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 68)

Label	Polynomial	Discriminant	Galois group	Class group
15.11.1456857821075439453125.1	x^15 - 15x^13 + 90x^11 - 2x^10 - 275x^9 + 20x^8 + 450x^7 - 70x^6 - 376x^5 + 100x^4 + 130x^3 - 50x^2 - 5x + 1	\( 5^{15}\cdot 7^{10}\cdot 13^{2} \)	15T59	Trivial (GRH)
15.11.6220372723292065649664.1	x^15 - 5x^14 - 6x^13 + 68x^12 - 58x^11 - 251x^10 + 376x^9 + 413x^8 - 851x^7 - 378x^6 + 989x^5 + 238x^4 - 605x^3 - 123x^2 + 152x + 39	\( 2^{10}\cdot 3\cdot 401^{6}\cdot 487 \)	15T86	Trivial
15.11.7249807263458251953125.1	x^15 - 15x^13 + 90x^11 - 4x^10 - 275x^9 + 40x^8 + 450x^7 - 140x^6 - 372x^5 + 200x^4 + 110x^3 - 100x^2 + 15x + 1	\( 5^{15}\cdot 7^{10}\cdot 29^{2} \)	15T59	Trivial (GRH)
15.11.19218853520172119140625.1	x^15 - 15x^13 + 90x^11 - 275x^9 + 450x^7 - 379x^5 + 145x^3 - 20x - 1	\( 5^{15}\cdot 229^{5} \)	15T68	Trivial (GRH)
15.11.34214932039093017578125.1	x^15 - 15x^13 + 90x^11 - x^10 - 275x^9 + 10x^8 + 450x^7 - 35x^6 - 379x^5 + 50x^4 + 145x^3 - 25x^2 - 20x + 3	\( 5^{15}\cdot 257^{5} \)	15T68	Trivial (GRH)
15.11.46113809309420128201728.1	x^15 - 18x^13 - 12x^12 + 90x^11 + 120x^10 + 13x^9 - 54x^8 - 522x^7 - 1304x^6 - 1053x^5 + 234x^4 + 984x^3 + 720x^2 + 240x + 32	\( 2^{10}\cdot 3^{15}\cdot 11^{12} \)	15T81	Trivial (GRH)
15.11.1640718037659516571403264.1	x^15 - 6x^14 + 71x^12 - 147x^11 - 100x^10 + 408x^9 + 134x^8 - 138x^7 - 1231x^6 + 68x^5 + 2191x^4 - 508x^3 - 1128x^2 + 195x + 191	\( 2^{10}\cdot 31^{2}\cdot 401^{7} \)	15T79	Trivial (GRH)
15.11.1982893800305065512674304.1	x^15 - 15x^13 - 2x^12 + 90x^11 + 24x^10 - 330x^9 - 108x^8 + 945x^7 + 64x^6 - 1863x^5 + 750x^4 + 1492x^3 - 1368x^2 + 384x - 32	\( 2^{10}\cdot 3^{15}\cdot 11^{12}\cdot 43 \)	15T81	Trivial (GRH)
15.11.2539789649549279880118272.1	x^15 - 6x^13 - 2x^12 - 27x^11 + 24x^10 + 107x^9 + 144x^8 + 249x^7 - 934x^6 - 819x^5 + 1164x^4 + 404x^3 - 360x^2 - 48x + 32	\( 2^{15}\cdot 3^{13}\cdot 36497^{3} \)	15T93	Trivial (GRH)
15.11.3508488995538327547915609.1	x^15 - 3x^14 - 16x^13 + 49x^12 + 32x^11 - 38x^10 - 174x^9 - 390x^8 + 969x^7 + 348x^6 - 1173x^5 + 120x^4 + 333x^3 + 24x^2 - 88x + 13	\( 7^{10}\cdot 2281^{2}\cdot 48859^{2} \)	15T50	Trivial (GRH)
15.11.5216987683582438141209600.1	x^15 - 15x^13 - 10x^12 + 36x^11 + 48x^10 + 313x^9 + 594x^8 - 981x^7 - 3584x^6 - 2457x^5 + 2418x^4 + 5128x^3 + 3600x^2 + 1200x + 160	\( 2^{10}\cdot 3^{15}\cdot 5^{2}\cdot 61^{3}\cdot 397^{3} \)	15T93	Trivial (GRH)
15.11.5788859223923856660105009.1	x^15 - 15x^13 - 11x^12 + 90x^11 + 132x^10 - 578x^9 - 594x^8 + 3177x^7 + 1925x^6 - 8559x^5 - 5313x^4 + 8129x^3 + 6633x^2 + 561x + 11	\( 3^{20}\cdot 11^{12}\cdot 23^{2} \)	15T71	Trivial (GRH)
15.11.5788859223923856660105009.2	x^15 - 27x^13 - 31x^12 + 252x^11 + 564x^10 - 664x^9 - 3123x^8 - 1641x^7 + 5490x^6 + 8388x^5 - 753x^4 - 9231x^3 - 3159x^2 + 3186x + 659	\( 3^{20}\cdot 11^{12}\cdot 23^{2} \)	15T71	Trivial (GRH)
15.11.6788010473180818605591552.1	x^15 - 18x^13 - 12x^12 + 81x^11 + 108x^10 + 117x^9 + 162x^8 - 783x^7 - 2352x^6 - 1647x^5 + 1374x^4 + 3064x^3 + 2160x^2 + 720x + 96	\( 2^{10}\cdot 3^{13}\cdot 401^{6} \)	15T86	Trivial (GRH)
15.11.9341736328125000000000000.1	x^15 - 15x^13 - 25x^12 + 90x^11 + 300x^10 - 90x^9 - 1350x^8 - 1215x^7 + 2250x^6 + 4617x^5 + 675x^4 - 4455x^3 - 4050x^2 - 1215x - 81	\( 2^{12}\cdot 3^{14}\cdot 5^{21} \)	15T85	Trivial
15.11.13931818106500000000000000.1	x^15 - 5x^14 - 15x^13 + 55x^12 - 5x^11 - 367x^10 + 365x^9 + 1255x^8 - 1015x^7 - 1825x^6 + 913x^5 + 1105x^4 - 285x^3 - 215x^2 + 35x + 5	\( 2^{14}\cdot 5^{15}\cdot 7^{6}\cdot 37^{2}\cdot 173 \)	15T87	Trivial (GRH)
15.11.1688547673828125000000000000.1	x^15 - 5x^13 - 35x^12 - 10x^11 + 318x^10 - 1030x^9 + 1520x^8 + 6095x^7 - 9150x^6 - 11729x^5 + 9225x^4 + 7485x^3 - 2150x^2 - 1005x + 11	\( 2^{12}\cdot 3^{10}\cdot 5^{21}\cdot 11^{4} \)	15T85	Trivial (GRH)
15.11.3037376633760000000000000000.1	x^15 - 30x^13 - 40x^12 + 330x^11 + 834x^10 - 1415x^9 - 5550x^8 + 795x^7 + 12190x^6 + 5259x^5 - 3480x^4 - 655x^3 - 390x^2 - 540x + 106	\( 2^{20}\cdot 3^{18}\cdot 5^{16}\cdot 7^{2} \)	15T84	Trivial (GRH)
15.11.3199760414337145928176600064.1	x^15 - 3x^14 - 28x^13 + 95x^12 - 316x^11 + 588x^10 + 533x^9 + 122x^8 + 1104x^7 - 9965x^6 - 4408x^5 + 12535x^4 - 465x^3 - 4676x^2 + 1839x - 193	\( 2^{10}\cdot 37^{4}\cdot 401^{7} \)	15T79	Trivial (GRH)
15.11.5020969537440000000000000000.1	x^15 - 45x^13 + 435x^11 - 378x^10 - 1365x^9 + 2130x^8 - 900x^7 - 420x^6 + 2880x^5 - 2520x^4 - 105x^3 + 450x^2 - 6	\( 2^{20}\cdot 3^{22}\cdot 5^{16} \)	15T84	Trivial (GRH)
15.11.16285100300048718327704518656.1	x^15 - 23x^13 - 2x^12 + 179x^11 + 80x^10 - 673x^9 - 594x^8 + 1912x^7 - 252x^6 - 760x^5 + 880x^4 - 912x^3 - 416x^2 + 448x + 128	\( 2^{16}\cdot 3^{12}\cdot 881^{6} \)	15T88	Trivial (GRH)
15.11.29334808557573827860354802688.1	x^15 - 33x^13 - 22x^12 + 63x^11 + 84x^10 + 4618x^9 + 9180x^8 - 13401x^7 - 50696x^6 - 93123x^5 - 160026x^4 - 186376x^3 - 121680x^2 - 40560x - 5408	\( 2^{10}\cdot 3^{20}\cdot 13^{2}\cdot 36497^{3} \)	15T91	Trivial (GRH)
15.11.82443320268996636534004125696.1	x^15 - 17x^13 - 20x^12 - 225x^11 + 128x^10 + 2139x^9 - 9852x^8 - 15448x^7 + 52520x^6 + 34464x^5 - 91328x^4 - 20160x^3 + 45312x^2 + 7168x - 4096	\( 2^{12}\cdot 3^{16}\cdot 881^{6} \)	15T88	Trivial (GRH)
15.11.110920318379317587571477873524.1	x^15 - 33x^13 - 64x^12 - 90x^11 + 1248x^10 + 5806x^9 - 10512x^8 - 31521x^7 + 41392x^6 + 28314x^5 - 35190x^4 + 28312x^3 - 17136x^2 + 816x + 544	\( 2^{2}\cdot 3^{20}\cdot 17^{2}\cdot 31^{3}\cdot 9739^{3} \)	15T91	Trivial (GRH)
15.11.126641586691841137969338115072.1	x^15 - 20x^13 - 39x^12 + 160x^11 + 624x^10 - 173x^9 - 3744x^8 - 4324x^7 + 7911x^6 + 21392x^5 + 6600x^4 - 26128x^3 - 33168x^2 - 15040x - 2304	\( 2^{10}\cdot 881^{6}\cdot 3769\cdot 70177 \)	15T90	Trivial (GRH)
15.11.133377494418846899377180737536.1	x^15 - 20x^13 - 18x^12 + 160x^11 + 288x^10 - 525x^9 - 1728x^8 - 100x^7 + 4286x^6 + 4496x^5 - 2032x^4 - 6975x^3 - 5152x^2 - 1540x - 144	\( 2^{15}\cdot 53^{9}\cdot 109\cdot 11316791 \)	15T87	Trivial (GRH)
15.11.164886640537993273068008251392.1	x^15 - 15x^13 - 7x^12 + 90x^11 + 84x^10 - 291x^9 - 378x^8 + 594x^7 + 822x^6 - 810x^5 - 963x^4 + 523x^3 + 594x^2 + 132x + 8	\( 2^{13}\cdot 3^{16}\cdot 881^{6} \)	15T90	Trivial (GRH)
15.11.2264485717039079949313600000000.1	x^15 - 5x^14 - 57x^13 + 289x^12 + 825x^11 - 4717x^10 - 3601x^9 + 31833x^8 + 1339x^7 - 83815x^6 + 2237x^5 + 55003x^4 + 36939x^3 + 1177x^2 - 4915x + 235	\( 2^{12}\cdot 5^{8}\cdot 13^{10}\cdot 101323^{2} \)	15T50	Trivial (GRH)
15.11.1685974836844506513033699781395456.1	x^15 - 24x^13 - 16x^12 - 207x^11 - 276x^10 + 5713x^9 + 11610x^8 + 369x^7 - 17936x^6 - 101547x^5 - 281706x^4 - 365416x^3 - 242640x^2 - 80880x - 10784	\( 2^{10}\cdot 3^{20}\cdot 337^{2}\cdot 401^{6} \)	15T80	Trivial (GRH)
15.11.3128917033950916372142938576036281.1	x^15 + 9x^13 - 6x^12 - 2646x^11 + 3528x^10 + 6330x^9 - 15012x^8 + 1341405x^7 - 3552616x^6 - 7159347x^5 + 34121178x^4 - 47335848x^3 + 31732560x^2 - 10577520x + 1410336	\( 3^{22}\cdot 59^{2}\cdot 83^{2}\cdot 401^{6} \)	15T80	Trivial (GRH)
15.11.41468326288645730146555835992264704.1	x^15 - 6x^14 - 135x^13 + 333x^12 + 6096x^11 + 7464x^10 - 63720x^9 - 277812x^8 - 732105x^7 - 1606206x^6 - 1637631x^5 + 2883087x^4 + 11810481x^3 + 13866012x^2 + 3584043x - 2191593	\( 2^{12}\cdot 3^{24}\cdot 17^{3}\cdot 37^{3}\cdot 379531^{2} \)	15T75	Trivial (GRH)
15.11.72122875390646654351987363783888896.1	x^15 - 4x^14 - 201x^13 + 121x^12 + 12616x^11 + 34020x^10 - 207932x^9 - 1372760x^8 - 2713681x^7 + 1113480x^6 + 16513183x^5 + 35754551x^4 + 36074673x^3 + 12241538x^2 - 11026275x - 10525969	\( 2^{12}\cdot 7^{10}\cdot 13^{3}\cdot 29^{2}\cdot 97^{3}\cdot 192263^{2} \)	15T75	Trivial (GRH)
15.11.288430689287392159449927031844765696.1	x^15 - 4x^14 - 82x^13 + 498x^12 + 4457x^11 - 20812x^10 - 97302x^9 + 419638x^8 + 726751x^7 - 3499132x^6 - 1752538x^5 + 12169158x^4 + 742731x^3 - 17291716x^2 + 715786x + 7403218	\( 2^{20}\cdot 37^{5}\cdot 43^{2}\cdot 139^{2}\cdot 317^{3}\cdot 1867^{2} \)	15T82	Trivial (GRH)
15.11.296854871574412530032892056987579392.1	x^15 - x^14 - 28x^13 - 79x^12 - 1100x^11 + 1753x^10 + 15805x^9 + 2562x^8 + 38320x^7 - 121800x^6 - 728448x^5 + 301216x^4 + 1038400x^3 - 167680x^2 - 76800x + 4096	\( 2^{10}\cdot 37^{5}\cdot 151^{2}\cdot 44269^{2}\cdot 305873^{2} \)	15T60	Trivial (GRH)
15.11.582873779843746055527120888504182961.1	x^15 - x^14 - 186x^13 - 169x^12 + 13042x^11 + 34845x^10 - 388062x^9 - 1748786x^8 + 3122317x^7 + 29742540x^6 + 42132858x^5 - 69864557x^4 - 294637932x^3 - 458139413x^2 - 439035709x - 204947137	\( 61^{4}\cdot 397^{4}\cdot 1301806921^{2} \)	15T89	$[3]$ (GRH)
15.11.1543040910519569546921019055910525041.1	x^15 - 3x^14 - 126x^13 + 531x^12 + 5769x^11 - 34514x^10 - 95880x^9 + 1029924x^8 - 622189x^7 - 13231140x^6 + 37048867x^5 + 26547802x^4 - 288701374x^3 + 540249339x^2 - 423492779x + 120987661	\( 61^{4}\cdot 397^{4}\cdot 28309^{2}\cdot 74821^{2} \)	15T89	$[3]$ (GRH)
15.11.1593894329827244387250162786359001088.1	x^15 - 4x^14 - 98x^13 + 222x^12 + 2460x^11 - 1774x^10 - 6038x^9 - 36416x^8 - 276240x^7 + 345120x^6 + 980608x^5 + 64640x^4 + 3744000x^3 - 2539520x^2 + 204800x + 32768	\( 2^{14}\cdot 37^{5}\cdot 252949^{2}\cdot 4682551^{2} \)	15T60	Trivial (GRH)
15.11.6726894232542085043013968658644455424.1	x^15 - 6x^14 - 148x^13 + 391x^12 + 6782x^11 + 5664x^10 - 78190x^9 - 247562x^8 - 512976x^7 - 1563298x^6 - 2430874x^5 + 4161024x^4 + 21891109x^3 + 29908420x^2 + 12024364x - 1344637	\( 2^{12}\cdot 13^{3}\cdot 29^{2}\cdot 53^{3}\cdot 229^{5}\cdot 97367^{2} \)	15T82	Trivial (GRH)
15.11.22639092611819562236124731312177152000000.1	x^15 - 234x^13 - 936x^12 + 10592x^11 + 91756x^10 + 318690x^9 + 925776x^8 + 2973004x^7 + 7361212x^6 + 11707090x^5 + 11784960x^4 + 7512850x^3 + 2948100x^2 + 651000x + 62000	\( 2^{24}\cdot 5^{6}\cdot 23^{2}\cdot 31^{4}\cdot 37^{5}\cdot 1596629^{2} \)	15T96	$[3]$ (GRH)
15.11.81917455001598033212058392787403072000000.1	x^15 - 153x^13 - 72x^12 + 5535x^11 + 25854x^10 - 75798x^9 - 687906x^8 - 542818x^7 + 3065428x^6 + 5465315x^5 + 600030x^4 - 3014275x^3 - 734500x^2 + 395500x + 113000	\( 2^{12}\cdot 5^{6}\cdot 7^{12}\cdot 13^{3}\cdot 113^{4}\cdot 508087^{2} \)	15T101	Trivial (GRH)
15.11.4041163971392929828955494668759105536000000.1	x^15 - 144x^13 - 936x^12 + 5540x^11 + 75392x^10 - 370134x^9 - 1459296x^8 + 10678864x^7 + 27161712x^6 - 73028000x^5 - 285963840x^4 - 324408800x^3 - 168640000x^2 - 41664000x - 3968000	\( 2^{21}\cdot 5^{6}\cdot 31^{4}\cdot 37^{5}\cdot 1387715921^{2} \)	15T97	Trivial (GRH)
15.11.14510776668759878086782120121838473216000000.1	x^15 - 360x^13 - 648x^12 + 39784x^11 + 127584x^10 - 1599876x^9 - 6284088x^8 + 21382724x^7 + 72393848x^6 + 18576960x^5 - 80928000x^4 - 45803000x^3 + 21018800x^2 + 15736000x + 2248000	\( 2^{18}\cdot 5^{6}\cdot 7^{10}\cdot 281^{4}\cdot 44850007^{2} \)	15T92	$[3]$ (GRH)
15.11.44842222891195545361422304391393705984000000.1	x^15 - 432x^13 - 2592x^12 + 31528x^11 + 680480x^10 - 787680x^9 - 56878848x^8 + 112700512x^7 + 1181988864x^6 - 2781299200x^5 - 5558538240x^4 + 21733222400x^3 - 23532339200x^2 + 10637312000x - 1736704000	\( 2^{28}\cdot 5^{6}\cdot 53^{4}\cdot 71^{5}\cdot 27404129^{2} \)	15T97	Trivial (GRH)
15.11.475252033381120627314724981746126946672848505.1	x^15 - 2x^14 - 23x^13 + 42x^12 + 182x^11 - 301x^10 - 614x^9 + 885x^8 + 918x^7 - 1112x^6 - 525x^5 + 508x^4 + 60x^3 - 65x^2 + x + 1	\( 5\cdot 11\cdot 433\cdot 2879\cdot 1581889\cdot 4381832042556033836676145004417 \)	15T104	Trivial (GRH)
15.11.1321365067721650998272614708394954813952000000.1	x^15 - 378x^13 - 864x^12 + 34944x^11 + 273216x^10 + 281880x^9 - 18133632x^8 - 120731040x^7 - 55931904x^6 + 1226545920x^5 + 2439797760x^4 - 632947200x^3 - 2466662400x^2 + 651264000	\( 2^{15}\cdot 3^{24}\cdot 5^{6}\cdot 53^{4}\cdot 1783^{2}\cdot 603557^{2} \)	15T95	Trivial (GRH)
15.11.1584541601971758745306546692340589068288000000.1	x^15 - 684x^13 - 432x^12 + 146384x^11 + 86128x^10 - 12084336x^9 - 4014720x^8 + 382478112x^7 - 471272384x^6 - 1146538240x^5 + 1889210880x^4 + 416368000x^3 - 1810022400x^2 + 879872000x - 125696000	\( 2^{22}\cdot 5^{6}\cdot 19^{2}\cdot 37^{5}\cdot 491^{4}\cdot 1307^{2}\cdot 3119^{2} \)	15T96	$[3]$ (GRH)
15.11.4248332612098651806088183712995608825856000000.1	x^15 - 306x^13 - 288x^12 + 24240x^11 + 2756x^10 - 112752x^9 + 5324544x^8 - 1338292x^7 - 40210112x^6 - 9352320x^5 + 85779360x^4 + 95779000x^3 + 41322000x^2 + 7952000x + 568000	\( 2^{18}\cdot 5^{6}\cdot 7^{10}\cdot 71^{4}\cdot 223^{2}\cdot 1709^{2}\cdot 31541^{2} \)	15T92	$[3]$ (GRH)
15.11.20460795210884509800211491460024203449856000000.1	x^15 - 1026x^13 - 8208x^12 + 237732x^11 + 4049952x^10 + 11537640x^9 - 234539712x^8 - 2907652896x^7 - 16113845376x^6 - 52098560640x^5 - 105057976320x^4 - 133947814400x^3 - 105124300800x^2 - 46427136000x - 8843264000	\( 2^{15}\cdot 3^{21}\cdot 5^{6}\cdot 17^{4}\cdot 127^{4}\cdot 1709^{2}\cdot 7759^{2} \)	15T95	Trivial (GRH)
15.11.37185061201306863596258469574643558678528000000.1	x^15 - 720x^13 - 7416x^12 + 77582x^11 + 1097648x^10 - 5022270x^9 - 46796256x^8 + 189147496x^7 + 426992368x^6 - 1799651680x^5 - 146822400x^4 + 4945060000x^3 - 5522153600x^2 + 2283904000x - 326272000	\( 2^{21}\cdot 5^{6}\cdot 13\cdot 37^{5}\cdot 293^{2}\cdot 2549^{4}\cdot 18637^{2} \)	15T102	Trivial (GRH)
15.11.89507366965151527968963227271529017344580464041.1	x^15 - 2x^14 - 23x^13 + 42x^12 + 183x^11 - 300x^10 - 614x^9 + 885x^8 + 918x^7 - 1112x^6 - 525x^5 + 508x^4 + 60x^3 - 65x^2 + x + 1	\( 135469\cdot 19903909\cdot 33195596675724214911337754996593321 \)	15T104	Trivial (GRH)