - 1068x^10 - 2034x^9 + 6944x^8 - 9330x^7 + 7730x^6 - 6010x^5 + 5691x^4 - 4180x^3 + 1160x^2 + 553x - 337	\( 2^{24}\cdot 83^{5}\cdot 983^{5} \)	20T965	Trivial (GRH)
20.12.6137624919604778598575554238087168.1	x^20 - 2x^19 - 28x^18 + 52x^17 + 180x^16 + 122x^15 - 1296x^14 - 2370x^13 + 4507x^12 + 8900x^11 - 534x^10 - 22878x^9 - 13201x^8 + 27386x^7 - 23540x^6 - 15414x^5 + 64907x^4 + 15882x^3 - 17440x^2 - 1098x + 857	\( 2^{30}\cdot 89417^{5} \)	20T965	Trivial (GRH)
20.16.6137624919604778598575554238087168.1	x^20 - 10x^19 + 2x^18 + 224x^17 - 320x^16 - 1938x^15 + 2974x^14 + 8182x^13 - 11627x^12 - 15160x^11 + 29428x^10 + 2814x^9 - 62391x^8 + 26706x^7 + 96694x^6 - 28146x^5 - 83435x^4 + 2606x^3 + 29658x^2 + 4686x - 1061	\( 2^{30}\cdot 89417^{5} \)	20T965	Trivial (GRH)
20.4.6137624919604778598575554238087168.1	x^20 + 14x^18 - 109x^16 - 3154x^14 - 21961x^12 - 54172x^10 + 47600x^8 + 485554x^6 + 845737x^4 + 536502x^2 + 89417	\( 2^{30}\cdot 89417^{5} \)	20T965	Trivial (GRH)
20.8.6137624919604778598575554238087168.1	x^20 - 26x^18 - 52x^17 + 114x^16 + 1114x^15 + 660x^14 - 6202x^13 - 6816x^12 + 2590x^11 + 29930x^10 + 27898x^9 - 54473x^8 - 366x^7 - 46534x^6 + 251128x^5 - 161650x^4 - 7582x^3 - 321116x^2 + 142390x - 9721	\( 2^{30}\cdot 89417^{5} \)	20T965	Trivial (GRH)
20.12.6137624919604778598575554238087168.2	x^20 - 8x^18 - 44x^17 - 99x^16 + 316x^15 - 116x^14 - 4252x^13 + 398x^12 + 23612x^11 + 20268x^10 - 2132x^9 + 73958x^8 - 57996x^7 - 748492x^6 - 679380x^5 + 842833x^4 + 1536084x^3 + 739708x^2 + 110384x - 1507	\( 2^{30}\cdot 89417^{5} \)	20T965	Trivial (GRH)
20.16.6137624919604778598575554238087168.2	x^20 - 14x^18 - 109x^16 + 3154x^14 - 21961x^12 + 54172x^10 + 47600x^8 - 485554x^6 + 845737x^4 - 536502x^2 + 89417	\( 2^{30}\cdot 89417^{5} \)	20T965	Trivial (GRH)
20.4.6137624919604778598575554238087168.2	x^20 - 10x^19 + 58x^18 - 178x^17 + 250x^16 + 426x^15 - 2472x^14 + 3734x^13 + 2912x^12 - 17860x^11 + 8920x^10 + 69404x^9 - 154021x^8 - 2374x^7 + 416040x^6 - 179144x^5 - 1685496x^4 + 4189308x^3 - 4970590x^2 + 3135134x - 807593	\( 2^{30}\cdot 89417^{5} \)	20T965	Trivial (GRH)
20.8.6137624919604778598575554238087168.2	x^20 - 4x^19 - 20x^18 + 72x^17 + 188x^16 - 236x^15 - 1824x^14 - 1304x^13 + 8035x^12 + 14802x^11 + 16700x^10 - 87116x^9 - 106866x^8 - 21442x^7 + 293328x^6 + 432972x^5 + 76430x^4 - 646564x^3 - 289610x^2 - 69246x - 323829	\( 2^{30}\cdot 89417^{5} \)	20T965	Trivial (GRH)