Number field search results

Results (1-50 of 57 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
35.1.109...339.1	x^35 - x - 1	$35$	[1,17]	$-\,19\cdot 43350623\cdot 10394177419177\cdot 12\!\cdots\!11$	$4$	$34.9892808332$			✓	$S_{35}$ (as 35T407)	trivial	$2$	$17$	$8151690409523.094$
35.1.403...123.1	x^35 + 2x - 1	$35$	[1,17]	$-\,256048319\cdot 15\!\cdots\!17$	$2$	$61.4826208706$			✓	$S_{35}$ (as 35T407)	trivial	$2$	$17$	$363349966210764900$
35.35.876...281.1	x^35 - x^34 - 34x^33 + 33x^32 + 528x^31 - 496x^30 - 4960x^29 + 4495x^28 + 31465x^27 - 27405x^26 - 142506x^25 + 118755x^24 + 475020x^23 - 376740x^22 - 1184040x^21 + 888030x^20 + 2220075x^19 - 1562275x^18 - 3124550x^17 + 2042975x^16 + 3268760x^15 - 1961256x^14 - 2496144x^13 + 1352078x^12 + 1352078x^11 - 646646x^10 - 497420x^9 + 203490x^8 + 116280x^7 - 38760x^6 - 15504x^5 + 3876x^4 + 969x^3 - 153x^2 - 18x + 1	$35$	[35,0]	$71^{34}$	$1$	$62.8586794536$		✓	✓	$C_{35}$ (as 35T1)	trivial	$2$	$34$	$190122458612916620000$
35.1.219...944.1	x^35 + 4x - 4	$35$	[1,17]	$-\,2^{34}\cdot 3\cdot 227\cdot 499\cdot 1637\cdot 252983\cdot 13122193474139\cdot 69164815108090306157070281$	$8$	$64.5284755537$			not computed	$S_{35}$ (as 35T407)	not computed	$2$	$17$	$$
35.1.181...504.1	x^35 - 4x - 4	$35$	[1,17]	$-\,2^{34}\cdot 2393\cdot 3027347\cdot 3480929\cdot 23465153\cdot 86816318477729\cdot 20545919111781857$	$7$	$68.5419242757$			not computed	$S_{35}$ (as 35T407)	trivial	$2$	$17$	$2024409859615809000$
35.1.185...752.1	x^35 - 2x - 2	$35$	[1,17]	$-\,2^{34}\cdot 3\cdot 101\cdot 181\cdot 20265277861\cdot 97\!\cdots\!61$	$6$	$68.5850855824$			✓	$S_{35}$ (as 35T407)	trivial	$2$	$17$	$2711307912253756400$
35.1.189...464.1	x^35 - x - 2	$35$	[1,17]	$-\,2^{35}\cdot 23\cdot 29\cdot 5408561\cdot 3295715551039421859593\cdot 46365427582714972609103$	$6$	$68.6273426958$			✓	$S_{35}$ (as 35T407)	trivial	$2$	$17$	$3872969546476688000$
35.1.189...671.1	x^35 - x - 4	$35$	[1,17]	$-\,21529\cdot 108949\cdot 6512477\cdot 1233879787294159\cdot 10\!\cdots\!57$	$5$	$68.6273426958$			not computed	$S_{35}$ (as 35T407)	trivial	$2$	$17$	$2369144174730249700$
35.1.189...000.1	x^35 - 2	$35$	[1,17]	$-\,2^{34}\cdot 5^{35}\cdot 7^{35}$	$3$	$68.6273426958$			✓	$C_7:(C_6\times F_5)$ (as 35T20)	not computed	$2$	$17$	$$
35.1.193...248.1	x^35 + 2x - 2	$35$	[1,17]	$-\,2^{34}\cdot 11\!\cdots\!47$	$2$	$68.668733247$			✓	$S_{35}$ (as 35T407)	not computed	$2$	$17$	$$
35.3.588...077.1	x^35 - 3x - 1	$35$	[3,16]	$263\cdot 22\!\cdots\!79$	$2$	$92.2239312988$			✓	$S_{35}$ (as 35T407)	not computed	$2$	$18$	$$
35.1.588...827.1	x^35 + 3x - 1	$35$	[1,17]	$-\,11\cdot 98621\cdot 1256737\cdot 43\!\cdots\!41$	$4$	$92.2239312988$			✓	$S_{35}$ (as 35T407)	not computed	$2$	$17$	$$
35.1.588...952.1	x^35 + 3x - 2	$35$	[1,17]	$-\,2^{35}\cdot 67\cdot 997\cdot 10501\cdot 21885937\cdot 61024809499\cdot 18\!\cdots\!47$	$7$	$92.2240161471$			✓	$S_{35}$ (as 35T407)	not computed	$2$	$17$	$$
35.1.165...904.1	x^35 + 4x - 2	$35$	[1,17]	$-\,2^{34}\cdot 3\cdot 291647\cdot 188120963917\cdot 64268062741853\cdot 129806582432617\cdot 699615044068223$	$7$	$101.441758241$			not computed	$S_{35}$ (as 35T407)	not computed	$2$	$17$	$$
35.1.177...923.1	x^35 - 3x - 3	$35$	[1,17]	$-\,3^{34}\cdot 953\cdot 6256153603608033049\cdot 17\!\cdots\!11$	$4$	$101.660870002$			✓	$S_{35}$ (as 35T407)	not computed	$2$	$17$	$$
35.1.183...339.1	x^35 - x - 3	$35$	[1,17]	$-\,31\cdot 59\!\cdots\!69$	$2$	$101.755352527$			✓	$S_{35}$ (as 35T407)	not computed	$2$	$17$	$$
35.1.183...875.1	x^35 - 3	$35$	[1,17]	$-\,3^{34}\cdot 5^{35}\cdot 7^{35}$	$3$	$101.755352527$			✓	$C_7:(C_6\times F_5)$ (as 35T20)	not computed	$2$	$17$	$$
35.1.189...827.1	x^35 + 3x - 3	$35$	[1,17]	$-\,3^{34}\cdot 13\cdot 241667\cdot 21805563631\cdot 7788124267751\cdot 2132536222168538736270533$	$6$	$101.846943286$			✓	$S_{35}$ (as 35T407)	not computed	$2$	$17$	$$
35.35.107...681.1	x^35 - 2x^34 - 91x^33 + 186x^32 + 3529x^31 - 7282x^30 - 77406x^29 + 160015x^28 + 1074054x^27 - 2215841x^26 - 9975621x^25 + 20528466x^24 + 63908089x^23 - 131541229x^22 - 286306729x^21 + 593348019x^20 + 897545333x^19 - 1896502635x^18 - 1942677455x^17 + 4283320775x^16 + 2804705170x^15 - 6752081061x^14 - 2493142459x^13 + 7254188151x^12 + 1058706744x^11 - 5105442290x^10 + 147588576x^9 + 2206890342x^8 - 365733379x^7 - 523140235x^6 + 145322301x^5 + 51716162x^4 - 20476030x^3 - 56585x^2 + 426253x - 7523	$35$	[35,0]	$11^{28}\cdot 29^{30}$	$2$	$122.066964904$		✓	not computed	$C_{35}$ (as 35T1)	trivial	$2$	$34$	$21825601175888975000000000$
35.3.138...264.1	x^35 - 4x - 2	$35$	[3,16]	$2^{34}\cdot 19\cdot 168467557\cdot 25\!\cdots\!87$	$4$	$122.965241727$			✓	$S_{35}$ (as 35T407)	not computed	$2$	$18$	$$
35.3.138...389.1	x^35 - 4x - 1	$35$	[3,16]	$13\cdot 7589\cdot 20542855181\cdot 1539824338977817412998292597\cdot 44\!\cdots\!61$	$5$	$122.965241732$			✓	$S_{35}$ (as 35T407)	not computed	$2$	$18$	$$
35.1.138...139.1	x^35 + 4x - 1	$35$	[1,17]	$-\,3\cdot 11\cdot 313\cdot 2039\cdot 7735841\cdot 2351499104023\cdot 659569685611056889\cdot 54928069223700611994891513947$	$8$	$122.965241732$			✓	$S_{35}$ (as 35T407)	not computed	$2$	$17$	$$
35.1.138...139.1	x^35 + 4x - 3	$35$	[1,17]	$-\,9138888871558869679\cdot 15\!\cdots\!41$	$2$	$122.969892839$			✓	$S_{35}$ (as 35T407)	not computed	$2$	$17$	$$
35.1.813...688.1	x^35 - 2x - 4	$35$	[1,17]	$-\,2^{66}\cdot 3\cdot 19661\cdot 769973\cdot 4451823287\cdot 54\!\cdots\!49$	$6$	$129.337543334$			not computed	$S_{35}$ (as 35T407)	not computed	$2$	$17$	$$
35.1.813...312.1	x^35 + 2x - 4	$35$	[1,17]	$-\,2^{66}\cdot 53\cdot 73\cdot 4799\cdot 29426707\cdot 2986177911580117\cdot 675732378059188256648497$	$7$	$129.337543334$			not computed	$S_{35}$ (as 35T407)	not computed	$2$	$17$	$$
35.1.325...048.1	x^35 - 3x - 4	$35$	[1,17]	$-\,2^{34}\cdot 1549\cdot 423786696769\cdot 86327107557848503\cdot 33\!\cdots\!79$	$5$	$134.563197778$			✓	$S_{35}$ (as 35T407)	not computed	$2$	$17$	$$
35.1.325...536.1	x^35 + x - 4	$35$	[1,17]	$-\,2^{34}\cdot 3\cdot 13\cdot 48\!\cdots\!11$	$4$	$134.563204728$			✓	$S_{35}$ (as 35T407)	not computed	$2$	$17$	$$
35.1.136...875.1	x^35 + 5x - 3	$35$	[1,17]	$-\,5^{33}\cdot 1098074000209\cdot 10\!\cdots\!67$	$3$	$140.201042986$			not computed	$S_{35}$ (as 35T407)	not computed	$2$	$17$	$$
35.1.855...000.1	x^35 + 5x - 2	$35$	[1,17]	$-\,2^{35}\cdot 5^{35}\cdot 29\cdot 37\cdot 4783\cdot 451109\cdot 36948068942212518669550297789$	$7$	$147.737473193$			not computed	$S_{35}$ (as 35T407)	not computed	$2$	$17$	$$
35.3.342...125.1	x^35 - 5x - 3	$35$	[3,16]	$5^{35}\cdot 47\cdot 2551\cdot 98\!\cdots\!77$	$4$	$153.706549805$			✓	$S_{35}$ (as 35T407)	not computed	$2$	$18$	$$
35.3.342...000.1	x^35 - 5x - 2	$35$	[3,16]	$2^{35}\cdot 3\cdot 5^{35}\cdot 846499\cdot 13\!\cdots\!69$	$5$	$153.706552165$			✓	$S_{35}$ (as 35T407)	not computed	$2$	$18$	$$
35.3.342...125.1	x^35 - 5x - 1	$35$	[3,16]	$3\cdot 5^{35}\cdot 10273\cdot 14843\cdot 25\!\cdots\!29$	$5$	$153.706552165$			✓	$S_{35}$ (as 35T407)	not computed	$2$	$18$	$$
35.1.342...875.1	x^35 + 5x - 1	$35$	[1,17]	$-\,5^{35}\cdot 11\cdot 241663\cdot 1377785519387\cdot 12423383848143479\cdot 258379951197664711$	$6$	$153.706552165$			✓	$S_{35}$ (as 35T407)	not computed	$2$	$17$	$$
35.1.345...000.1	x^35 + 5x - 4	$35$	[1,17]	$-\,2^{34}\cdot 5^{35}\cdot 23\cdot 30\!\cdots\!67$	$4$	$153.748125419$			✓	$S_{35}$ (as 35T407)	not computed	$2$	$17$	$$
35.1.675...875.1	x^35 - 5x - 5	$35$	[1,17]	$-\,5^{35}\cdot 29\cdot 2243199001\cdot 214847929968602317\cdot 1659496377096759652722647$	$5$	$156.719676569$			not computed	$S_{35}$ (as 35T407)	not computed	$2$	$17$	$$
35.1.641...339.1	x^35 - x - 5	$35$	[1,17]	$-\,137320571\cdot 46\!\cdots\!09$	$2$	$167.135027491$			✓	$S_{35}$ (as 35T407)	not computed	$2$	$17$	$$
35.1.641...875.1	x^35 - 5	$35$	[1,17]	$-\,5^{69}\cdot 7^{35}$	$2$	$167.135027491$			✓	$C_7:(C_6\times F_5)$ (as 35T20)	not computed	$2$	$17$	$$
35.1.641...411.1	x^35 + x - 5	$35$	[1,17]	$-\,3\cdot 29\cdot 83\cdot 14920870913449\cdot 59\!\cdots\!59$	$5$	$167.135027491$			✓	$S_{35}$ (as 35T407)	not computed	$2$	$17$	$$
35.1.641...827.1	x^35 + 3x - 5	$35$	[1,17]	$-\,47\cdot 397\cdot 1877\cdot 119039\cdot 441804439\cdot 34\!\cdots\!09$	$6$	$167.135027495$			✓	$S_{35}$ (as 35T407)	not computed	$2$	$17$	$$
35.1.675...875.1	x^35 + 5x - 5	$35$	[1,17]	$-\,5^{35}\cdot 1481\cdot 13004394089\cdot 2075469389711\cdot 5810445451732846110092217889$	$5$	$167.383263545$			✓	$S_{35}$ (as 35T407)	not computed	$2$	$17$	$$
35.35.145...169.1	x^35 - 2x^34 - 121x^33 + 124x^32 + 6435x^31 - 1020x^30 - 195036x^29 - 112597x^28 + 3683986x^27 + 4452851x^26 - 44769607x^25 - 80359740x^24 + 347984933x^23 + 850835561x^22 - 1630509423x^21 - 5621246939x^20 + 3615565971x^19 + 23234081997x^18 + 3088781711x^17 - 57619940147x^16 - 39347873390x^15 + 76695393961x^14 + 92864249975x^13 - 38675667681x^12 - 94158719636x^11 - 10380297650x^10 + 42855721796x^9 + 16263455858x^8 - 7226936109x^7 - 4634581071x^6 - 47622511x^5 + 349101928x^4 + 70736582x^3 + 5060011x^2 + 136327x + 859	$35$	[35,0]	$11^{28}\cdot 43^{30}$	$2$	$171.092104053$		✓	not computed	$C_{35}$ (as 35T1)	trivial	$2$	$34$	$8063096359873239000000000000$
35.35.106...241.1	x^35 - x^34 - 102x^33 + 231x^32 + 4336x^31 - 15350x^30 - 93149x^29 + 492148x^28 + 885684x^27 - 8797227x^26 + 2494886x^25 + 89830596x^24 - 154446290x^23 - 471756827x^22 + 1664362308x^21 + 444168124x^20 - 8565464505x^19 + 8653560326x^18 + 19862461891x^17 - 47903559470x^16 + 736744022x^15 + 100720726682x^14 - 96083394992x^13 - 62920019542x^12 + 165504701751x^11 - 60624002242x^10 - 87564669300x^9 + 86642725878x^8 - 451900172x^7 - 32473918206x^6 + 11871839347x^5 + 3432884529x^4 - 2696920777x^3 + 146105313x^2 + 172726939x - 27756643	$35$	[35,0]	$211^{34}$	$1$	$181.081625838$		✓	not computed	$C_{35}$ (as 35T1)	trivial	$2$	$34$	$24168639235544094000000000000$
35.35.732...081.1	x^35 - 7x^34 - 112x^33 + 742x^32 + 5845x^31 - 34447x^30 - 188041x^29 + 918544x^28 + 4120599x^27 - 15488536x^26 - 63930916x^25 + 170889838x^24 + 709660070x^23 - 1224719069x^22 - 5607885533x^21 + 5331715046x^20 + 31035849173x^19 - 10542390278x^18 - 116936498434x^17 - 15812866636x^16 + 286852619543x^15 + 146466192098x^14 - 426702558436x^13 - 357822103121x^12 + 338413935629x^11 + 421000631443x^10 - 94811511375x^9 - 240823440823x^8 - 25297046987x^7 + 58988457696x^6 + 13678049308x^5 - 6371815744x^4 - 1687698845x^3 + 280068103x^2 + 55092156x - 2660503	$35$	[35,0]	$7^{60}\cdot 11^{28}$	$2$	$191.361094063$		✓	not computed	$C_{35}$ (as 35T1)	trivial	$2$	$34$	$103376387230934820000000000000$
35.35.103...625.1	x^35 - 5x^34 - 120x^33 + 560x^32 + 6265x^31 - 27063x^30 - 188895x^29 + 746800x^28 + 3677845x^27 - 13130310x^26 - 48923530x^25 + 155517810x^24 + 458129250x^23 - 1279983515x^22 - 3063191465x^21 + 7446901792x^20 + 14674072475x^19 - 30859715040x^18 - 50096318770x^17 + 91037787910x^16 + 120155286235x^15 - 189447334860x^14 - 197298653000x^13 + 272612081065x^12 + 212356717105x^11 - 261877354307x^10 - 139209319745x^9 + 158110983885x^8 + 48766657725x^7 - 53789658890x^6 - 7150843552x^5 + 8233276160x^4 + 456884545x^3 - 363355535x^2 - 50594420x - 1782107	$35$	[35,0]	$5^{56}\cdot 29^{30}$	$2$	$235.416015661$		✓	not computed	$C_{35}$ (as 35T1)	trivial	$2$	$34$	$2479808589614732200000000000000$
35.35.180...921.1	x^35 - x^34 - 136x^33 + 115x^32 + 7922x^31 - 5864x^30 - 262379x^29 + 176786x^28 + 5536174x^27 - 3463751x^26 - 78912031x^25 + 45605901x^24 + 785104244x^23 - 406720184x^22 - 5548252572x^21 + 2436396552x^20 + 28031325744x^19 - 9529852980x^18 - 100888672963x^17 + 22693210859x^16 + 254967397769x^15 - 26498170926x^14 - 440501997963x^13 - 3333796454x^12 + 500538383949x^11 + 44640325883x^10 - 358942724140x^9 - 43476115800x^8 + 159203701176x^7 + 16418359222x^6 - 42718375268x^5 - 1999390430x^4 + 6413147106x^3 - 204719982x^2 - 415325205x + 48529823	$35$	[35,0]	$281^{34}$	$1$	$239.190145058$		✓	not computed	$C_{35}$ (as 35T1)	trivial	$2$	$34$	$6612930761186456000000000000000$
35.35.497...681.1	x^35 - 2x^34 - 181x^33 + 470x^32 + 14259x^31 - 45478x^30 - 638530x^29 + 2447153x^28 + 17767052x^27 - 82345759x^26 - 312539633x^25 + 1833247298x^24 + 3264215879x^23 - 27715265019x^22 - 13487454777x^21 + 286033632049x^20 - 123264134993x^19 - 1983204888009x^18 + 2337315606897x^17 + 8777927035267x^16 - 17238219604018x^15 - 21289728738165x^14 + 71563023595709x^13 + 8692436762607x^12 - 169783075654432x^11 + 94786315419610x^10 + 202072200901306x^9 - 240242794434974x^8 - 58566297948415x^7 + 212040077699383x^6 - 73316281317651x^5 - 51014137537536x^4 + 37974482870362x^3 - 1868368126575x^2 - 3872034006535x + 804494744591	$35$	[35,0]	$11^{28}\cdot 71^{30}$	$2$	$262.970491728$		✓	not computed	$C_{35}$ (as 35T1)	trivial	$2$	$34$	$14144996650663707000000000000000$
35.35.426...641.1	x^35 - 2x^34 - 147x^33 + 384x^32 + 8999x^31 - 28384x^30 - 300934x^29 + 1116603x^28 + 6027458x^27 - 26518095x^26 - 73782007x^25 + 404019590x^24 + 521840181x^23 - 4069268247x^22 - 1503940067x^21 + 27441438677x^20 - 6471979421x^19 - 124171354119x^18 + 81524582969x^17 + 375114725905x^16 - 364687984188x^15 - 747339096335x^14 + 926308497451x^13 + 961292881275x^12 - 1451786049968x^11 - 771321612374x^10 + 1427632011474x^9 + 365928432486x^8 - 868346663001x^7 - 97103750919x^6 + 312022190475x^5 + 17703737306x^4 - 59996070990x^3 - 4579250401x^2 + 4824514261x + 750695467	$35$	[35,0]	$29^{30}\cdot 31^{28}$	$2$	$279.623297743$		✓	not computed	$C_{35}$ (as 35T1)	trivial	$2$	$34$	$51550321315774970000000000000000$
35.35.168...681.1	x^35 - x^34 - 204x^33 + 437x^32 + 17534x^31 - 54290x^30 - 824862x^29 + 3275941x^28 + 23317913x^27 - 115242097x^26 - 407103864x^25 + 2577740505x^24 + 4218284220x^23 - 38412158946x^22 - 19912715245x^21 + 391393011501x^20 - 73963916883x^19 - 2766871309456x^18 + 1816877075105x^17 + 13678303310453x^16 - 13286645514747x^15 - 47446655533795x^14 + 55834172665771x^13 + 115251505419203x^12 - 148585020568878x^11 - 193921735357495x^10 + 253198008831294x^9 + 219700193289987x^8 - 266521489745621x^7 - 156623228737724x^6 + 157601287591422x^5 + 59099363823325x^4 - 42232493776557x^3 - 6358323449919x^2 + 3052649440546x - 157964821171	$35$	[35,0]	$421^{34}$	$1$	$354.244085038$		✓		$C_{35}$ (as 35T1)	not computed	$2$	$34$	$$
35.35.705...625.1	x^35 - 175x^33 - 70x^32 + 13125x^31 + 9702x^30 - 556640x^29 - 573225x^28 + 14844900x^27 + 19050185x^26 - 261854635x^25 - 394847250x^24 + 3128435905x^23 + 5347852195x^22 - 25515383355x^21 - 48297678121x^20 + 141795944465x^19 + 292585456625x^18 - 533394487115x^17 - 1187150912745x^16 + 1349113537702x^15 + 3207931617015x^14 - 2286376450785x^13 - 5710072444965x^12 + 2606036871270x^11 + 6560227221870x^10 - 2026242763720x^9 - 4691478893710x^8 + 1084067118185x^7 + 1962115542205x^6 - 373976828869x^5 - 432767079290x^4 + 65717425060x^3 + 43746645075x^2 - 3865111915x - 1645272349	$35$	[35,0]	$5^{56}\cdot 7^{60}$	$2$	$369.05534886$		✓	not computed	$C_{35}$ (as 35T1)	not computed	$2$	$34$	$$
35.35.313...761.1	x^35 - x^34 - 238x^33 + 173x^32 + 24286x^31 - 16434x^30 - 1418466x^29 + 1081623x^28 + 53047154x^27 - 49719432x^26 - 1339060322x^25 + 1572006663x^24 + 23323700077x^23 - 34062526929x^22 - 280163543133x^21 + 504952475173x^20 + 2262920124956x^19 - 5071803868827x^18 - 11476437360382x^17 + 33655878701114x^16 + 29727135340615x^15 - 140118838407360x^14 + 3247425380495x^13 + 329245748251530x^12 - 225104736115922x^11 - 332674574789057x^10 + 467468058300787x^9 - 15355505673450x^8 - 263968105366926x^7 + 131023125506686x^6 + 23123425964865x^5 - 32591926570801x^4 + 5190946345187x^3 + 1696655472839x^2 - 515233369184x + 22178194211	$35$	[35,0]	$491^{34}$	$1$	$411.332901928$		✓	not computed	$C_{35}$ (as 35T1)	not computed	$2$	$34$	$$