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 66)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.33956209217798320520429568.1	x^20 - 13x^18 + 83x^16 - 346x^14 + 1032x^12 - 2244x^10 + 3627x^8 - 4135x^6 + 3190x^4 - 1515x^2 + 327	\( 2^{20}\cdot 3^{11}\cdot 109^{7} \)	20T955	Trivial
20.0.79750362933544679387430912.1	x^20 - 10x^18 + 50x^16 - 142x^14 + 294x^12 - 432x^10 + 450x^8 - 310x^6 + 130x^4 - 30x^2 + 3	\( 2^{28}\cdot 3^{11}\cdot 109^{6} \)	20T955	Trivial (GRH)
20.2.878763561130467602500000000.1	x^20 - x^19 - x^18 + 13x^17 - 4x^16 - 44x^15 + 130x^14 - 212x^13 + 326x^12 - 497x^11 + 741x^10 - 864x^9 + 776x^8 - 471x^7 + 179x^6 + 16x^5 - 50x^4 + 28x^3 - 5x^2 - 3x + 1	\( -\,2^{8}\cdot 5^{10}\cdot 29^{4}\cdot 89^{6} \)	20T955	Trivial (GRH)
20.2.878763561130467602500000000.2	x^20 - 7x^19 + 14x^18 + 4x^17 - 21x^16 - 88x^15 + 227x^14 + 14x^13 - 455x^12 + 221x^11 + 584x^10 - 853x^9 + 490x^8 - 268x^7 + 157x^6 + 244x^5 - 569x^4 + 482x^3 - 241x^2 + 71x - 11	\( -\,2^{8}\cdot 5^{10}\cdot 29^{4}\cdot 89^{6} \)	20T955	Trivial (GRH)
20.4.7963794772744862647656250000.1	x^20 - 2x^19 - 5x^18 + 5x^17 + 41x^16 - 9x^15 - 174x^14 - 67x^13 + 698x^12 - 51x^11 - 924x^10 - 92x^9 + 155x^8 + 1056x^7 + 39x^6 - 1003x^5 + 307x^4 + 56x^3 - 120x^2 + 80x - 16	\( 2^{4}\cdot 5^{11}\cdot 29^{5}\cdot 89^{6} \)	20T955	Trivial (GRH)
20.6.54358621807848867360458984375.1	x^20 - x^19 + 3x^18 + 3x^17 - 21x^16 + 29x^15 - 34x^14 + 88x^13 + 332x^12 + 228x^11 - 225x^10 - 1367x^9 - 2252x^8 + 242x^7 + 1914x^6 + 406x^5 - 568x^4 - 160x^3 + 47x^2 + 39x - 9	\( -\,5^{10}\cdot 19^{9}\cdot 29^{7} \)	20T955	Trivial (GRH)
20.0.88755119674177227852500000000.1	x^20 - 2x^19 - 3x^18 + 19x^17 - 10x^16 - 61x^15 + 108x^14 + 38x^13 - 204x^12 + 43x^11 + 211x^10 - 44x^9 - 250x^8 - 93x^7 + 981x^6 - 1520x^5 + 1286x^4 - 690x^3 + 239x^2 - 50x + 5	\( 2^{8}\cdot 5^{10}\cdot 29^{4}\cdot 89^{6}\cdot 101 \)	20T955	Trivial (GRH)
20.4.127420716363917802362500000000.1	x^20 - 3x^19 + 7x^18 - 22x^17 + 33x^16 - 20x^15 - 75x^14 + 474x^13 - 1429x^12 + 3404x^11 - 6544x^10 + 10182x^9 - 13151x^8 + 13304x^7 - 10821x^6 + 6146x^5 - 2606x^4 + 355x^3 + 9x^2 + 84x + 16	\( 2^{8}\cdot 5^{11}\cdot 29^{5}\cdot 89^{6} \)	20T955	Trivial (GRH)
20.0.407746292364536967560000000000.1	x^20 + 11x^18 + 74x^16 + 352x^14 + 1136x^12 + 2564x^10 + 3708x^8 + 2645x^6 + 959x^4 + 240x^2 + 29	\( 2^{12}\cdot 5^{10}\cdot 29^{5}\cdot 89^{6} \)	20T955	Trivial (GRH)
20.6.1171522021720880762078857421875.1	x^20 - 2x^19 + x^18 + 5x^17 - 62x^16 - 118x^15 - 74x^14 - 121x^13 + 174x^12 + 1042x^11 + 2186x^10 + 3878x^9 + 4441x^8 + 2115x^7 + 47x^6 + 260x^5 - 23x^4 - 85x^3 + 33x^2 - 10x - 4	\( -\,5^{14}\cdot 19^{9}\cdot 29^{6} \)	20T955	Trivial (GRH)
20.6.1576400032427617153453310546875.1	x^20 - 3x^19 - 10x^18 + 32x^17 + 38x^16 - 215x^15 + 273x^14 + 47x^13 - 753x^12 + 1484x^11 - 1465x^10 - 5x^9 + 720x^8 - 6x^7 + 354x^6 + 901x^5 + 480x^4 - 61x^2 - 15x - 1	\( -\,5^{10}\cdot 19^{9}\cdot 29^{8} \)	20T955	$[2]$ (GRH)
20.4.11000468465851520789524462890625.1	x^20 - 10x^19 + 51x^18 - 174x^17 + 436x^16 - 836x^15 + 1246x^14 - 1436x^13 + 1232x^12 - 684x^11 + 56x^10 + 374x^9 - 472x^8 + 290x^7 - 18x^6 - 151x^5 + 123x^4 - 15x^3 - 34x^2 + 21x + 9	\( 5^{11}\cdot 19^{8}\cdot 29^{7}\cdot 769 \)	20T955	Trivial (GRH)
20.6.33974138629905542100286865234375.1	x^20 - 6x^19 + 21x^18 - 14x^17 + 6x^16 - x^15 + 689x^14 - 845x^13 + 2137x^12 + 560x^11 - 2812x^10 + 2170x^9 - 1466x^8 - 723x^7 + 428x^6 - 144x^5 + 253x^4 + 23x^3 + 51x^2 - 8x - 1	\( -\,5^{14}\cdot 19^{9}\cdot 29^{7} \)	20T955	$[2]$ (GRH)
20.4.319013585509694102896209423828125.1	x^20 - 2x^19 + 13x^18 - 32x^17 - 12x^16 - 312x^15 + 31x^14 + 117x^13 + 1446x^12 + 444x^11 - 1359x^10 - 1629x^9 - 1789x^8 + 2027x^7 + 2918x^6 - 1399x^5 - 334x^4 - 1285x^3 + 540x^2 + 1735x - 995	\( 5^{11}\cdot 19^{8}\cdot 29^{8}\cdot 769 \)	20T955	$[2]$ (GRH)
20.10.1068583407413817193418066406250000.1	x^20 + 5x^18 - 7x^16 - 47x^14 + 25x^12 + 136x^10 - 78x^8 - 113x^6 + 65x^4 + 28x^2 - 16	\( -\,2^{4}\cdot 5^{14}\cdot 19^{4}\cdot 29^{6}\cdot 109^{4} \)	20T955	Trivial (GRH)
20.6.1068583407413817193418066406250000.1	x^20 - 4x^19 + 8x^18 + 5x^17 - 13x^16 - 58x^15 - 164x^14 + 1579x^13 - 4695x^12 + 6616x^11 - 14259x^10 + 39740x^9 - 41312x^8 + 8098x^7 - 14078x^6 + 27251x^5 - 2620x^4 - 2820x^3 - 2259x^2 - 1303x + 31	\( -\,2^{4}\cdot 5^{14}\cdot 19^{4}\cdot 29^{6}\cdot 109^{4} \)	20T955	Trivial (GRH)
20.10.5342917037069085967090332031250000.1	x^20 - 5x^18 - 90x^16 + 400x^14 + 2125x^12 - 7375x^10 - 19375x^8 + 38125x^6 + 70625x^4 - 37500x^2 - 50000	\( -\,2^{4}\cdot 5^{15}\cdot 19^{4}\cdot 29^{6}\cdot 109^{4} \)	20T955	Trivial (GRH)
20.14.5342917037069085967090332031250000.1	x^20 - 5x^19 - 18x^18 + 150x^17 - 102x^16 - 1252x^15 + 3194x^14 + 1042x^13 - 15415x^12 + 21750x^11 + 6358x^10 - 52990x^9 + 61277x^8 - 11240x^7 - 47639x^6 + 64284x^5 - 43040x^4 + 17279x^3 - 4151x^2 + 542x - 29	\( -\,2^{4}\cdot 5^{15}\cdot 19^{4}\cdot 29^{6}\cdot 109^{4} \)	20T955	Trivial (GRH)
20.8.6329352282423861537868725791015625.1	x^20 - 10x^19 + 31x^18 + 6x^17 - 212x^16 + 268x^15 + 486x^14 - 1156x^13 - 336x^12 + 2276x^11 - 592x^10 - 2546x^9 + 1756x^8 + 1626x^7 - 2150x^6 - 475x^5 + 1385x^4 - 43x^3 - 400x^2 + 85x + 71	\( 3^{2}\cdot 5^{10}\cdot 19^{8}\cdot 29^{6}\cdot 7128529 \)	20T955	Trivial (GRH)
20.12.7279724463006629630160577392578125.1	x^20 - 10x^19 + 44x^18 - 111x^17 + 1224x^15 - 4250x^14 + 5984x^13 - 999x^12 - 8592x^11 + 11941x^10 - 4150x^9 - 5739x^8 + 7404x^7 - 2442x^6 - 1448x^5 + 1573x^4 - 403x^3 - 88x^2 + 61x - 1	\( 5^{14}\cdot 19^{4}\cdot 29^{6}\cdot 109^{5} \)	20T955	Trivial (GRH)
20.8.7279724463006629630160577392578125.1	x^20 - 5x^19 + 3x^18 + 24x^17 - 63x^16 + 72x^15 - 36x^14 - 20x^13 + 53x^12 - 44x^11 + 29x^10 - 44x^9 + 53x^8 - 20x^7 - 36x^6 + 72x^5 - 63x^4 + 24x^3 + 3x^2 - 5x + 1	\( 5^{14}\cdot 19^{4}\cdot 29^{6}\cdot 109^{5} \)	20T955	Trivial (GRH)
20.8.7279724463006629630160577392578125.2	x^20 - x^18 - 19x^17 - 40x^16 + 226x^15 - 245x^14 - 604x^13 + 1621x^12 - 368x^11 - 1324x^10 + 3115x^9 - 1869x^8 - 4844x^7 + 618x^6 + 2943x^5 + 1743x^4 + 588x^3 + 97x^2 - x - 1	\( 5^{14}\cdot 19^{4}\cdot 29^{6}\cdot 109^{5} \)	20T955	Trivial (GRH)
20.8.7344717571099586769213440000000000.1	x^20 - 14x^18 + 82x^16 - 256x^14 + 431x^12 - 268x^10 - 319x^8 + 673x^6 - 315x^4 - 85x^2 + 71	\( 2^{20}\cdot 5^{10}\cdot 19^{8}\cdot 29^{6}\cdot 71 \)	20T955	Trivial (GRH)
20.12.9015444211941674311316942689927168.1	x^20 - 10x^18 - 4x^17 + 26x^16 + 40x^15 - 12x^14 - 120x^13 + 66x^12 + 176x^11 - 288x^10 - 440x^9 + 344x^8 + 704x^7 - 48x^6 - 488x^5 - 120x^4 + 144x^3 + 48x^2 - 16x - 4	\( 2^{46}\cdot 457\cdot 809^{6} \)	20T955	Trivial (GRH)
20.8.9015444211941674311316942689927168.1	x^20 - 4x^17 - 9x^16 - 8x^15 - 52x^14 + 8x^12 + 136x^11 + 56x^10 + 96x^9 + 252x^8 + 136x^7 - 324x^6 - 632x^5 - 145x^4 + 248x^3 + 80x^2 - 36x + 1	\( 2^{46}\cdot 457\cdot 809^{6} \)	20T955	Trivial (GRH)
20.10.10241225908998015354255360000000000.1	x^20 - 24x^18 + 253x^16 - 1536x^14 + 5905x^12 - 14838x^10 + 24160x^8 - 24199x^6 + 13118x^4 - 2670x^2 - 99	\( -\,2^{20}\cdot 3^{2}\cdot 5^{10}\cdot 11\cdot 19^{8}\cdot 29^{6} \)	20T955	Trivial (GRH)
20.2.10241225908998015354255360000000000.1	x^20 + 24x^18 + 253x^16 + 1536x^14 + 5905x^12 + 14838x^10 + 24160x^8 + 24199x^6 + 13118x^4 + 2670x^2 - 99	\( -\,2^{20}\cdot 3^{2}\cdot 5^{10}\cdot 11\cdot 19^{8}\cdot 29^{6} \)	20T955	$[2]$ (GRH)
20.14.20303084740862526674943261718750000.1	x^20 - 26x^18 + 48x^16 + 2845x^14 - 16101x^12 - 13212x^10 + 74997x^8 - 39115x^6 - 16099x^4 + 11556x^2 - 1539	\( -\,2^{4}\cdot 5^{14}\cdot 19^{5}\cdot 29^{6}\cdot 109^{4} \)	20T955	Trivial (GRH)
20.12.20303084740862526674943261718750000.1	x^20 - 27x^18 + 212x^16 + 46x^14 - 6324x^12 + 12641x^10 + 48774x^8 - 109214x^6 - 51082x^4 + 8598x^2 + 2299	\( 2^{4}\cdot 5^{14}\cdot 19^{5}\cdot 29^{6}\cdot 109^{4} \)	20T955	Trivial (GRH)
20.12.29249765784512303437008509853515625.1	x^20 - 10x^19 + 35x^18 - 30x^17 - 123x^16 + 372x^15 - 281x^14 - 463x^13 + 1254x^12 - 933x^11 - 561x^10 + 1666x^9 - 1196x^8 - 103x^7 + 731x^6 - 393x^5 - 51x^4 + 124x^3 - 29x^2 - 10x + 4	\( 3^{12}\cdot 5^{10}\cdot 11^{4}\cdot 109^{6}\cdot 229529 \)	20T955	Trivial (GRH)
20.6.30128053005420888440856222072045568.1	x^20 - 10x^19 + 55x^18 - 210x^17 + 601x^16 - 1340x^15 + 2342x^14 - 3144x^13 + 2987x^12 - 1334x^11 - 1429x^10 + 3938x^9 - 4721x^8 + 3468x^7 - 1292x^6 - 332x^5 + 791x^4 - 522x^3 + 181x^2 - 30x + 1	\( -\,2^{38}\cdot 809^{6}\cdot 390967 \)	20T955	Trivial (GRH)
20.18.30189084800892867773242735838887936.1	x^20 - 10x^19 + 25x^18 + 60x^17 - 344x^16 + 100x^15 + 1598x^14 - 1716x^13 - 3649x^12 + 5878x^11 + 4355x^10 - 9868x^9 - 2384x^8 + 9024x^7 - 2x^6 - 4412x^5 + 632x^4 + 1056x^3 - 248x^2 - 96x + 28	\( -\,2^{38}\cdot 23\cdot 809^{6}\cdot 17033 \)	20T955	Trivial (GRH)
20.10.30988918815000698609123925781250000.1	x^20 - 7x^19 - 17x^18 + 208x^17 + 25x^16 - 2932x^15 + 2911x^14 + 20856x^13 - 36650x^12 - 71250x^11 + 194388x^10 + 70531x^9 - 495686x^8 + 200817x^7 + 513998x^6 - 493597x^5 - 37839x^4 + 194338x^3 - 47894x^2 - 19907x + 7681	\( -\,2^{4}\cdot 5^{14}\cdot 19^{4}\cdot 29^{7}\cdot 109^{4} \)	20T955	Trivial (GRH)
20.2.30988918815000698609123925781250000.1	x^20 + 21x^18 + 105x^16 - 696x^14 - 10001x^12 - 45946x^10 - 103315x^8 - 117044x^6 - 63104x^4 - 14065x^2 - 725	\( -\,2^{4}\cdot 5^{14}\cdot 19^{4}\cdot 29^{7}\cdot 109^{4} \)	20T955	$[3]$ (GRH)
20.2.30988918815000698609123925781250000.2	x^20 - 7x^19 + 29x^18 - 63x^17 + 87x^16 - 161x^15 + 715x^14 - 306x^13 + 153x^12 - 2650x^11 - 1742x^10 - 2145x^9 - 43266x^8 + 27270x^7 + 82710x^6 + 143415x^5 + 301880x^4 - 647150x^3 - 955925x^2 + 607525x + 754525	\( -\,2^{4}\cdot 5^{14}\cdot 19^{4}\cdot 29^{7}\cdot 109^{4} \)	20T955	$[3]$ (GRH)
20.12.33949922505144304687623040000000000.1	x^20 - 26x^18 + 298x^16 - 1984x^14 + 8495x^12 - 24412x^10 + 47585x^8 - 62001x^6 + 51633x^4 - 24835x^2 + 5251	\( 2^{16}\cdot 5^{10}\cdot 19^{8}\cdot 29^{6}\cdot 59\cdot 89 \)	20T955	Trivial (GRH)
20.8.36398622315033148150802886962890625.1	x^20 - 3x^19 - 5x^18 + 9x^17 - 50x^16 + 340x^15 - 703x^14 + 1576x^13 - 2553x^12 + 2799x^11 - 5928x^10 + 7494x^9 - 12004x^8 + 34606x^7 - 43465x^6 + 28777x^5 - 36533x^4 + 48816x^3 - 30355x^2 + 7721x - 539	\( 5^{15}\cdot 19^{4}\cdot 29^{6}\cdot 109^{5} \)	20T955	Trivial (GRH)
20.2.57678015362481878140979840000000000.1	x^20 + 38x^18 + 594x^16 + 4992x^14 + 24159x^12 + 62316x^10 + 55353x^8 - 14709x^6 + 138861x^4 + 32561x^2 - 8921	\( -\,2^{16}\cdot 5^{10}\cdot 11\cdot 19^{8}\cdot 29^{6}\cdot 811 \)	20T955	Trivial (GRH)
20.6.116475591408106074082569238281250000.1	x^20 - 5x^19 + 52x^17 - 176x^16 + 421x^15 - 887x^14 + 686x^13 + 1300x^12 - 1852x^11 + 1411x^10 - 8160x^9 + 7391x^8 + 15201x^7 - 19980x^6 - 3538x^5 + 11245x^4 - 3169x^3 - 1196x^2 + 772x + 719	\( -\,2^{4}\cdot 5^{14}\cdot 19^{4}\cdot 29^{6}\cdot 109^{5} \)	20T955	Trivial (GRH)
20.4.116475591408106074082569238281250000.1	x^20 - 4x^19 - 8x^18 + 15x^17 - 32x^16 + 14x^15 + 196x^14 - 356x^13 + 264x^12 + 1087x^11 - 1790x^10 + 3261x^9 + 2376x^8 - 9612x^7 + 15876x^6 + 3402x^5 - 23328x^4 + 32805x^3 - 52488x^2 - 78732x + 59049	\( 2^{4}\cdot 5^{14}\cdot 19^{4}\cdot 29^{6}\cdot 109^{5} \)	20T955	Trivial (GRH)
20.10.154944594075003493045619628906250000.1	x^20 + 4x^18 - 330x^16 - 2229x^14 + 434x^12 + 21001x^10 + 13625x^8 - 56566x^6 - 39034x^4 + 29650x^2 - 3625	\( -\,2^{4}\cdot 5^{15}\cdot 19^{4}\cdot 29^{7}\cdot 109^{4} \)	20T955	Trivial (GRH)
20.18.154944594075003493045619628906250000.1	x^20 - x^19 - 48x^18 + 43x^17 + 915x^16 - 876x^15 - 9157x^14 + 10182x^13 + 52575x^12 - 70067x^11 - 174991x^10 + 283398x^9 + 317729x^8 - 639806x^7 - 254704x^6 + 701537x^5 + 19456x^4 - 249175x^3 + 23965x^2 + 12130x - 295	\( -\,2^{4}\cdot 5^{15}\cdot 19^{4}\cdot 29^{7}\cdot 109^{4} \)	20T955	Trivial (GRH)
20.12.194158018925084147652374366025390625.1	x^20 - 10x^19 + 21x^18 + 96x^17 - 401x^16 - 260x^15 + 2734x^14 - 512x^13 - 10612x^12 + 5016x^11 + 26846x^10 - 13654x^9 - 46144x^8 + 17846x^7 + 52476x^6 - 9205x^5 - 35319x^4 - 2037x^3 + 10448x^2 + 2670x - 99	\( 5^{10}\cdot 11\cdot 19^{8}\cdot 29^{6}\cdot 41\cdot 4363771 \)	20T955	Trivial (GRH)
20.16.221914074267247033540490784067813376.1	x^20 - 20x^18 - 4x^17 + 151x^16 + 56x^15 - 548x^14 - 272x^13 + 1056x^12 + 584x^11 - 1352x^10 - 752x^9 + 1580x^8 + 904x^7 - 1380x^6 - 808x^5 + 551x^4 + 280x^3 - 76x^2 - 20x + 1	\( 2^{46}\cdot 7\cdot 809^{6}\cdot 1607 \)	20T955	Trivial (GRH)
20.4.221914074267247033540490784067813376.1	x^20 + 10x^18 - 4x^17 + 46x^16 - 24x^15 + 84x^14 - 72x^13 - 38x^12 + 16x^11 - 648x^10 + 296x^9 - 1400x^8 + 896x^7 - 1648x^6 + 408x^5 - 760x^4 + 1008x^3 - 1072x^2 - 48x + 28	\( 2^{46}\cdot 7\cdot 809^{6}\cdot 1607 \)	20T955	Trivial (GRH)
20.10.296995551360942445273405440000000000.1	x^20 - 22x^18 + 133x^16 - 347x^14 + 4482x^12 - 16737x^10 - 78088x^8 + 69764x^6 + 465539x^4 - 180768x^2 - 45936	\( -\,2^{20}\cdot 3^{2}\cdot 5^{10}\cdot 11\cdot 19^{8}\cdot 29^{7} \)	20T955	$[2]$ (GRH)
20.0.543198760082308875001968640000000000.1	x^20 + 26x^18 + 298x^16 + 1984x^14 + 8495x^12 + 24412x^10 + 47585x^8 + 62001x^6 + 51633x^4 + 24835x^2 + 5251	\( 2^{20}\cdot 5^{10}\cdot 19^{8}\cdot 29^{6}\cdot 59\cdot 89 \)	20T955	$[2, 6]$ (GRH)
20.16.565625418916393185676322496292323328.1	x^20 - 20x^18 + 166x^16 - 732x^14 + 1794x^12 - 2172x^10 + 240x^8 + 2544x^6 - 2712x^4 + 864x^2 + 28	\( 2^{58}\cdot 7\cdot 809^{6} \)	20T955	Trivial (GRH)
20.14.582377957040530370412846191406250000.1	x^20 - 5x^19 - 2x^18 + 30x^17 - 247x^16 + 844x^15 + 3451x^14 - 9501x^13 - 28505x^12 + 25240x^11 + 157102x^10 + 56970x^9 - 455873x^8 - 406700x^7 + 500144x^6 + 721433x^5 + 14175x^4 - 374268x^3 - 145144x^2 + 55104x + 24256	\( -\,2^{4}\cdot 5^{15}\cdot 19^{4}\cdot 29^{6}\cdot 109^{5} \)	20T955	Trivial (GRH)
20.8.588789457485013273573354589843750000.1	x^20 + 14x^18 - 186x^16 - 3535x^14 - 9334x^12 + 57335x^10 + 232726x^8 + 237935x^6 + 55914x^4 - 13041x^2 + 551	\( 2^{4}\cdot 5^{14}\cdot 19^{5}\cdot 29^{7}\cdot 109^{4} \)	20T955	Trivial (GRH)