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 all 38 matches)

Label	Polynomial	Discriminant	Galois group	Class group
15.9.1373787160843911247.1	x^15 - 4x^14 - 5x^13 + 39x^12 - 17x^11 - 126x^10 + 132x^9 + 157x^8 - 232x^7 - 95x^6 + 178x^5 + 49x^4 - 76x^3 - 19x^2 + 18x - 1	\( -\,7^{12}\cdot 463^{3} \)	$S_5 \times C_3$ (as 15T24)	Trivial
15.9.3132021267584993727.1	x^15 - 3x^13 - 9x^12 - 9x^11 + 21x^10 + 3x^9 + 99x^7 + 63x^6 - 36x^5 - 9x^4 - 27x^2 - 18x - 3	\( -\,3^{24}\cdot 223^{3} \)	$S_5 \times C_3$ (as 15T24)	Trivial
15.9.3534005780678716416.1	x^15 - 4x^13 - 2x^12 + 5x^11 - 19x^10 - 47x^9 + 51x^8 + 90x^7 - 72x^6 - 62x^5 + 57x^4 + 19x^3 - 15x^2 - 2x + 1	\( -\,2^{10}\cdot 3^{5}\cdot 61^{3}\cdot 397^{3} \)	15T93	Trivial
15.9.35059114707591389519.1	x^15 - 5x^14 - x^13 + 42x^12 - 49x^11 - 97x^10 + 192x^9 + 46x^8 - 247x^7 + 47x^6 + 152x^5 - 78x^4 - 29x^3 + 34x^2 - 10x + 1	\( -\,13^{3}\cdot 347^{3}\cdot 19543^{2} \)	15T78	Trivial
15.9.48986909510143987031.1	x^15 - 3x^14 + 9x^12 - 33x^11 + 74x^10 - 19x^9 - 223x^8 + 465x^7 - 288x^6 - 409x^5 + 806x^4 - 298x^3 - 234x^2 + 172x - 19	\( -\,13^{5}\cdot 347^{3}\cdot 1777^{2} \)	15T78	Trivial
15.9.100133149236970913792.1	x^15 - 6x^14 + 7x^13 + 26x^12 - 82x^11 + 70x^10 + 29x^9 - 100x^8 + 78x^7 + 2x^6 - 69x^5 + 42x^4 + 29x^3 - 26x^2 - 4x + 4	\( -\,2^{18}\cdot 37^{6}\cdot 53^{3} \)	$S_5 \times S_3$ (as 15T29)	Trivial
15.9.171959209292585208832.1	x^15 - 5x^13 - 17x^12 - 24x^11 + 61x^10 + 214x^9 + 111x^8 - 303x^7 - 468x^6 - 151x^5 + 176x^4 + 200x^3 + 82x^2 + 15x + 1	\( -\,2^{10}\cdot 13^{3}\cdot 31^{3}\cdot 37^{6} \)	$S_5 \times S_3$ (as 15T29)	Trivial
15.9.320068972520322321231.1	x^15 - 15x^13 - 3x^12 + 81x^11 + 72x^10 - 271x^9 - 360x^8 + 498x^7 + 766x^6 - 225x^5 - 663x^4 - 158x^3 + 225x^2 + 96x - 31	\( -\,3^{20}\cdot 13^{3}\cdot 347^{3} \)	15T63	Trivial (GRH)
15.9.356254943672084924883.1	x^15 - x^14 - x^13 - 10x^12 - x^11 + 10x^10 + 56x^9 + 63x^8 - 50x^7 - 211x^6 - 184x^5 + 188x^4 + 219x^3 + 25x^2 - 18x - 3	\( -\,3\cdot 13^{4}\cdot 401^{6} \)	15T86	Trivial
15.9.12274698536106109012992.1	x^15 - 4x^14 - 5x^13 + 43x^12 - 64x^11 - 63x^10 + 340x^9 - 375x^8 - 161x^7 + 842x^6 - 821x^5 + 86x^4 + 384x^3 - 294x^2 + 117x - 27	\( -\,2^{10}\cdot 3\cdot 31^{2}\cdot 401^{6} \)	15T86	Trivial
15.9.43085608345654444113759.1	x^15 - 15x^13 - 8x^12 + 9x^11 - 6x^10 + 250x^9 + 288x^8 + 147x^7 - 534x^6 - 1413x^5 + 636x^4 + 120x^3 - 648x^2 + 288x - 32	\( -\,3^{20}\cdot 61^{3}\cdot 379^{3} \)	15T63	Trivial (GRH)
15.9.46113809309420128201728.1	x^15 - 3x^13 - 2x^12 - 36x^11 - 48x^10 + 65x^9 + 162x^8 + 351x^7 + 672x^6 + 405x^5 - 522x^4 - 1032x^3 - 720x^2 - 240x - 32	\( -\,2^{10}\cdot 3^{15}\cdot 11^{12} \)	15T81	Trivial (GRH)
15.9.70458445469175544329419.1	x^15 - 20x^13 - 2x^12 + 160x^11 + 32x^10 - 639x^9 - 192x^8 + 1268x^7 + 508x^6 - 976x^5 - 480x^4 - 60x^3 - 64x^2 - 16x - 1	\( -\,13^{4}\cdot 23\cdot 347^{3}\cdot 2567103551 \)	15T93	Trivial (GRH)
15.9.82869195291086460173443.1	x^15 - 20x^13 - 3x^12 + 160x^11 + 48x^10 - 637x^9 - 288x^8 + 1244x^7 + 764x^6 - 880x^5 - 736x^4 - 187x^3 - 64x^2 - 20x - 1	\( -\,4903^{3}\cdot 38569\cdot 18229261 \)	15T93	Trivial (GRH)
15.9.208679507343297525648384.1	x^15 - 15x^13 - 10x^12 + 90x^11 + 120x^10 - 254x^9 - 540x^8 + 261x^7 + 1120x^6 + 189x^5 - 1050x^4 - 512x^3 + 360x^2 + 240x + 32	\( -\,2^{10}\cdot 3^{15}\cdot 61^{3}\cdot 397^{3} \)	15T93	Trivial (GRH)
15.9.327750627860810056940544.1	x^15 - 21x^13 - 22x^12 + 216x^11 + 438x^10 - 1155x^9 - 3384x^8 + 1827x^7 + 10638x^6 + 3987x^5 - 11112x^4 - 8556x^3 + 4320x^2 + 3744x - 608	\( -\,2^{10}\cdot 3^{20}\cdot 13^{3}\cdot 347^{3} \)	15T91	Trivial (GRH)
15.9.349046216993499621221376.1	x^15 - 15x^13 - x^12 + 79x^11 + 25x^10 - 219x^9 - 173x^8 + 611x^7 + 265x^6 - 1279x^5 + 531x^4 + 434x^3 - 303x^2 + 44x + 4	\( -\,2^{10}\cdot 3^{6}\cdot 881^{6} \)	15T90	Trivial
15.9.893591792459039867256832.1	x^15 - x^14 - 10x^13 + 6x^12 + 38x^11 - 6x^10 - 67x^9 - 25x^8 + 52x^7 + 62x^6 - 10x^5 - 46x^4 - 5x^3 + 13x^2 + x - 1	\( -\,2^{14}\cdot 83\cdot 181\cdot 10301\cdot 53681\cdot 6565421 \)	15T104	Trivial (GRH)
15.9.1060617614116662948639744.1	x^15 - 15x^13 - 4x^12 + 90x^11 + 48x^10 - 290x^9 - 216x^8 + 585x^7 + 536x^6 - 783x^5 - 948x^4 + 428x^3 + 936x^2 + 336x + 32	\( -\,2^{10}\cdot 3^{15}\cdot 11^{12}\cdot 23 \)	15T81	Trivial (GRH)
15.9.3141415952941496590992384.1	x^15 - 15x^13 - 4x^12 + 90x^11 + 48x^10 - 279x^9 - 216x^8 + 486x^7 + 480x^6 - 486x^5 - 612x^4 + 211x^3 + 432x^2 + 96x - 16	\( -\,2^{10}\cdot 3^{8}\cdot 881^{6} \)	15T90	Trivial (GRH)
15.9.773560756544273759852688384.1	x^15 - 33x^13 - 40x^12 - 90x^11 + 54x^10 + 1791x^9 - 954x^8 + 6819x^7 + 25096x^6 - 2367x^5 - 52062x^4 - 63600x^3 - 29592x^2 + 6576x + 4384	\( -\,2^{10}\cdot 3^{21}\cdot 137^{2}\cdot 1567^{3} \)	15T83	Trivial (GRH)
15.9.1661733554869524611658797104.1	x^15 - 2x^14 - 5x^13 + 10x^12 + 3x^11 - 12x^10 + 14x^9 - 6x^8 - 11x^7 + 20x^6 - 12x^5 - 21x^4 + 11x^3 + 10x^2 - x - 1	\( -\,2^{4}\cdot 8009\cdot 12967704729597363994091 \)	15T104	Trivial (GRH)
15.9.4798596942510120043666504704.1	x^15 - 36x^13 - 26x^12 + 495x^11 + 840x^10 - 3406x^9 - 9972x^8 + 10698x^7 + 49848x^6 + 9009x^5 - 81840x^4 - 69036x^3 + 52272x^2 + 34848x - 3872	\( -\,2^{10}\cdot 3^{20}\cdot 11^{4}\cdot 13^{3}\cdot 347^{3} \)	15T91	Trivial (GRH)
15.9.50068967077842268536000000000.1	x^15 - 17x^13 - 89x^12 - 6x^11 + 2412x^10 - 250x^9 - 18072x^8 + 10091x^7 + 32534x^6 - 1671x^5 - 39915x^4 + 21349x^3 - 5292x^2 - 28493x + 43	\( -\,2^{12}\cdot 3^{16}\cdot 5^{9}\cdot 23\cdot 43^{6} \)	15T87	Trivial (GRH)
15.9.395638255629389500000000000000.1	x^15 - 20x^13 - 20x^12 + 160x^11 + 320x^10 - 500x^9 - 1920x^8 - 400x^7 + 4720x^6 + 5696x^5 - 1920x^4 - 8560x^3 - 6400x^2 - 1600x - 16	\( -\,2^{14}\cdot 5^{15}\cdot 7^{6}\cdot 13\cdot 517364567 \)	15T87	Trivial (GRH)
15.9.2193046267403549887000547200000.1	x^15 - 2x^14 - 62x^13 + 277x^12 + 528x^11 - 6311x^10 - 4807x^9 + 35528x^8 + 482688x^7 + 926663x^6 - 6248483x^5 - 33152761x^4 + 2783240x^3 + 376105913x^2 + 110428690x - 1265140391	\( -\,2^{10}\cdot 5^{5}\cdot 13^{3}\cdot 19^{2}\cdot 31^{2}\cdot 347^{3}\cdot 4639^{2} \)	15T83	$[3]$ (GRH)
15.9.98150665663307736000000000000000.1	x^15 - 90x^13 - 180x^12 + 2865x^11 + 10236x^10 - 29950x^9 - 184260x^8 - 61170x^7 + 1026160x^6 + 1707168x^5 - 775200x^4 - 3783375x^3 - 2205900x^2 + 798000x + 764864	\( -\,2^{18}\cdot 3^{23}\cdot 5^{15}\cdot 19^{4} \)	15T95	Trivial (GRH)
15.9.220573586958400000000000000000000.1	x^15 + 20x^13 - 40x^12 - 590x^11 + 1192x^10 - 7900x^9 + 33640x^8 + 19520x^7 - 201920x^6 + 244752x^5 + 132000x^4 - 778600x^3 - 120800x^2 + 310400x + 79360	\( -\,2^{24}\cdot 5^{20}\cdot 13^{10} \)	15T101	Trivial (GRH)
15.9.29492759518563811794405922500363613000000.1	x^15 - 99x^13 - 396x^12 - 1843x^11 - 11774x^10 + 108945x^9 + 1674756x^8 + 8533899x^7 + 23061222x^6 + 37151415x^5 + 37445760x^4 + 23871475x^3 + 9367350x^2 + 2068500x + 197000	\( -\,2^{6}\cdot 5^{6}\cdot 7^{10}\cdot 13\cdot 197^{4}\cdot 6791^{2}\cdot 10753^{2} \)	15T101	Trivial (GRH)
15.9.236400461395948294457915703984996352000000.1	x^15 + 9x^13 - 792x^12 - 2395x^11 + 95676x^10 - 483381x^9 + 225648x^8 + 4223644x^7 - 8858444x^6 - 4794300x^5 + 25180920x^4 - 13571300x^3 - 5876000x^2 + 3164000x + 904000	\( -\,2^{20}\cdot 5^{6}\cdot 37^{5}\cdot 113^{4}\cdot 139^{2}\cdot 257003^{2} \)	15T102	Trivial (GRH)
15.9.31256653180970842100294052450870850335221875.1	x^15 - 4x^14 - 1264x^13 - 3539x^12 + 194086x^11 + 14315825x^10 + 207980393x^9 - 11155818269x^8 - 106782015292x^7 + 2695173632356x^6 + 60691267440950x^5 - 75831436048429x^4 - 19327557996736266x^3 + 33906382851120779x^2 + 414276426535790729x - 414601786688651713	\( -\,5^{5}\cdot 13^{3}\cdot 19^{6}\cdot 31^{10}\cdot 41^{4}\cdot 347^{3} \)	15T70	$[3]$ (GRH)
15.9.95997288591377091612527656182883144142091264.1	x^15 - 2055x^13 - 7672x^12 + 1689210x^11 + 12612768x^10 - 716487806x^9 - 7775771472x^8 + 170071858773x^7 + 2260733557600x^6 - 22989137783499x^5 - 325916709388536x^4 + 1930435159845344x^3 + 21988813850200512x^2 - 159305388838030848x + 215817165520608256	\( -\,2^{10}\cdot 3^{21}\cdot 137^{10}\cdot 1567^{3} \)	15T70	Trivial (GRH)
15.9.4831264310017778731576326598323772072448000000.1	x^15 - 126x^13 - 1008x^12 - 72268x^11 - 1126048x^10 - 2073960x^9 + 91965888x^8 + 1073983904x^7 + 5909943424x^6 + 19089311360x^5 + 38490439680x^4 + 49074905600x^3 + 38514739200x^2 + 17009664000x + 3239936000	\( -\,2^{15}\cdot 5^{6}\cdot 7^{14}\cdot 113^{4}\cdot 292113919^{2} \)	15T101	Trivial (GRH)
15.9.6381262105849605201341604346805613756416000000.1	x^15 - 99x^13 - 396x^12 - 3868x^11 - 27974x^10 + 97245x^9 + 2044656x^8 + 10660124x^7 + 28900022x^6 + 46578665x^5 + 46949760x^4 + 29930225x^3 + 11744850x^2 + 2593500x + 247000	\( -\,2^{24}\cdot 5^{6}\cdot 13^{4}\cdot 17\cdot 19^{4}\cdot 37^{5}\cdot 74483599^{2} \)	15T102	Trivial (GRH)
15.9.509130717075076439975600141140915908481024000000.1	x^15 + 378x^13 - 3024x^12 + 61040x^11 - 598528x^10 + 3949848x^9 - 33288192x^8 + 67412352x^7 + 486419584x^6 - 1876640640x^5 + 409167360x^4 + 4110937600x^3 - 2003456000x^2 - 2157568000x + 1232896000	\( -\,2^{18}\cdot 5^{6}\cdot 7^{14}\cdot 43^{4}\cdot 20509^{2}\cdot 356999^{2} \)	15T95	Trivial (GRH)
15.9.672560372209647616583874741225333544667034419200000.1	x^15 + 522x^13 - 5256x^12 + 90798x^11 - 1156208x^10 + 8741070x^9 - 58030848x^8 + 185704640x^7 + 7128368x^6 - 1113803840x^5 + 1484167680x^4 + 433160800x^3 - 1125382400x^2 + 222848000	\( -\,2^{21}\cdot 5^{5}\cdot 37^{5}\cdot 1741^{4}\cdot 10433^{2}\cdot 1216507^{2} \)	15T102	Trivial (GRH)
15.9.17517842124064884881429616734159236380876841984000000.1	x^15 + 639x^13 - 6552x^12 + 106045x^11 - 1415004x^10 + 9994509x^9 - 54899712x^8 + 193325164x^7 - 284112164x^6 - 102417300x^5 + 624620520x^4 - 336640300x^3 - 145756000x^2 + 78484000x + 22424000	\( -\,2^{16}\cdot 5^{6}\cdot 17^{2}\cdot 37^{6}\cdot 2803^{4}\cdot 4003^{2}\cdot 152723^{2} \)	15T102	Trivial (GRH)
15.9.38583234404050627753560028547647715274328642905059328000000.1	x^15 + 846x^13 - 13536x^12 + 239912x^11 - 6052864x^10 + 82904760x^9 - 959105664x^8 + 12280855424x^7 - 121534297088x^6 + 773045872640x^5 - 3112713584640x^4 + 7937354137600x^3 - 12458714726400x^2 + 11004542976000x - 4192206848000	\( -\,2^{18}\cdot 3^{6}\cdot 5^{6}\cdot 79^{2}\cdot 107^{5}\cdot 1999^{4}\cdot 4987^{2}\cdot 609683^{2} \)	15T97	Trivial (GRH)