Global number field search results

Further refine search

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 165)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.40875195271187982639533.1	x^20 - 3x^19 + 8x^18 - 13x^17 + 15x^16 - 9x^15 - 7x^14 + 25x^13 - 34x^12 + 26x^11 - 3x^10 - 19x^9 + 27x^8 - 18x^7 + 3x^6 + 6x^5 - 4x^4 - x^3 + 4x^2 - 3x + 1	\( 6737\cdot 6067269596435799709 \)	20T1117	Trivial (GRH)
20.0.44048432711756395305029.1	x^20 - 2x^19 + 5x^18 - 11x^17 + 18x^16 - 29x^15 + 41x^14 - 54x^13 + 65x^12 - 72x^11 + 76x^10 - 72x^9 + 65x^8 - 53x^7 + 40x^6 - 28x^5 + 18x^4 - 10x^3 + 5x^2 - 2x + 1	\( 29\cdot 269\cdot 5646511051372438829 \)	20T1117	Trivial (GRH)
20.2.507468787169602318458907.1	x^20 - 2x^19 + 5x^18 - 10x^17 + 17x^16 - 26x^15 + 37x^14 - 48x^13 + 58x^12 - 68x^11 + 71x^10 - 70x^9 + 66x^8 - 58x^7 + 46x^6 - 35x^5 + 24x^4 - 14x^3 + 8x^2 - 4x + 1	\( -\,149\cdot 3405830786373169922543 \)	20T1117	Trivial (GRH)
20.2.1623322664350871304980951.1	x^20 - x^19 + 5x^18 - 6x^17 + 14x^16 - 16x^15 + 27x^14 - 30x^13 + 39x^12 - 42x^11 + 45x^10 - 45x^9 + 41x^8 - 37x^7 + 29x^6 - 23x^5 + 15x^4 - 10x^3 + 6x^2 - 3x + 1	\( -\,11^{2}\cdot 1715717\cdot 7819407156322243 \)	20T1117	Trivial (GRH)
20.4.71591279848050805509607529.1	x^20 - 2x^19 + 5x^17 - 6x^16 - 4x^15 + 15x^14 - 10x^13 - 9x^12 + 22x^11 - 14x^10 - 6x^9 + 17x^8 - 14x^7 + 9x^5 - 8x^4 + 2x^3 + 2x^2 - 2x + 1	\( 1543\cdot 46397459396014779980303 \)	20T1117	Trivial (GRH)
20.4.84403903732404939239448257.1	x^20 - x^19 - x^18 + x^17 + 3x^16 - 6x^14 + x^13 + 4x^12 + 2x^11 - 6x^10 - 5x^9 + 7x^8 + 4x^7 - 3x^6 - 6x^5 + x^4 + 6x^3 - 2x^2 - 2x + 1	\( 23\cdot 5003\cdot 322537\cdot 2274179039448269 \)	20T1117	Trivial (GRH)
20.2.106836019655660313589123979.1	x^20 - x - 1	\( -\,47\cdot 233\cdot 443\cdot 22022174223585405703 \)	20T1117	Trivial (GRH)
20.6.3630677113470048245022922855.1	x^20 - 2x^19 - 2x^18 + 7x^17 - 4x^16 - 6x^15 + 14x^14 - 4x^13 - 14x^12 + 12x^11 + 5x^10 - 14x^9 + 4x^8 + 9x^7 - 7x^6 - 3x^5 + 5x^4 - 4x^2 + x + 1	\( -\,5\cdot 11\cdot 71761\cdot 718519421\cdot 1280259316181 \)	20T1117	Trivial (GRH)
20.2.603312531903136101674066640896.1	x^20 - 4x - 4	\( -\,2^{20}\cdot 84673\cdot 6795125558820960827 \)	20T1117	Trivial (GRH)
20.2.2074523368953668982029265403904.1	x^20 - 4x - 1	\( -\,2^{22}\cdot 389\cdot 33343\cdot 165457\cdot 230472444109 \)	20T1117	Trivial (GRH)
20.2.2074628226453668982029265403904.1	x^20 - 2x - 1	\( -\,2^{20}\cdot 7\cdot 91591\cdot 277790189\cdot 11108940103 \)	20T1117	Trivial (GRH)
20.0.2823696369505147890885637177344.1	x^20 - 4x + 4	\( 2^{20}\cdot 3\cdot 44131\cdot 1339907983\cdot 15180220651 \)	20T1117	Trivial (GRH)
20.0.46677487913385324071882938384384.1	x^20 - 8x + 8	\( 2^{22}\cdot 11\cdot 17\cdot 79\cdot 58787\cdot 2592521\cdot 4942825651 \)	20T1117	Trivial (GRH)
20.0.52901058019946331017970734596096.1	x^20 - 2x + 2	\( 2^{20}\cdot 29\cdot 31\cdot 71\cdot 2503\cdot 315780679311287383 \)	20T1117	Trivial (GRH)
20.0.54975579410380344339686410876021.1	x^20 - x + 2	\( 13\cdot 31\cdot 6373\cdot 731487049\cdot 29262687491040691 \)	20T1117	Trivial (GRH)
20.2.57050104757653668982029265403904.1	x^20 - 2x - 2	\( -\,2^{20}\cdot 3\cdot 23\cdot 2693\cdot 292800011062821558787 \)	20T1117	Trivial (GRH)
20.2.63273674864214675928117061615616.1	x^20 - 8x - 8	\( -\,2^{22}\cdot 3\cdot 2417\cdot 5237\cdot 8563\cdot 14461\cdot 3208177619 \)	20T1117	Trivial (GRH)
20.2.431520591111477505752890101202944.1	x^20 - 8x + 3	\( -\,2^{20}\cdot 71\cdot 34141\cdot 45599\cdot 12974267\cdot 286964963 \)	20T1117	Trivial (GRH)
20.6.1932463314360644067934756475085896.1	x^20 - 3x^19 + x^18 + 4x^17 - 8x^16 + 15x^15 - 5x^14 - 21x^13 + 17x^12 - 12x^11 + 17x^10 + 17x^9 - 23x^8 - 11x^6 + x^5 + 11x^4 + 2x^3 + x^2 - x - 1	\( -\,2^{3}\cdot 73\cdot 452375002463\cdot 7314755471840621663 \)	20T1117	Trivial (GRH)
20.2.2124285086160557037597967773597696.1	x^20 - 8x + 4	\( -\,2^{30}\cdot 3\cdot 348637\cdot 1891551628829138989 \)	20T1117	Trivial (GRH)
20.2.2124311929706157135254217773597696.1	x^20 - 8x - 1	\( -\,2^{10}\cdot 11443\cdot 20507\cdot 2525801\cdot 3500073554229929 \)	20T1117	Trivial (GRH)
20.2.2124338773251757037597967773597696.1	x^20 - 8x - 4	\( -\,2^{30}\cdot 1543\cdot 1282206516954188975453 \)	20T1117	Trivial (GRH)
20.14.6596444062778575692259474694903036.1	x^20 - 6x^19 - 3x^18 + 72x^17 - 43x^16 - 369x^15 + 312x^14 + 1064x^13 - 858x^12 - 1892x^11 + 1158x^10 + 2101x^9 - 753x^8 - 1396x^7 + 176x^6 + 505x^5 + 23x^4 - 84x^3 - 12x^2 + 5x + 1	\( -\,2^{2}\cdot 31\cdot 367\cdot 2909789\cdot 49815057601948016135803 \)	20T1117	Trivial (GRH)
20.2.6898322689130572777325813232251579.1	x^20 - 3x + 1	\( -\,1277\cdot 10153388466449\cdot 532036718457786023 \)	20T1117	Trivial (GRH)
20.2.6898322898845772777325813232251579.1	x^20 - 3x - 1	\( -\,31253\cdot 158831432499427\cdot 1389681750494309 \)	20T1117	Trivial (GRH)
20.2.6953298375376972777325813232251579.1	x^20 - 3x - 2	\( -\,37\cdot 2605646194199\cdot 72122985667310474233 \)	20T1117	Trivial (GRH)
20.12.14785775529558449808509909620516096.1	x^20 - 8x^19 + 11x^18 + 65x^17 - 182x^16 - 162x^15 + 879x^14 - 13x^13 - 2124x^12 + 731x^11 + 2905x^10 - 1328x^9 - 2313x^8 + 1032x^7 + 1043x^6 - 373x^5 - 245x^4 + 57x^3 + 26x^2 - 3x - 1	\( 2^{8}\cdot 31\cdot 15731\cdot 118436650998004135176878681 \)	20T1117	Trivial (GRH)
20.18.19550982321594346663126636979348528.1	x^20 - 4x^19 - 12x^18 + 61x^17 + 51x^16 - 390x^15 - 66x^14 + 1357x^13 - 152x^12 - 2790x^11 + 638x^10 + 3442x^9 - 872x^8 - 2470x^7 + 533x^6 + 948x^5 - 123x^4 - 166x^3 + x^2 + 10x + 1	\( -\,2^{4}\cdot 7\cdot 2069\cdot 135002711\cdot 624953320648889659991 \)	20T1117	Trivial (GRH)
20.16.19798438370516234940186682983712009.1	x^20 - 8x^19 + 11x^18 + 65x^17 - 182x^16 - 162x^15 + 879x^14 - 13x^13 - 2124x^12 + 731x^11 + 2905x^10 - 1328x^9 - 2313x^8 + 1032x^7 + 1043x^6 - 373x^5 - 245x^4 + 60x^3 + 26x^2 - 3x - 1	\( 72889\cdot 14236377761\cdot 19079607690028483121 \)	20T1117	Trivial (GRH)
20.0.33725659873378227222674186767748421.1	x^20 - 9x + 9	\( 3^{18}\cdot 33330605479\cdot 2611768428686491 \)	20T1117	$[2]$ (GRH)
20.18.38975590571565076699203650521995899.1	x^20 - 4x^19 - 12x^18 + 59x^17 + 55x^16 - 362x^15 - 119x^14 + 1200x^13 + 122x^12 - 2332x^11 - 73x^10 + 2694x^9 + 113x^8 - 1791x^7 - 174x^6 + 630x^5 + 106x^4 - 97x^3 - 22x^2 + 4x + 1	\( -\,162529\cdot 3567372786643\cdot 67222296673312217 \)	20T1117	Trivial (GRH)
20.2.47522305461354572777325813232251579.1	x^20 - 9x - 9	\( -\,3^{18}\cdot 17\cdot 4002959\cdot 866580853\cdot 2080059529 \)	20T1117	Trivial (GRH)
20.0.114973625208111027222674186767748421.1	x^20 - 3x + 3	\( 3^{19}\cdot 7\cdot 43\cdot 53\cdot 6200861344763935261871 \)	20T1117	$[2]$ (GRH)
20.0.121869873478730346331017970734596096.1	x^20 - 2x + 3	\( 2^{20}\cdot 1489\cdot 188827\cdot 413368763645047857407 \)	20T1117	Trivial (GRH)
20.0.121871948000120780344339686410876021.1	x^20 - x + 3	\( 139\cdot 1019\cdot 6343\cdot 207908341931\cdot 652451362447457 \)	20T1117	Trivial (GRH)
20.2.121871948004077619655660313589123979.1	x^20 - x - 3	\( -\,11\cdot 67\cdot 281\cdot 449\cdot 1991929\cdot 657975540874249175867 \)	20T1117	Trivial (GRH)
20.2.128770270796087372777325813232251579.1	x^20 - 3x - 3	\( -\,3^{19}\cdot 11\cdot 317\cdot 24391\cdot 1302657414478831561 \)	20T1117	Trivial (GRH)
20.16.152091764331867572167292799980089465.1	x^20 - 8x^19 + 11x^18 + 65x^17 - 182x^16 - 162x^15 + 879x^14 - 13x^13 - 2124x^12 + 731x^11 + 2905x^10 - 1328x^9 - 2313x^8 + 1032x^7 + 1043x^6 - 371x^5 - 245x^4 + 58x^3 + 26x^2 - 3x - 1	\( 5\cdot 4860586389913\cdot 6258165255430831836461 \)	20T1117	Trivial (GRH)
20.0.1139887444013945446331017970734596096.1	x^20 - 4x + 7	\( 2^{22}\cdot 3\cdot 10531445190787\cdot 8601869284925359 \)	20T1117	Trivial (GRH)
20.2.2175240440437716006500319000164040704.1	x^20 - 4x + 2	\( -\,2^{40}\cdot 31\cdot 127\cdot 137\cdot 173\cdot 1073393\cdot 19752251119 \)	20T1117	Trivial (GRH)
20.2.2175295415914247206500319000164040704.1	x^20 - 4x + 1	\( -\,2^{41}\cdot 3\cdot 323811320123\cdot 1018298585533 \)	20T1117	Trivial (GRH)
20.2.2175350391600493606500319000164040704.1	x^20 - 4x - 2	\( -\,2^{40}\cdot 3\cdot 4363\cdot 3809123\cdot 39682399900057 \)	20T1117	Trivial (GRH)
20.2.2177202764651917306500319000164040704.1	x^20 - 8x - 5	\( -\,2^{20}\cdot 3\cdot 692114119419071612835031827343 \)	20T1117	Trivial (GRH)
20.2.2297167364021204006500319000164040704.1	x^20 - 4x - 3	\( -\,2^{41}\cdot 11\cdot 73\cdot 3571\cdot 1127981\cdot 322965130559 \)	20T1117	Trivial (GRH)
20.10.2548455431073477016604170857585804856.1	x^20 - 2x^19 - 18x^18 + 32x^17 + 134x^16 - 209x^15 - 533x^14 + 724x^13 + 1229x^12 - 1447x^11 - 1676x^10 + 1708x^9 + 1327x^8 - 1182x^7 - 571x^6 + 466x^5 + 111x^4 - 96x^3 - 3x^2 + 8x - 1	\( -\,2^{3}\cdot 31\cdot 17715098927\cdot 20327576459\cdot 28536202405829 \)	20T1117	Trivial (GRH)
20.0.3602879183265554586582754492683649024.1	x^20 - 4x + 8	\( 2^{18}\cdot 11\cdot 40370021\cdot 30949819216276950435091 \)	20T1117	Trivial (GRH)
20.2.3602880220527239013417245507316350976.1	x^20 - 4x - 8	\( -\,2^{18}\cdot 3\cdot 17\cdot 19457\cdot 13850448828456975170298697 \)	20T1117	Trivial (GRH)
20.0.7205758885161951386582754492683649024.1	x^20 - 2x + 4	\( 2^{18}\cdot 3\cdot 3947\cdot 253479091\cdot 9158182249623900791 \)	20T1117	Trivial (GRH)
20.2.7205759922423635813417245507316350976.1	x^20 - 2x - 4	\( -\,2^{18}\cdot 397\cdot 1277\cdot 1873\cdot 28948141385001745995667 \)	20T1117	Trivial (GRH)
20.8.8207895696809367749179738665307721489.1	x^20 - 4x^19 + 3x^18 + 11x^17 - 30x^16 + 27x^15 + 13x^14 - 70x^13 + 98x^12 - 56x^11 - 42x^10 + 121x^9 - 113x^8 + 36x^7 + 35x^6 - 52x^5 + 30x^4 - 4x^3 - 5x^2 + 4x - 1	\( 31\cdot 211\cdot 527466481\cdot 2378991077155845986721509 \)	20T1117	Trivial (GRH)