Number field search results

Results (25 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
47.1.384...167.1	x^47 - x - 1	$47$	[1,23]	$-\,11\cdot 199\cdot 227153\cdot 393351713\cdot 3297807724117\cdot 73745876125109\cdot 80\!\cdots\!59$	$7$	$46.9920576706$			✓	$S_{47}$ (as 47T6)	not computed	$2$	$23$	$$
47.1.312...512.1	x^47 + 4x - 4	$47$	[1,23]	$-\,2^{46}\cdot 3\cdot 521\cdot 11213\cdot 282143\cdot 89\!\cdots\!99$	$6$	$88.452032442$			not computed	$S_{47}$ (as 47T6)	not computed	$2$	$23$	$$
47.1.264...456.1	x^47 - 4x - 4	$47$	[1,23]	$-\,2^{46}\cdot 1630520977\cdot 36906152269379\cdot 62\!\cdots\!13$	$4$	$92.5605257743$			not computed	$S_{47}$ (as 47T6)	not computed	$2$	$23$	$$
47.1.268...744.1	x^47 - 2x - 2	$47$	[1,23]	$-\,2^{46}\cdot 3\cdot 919\cdot 34591\cdot 40\!\cdots\!33$	$5$	$92.5924511038$			✓	$S_{47}$ (as 47T6)	not computed	$2$	$23$	$$
47.1.272...336.1	x^47 - x - 2	$47$	[1,23]	$-\,2^{47}\cdot 31\cdot 39010490269\cdot 2162799135849959\cdot 1173213609967733880077131\cdot 631877578695978213816509977$	$6$	$92.6238779755$			✓	$S_{47}$ (as 47T6)	not computed	$2$	$23$	$$
47.1.272...032.1	x^47 - 2	$47$	[1,23]	$-\,2^{46}\cdot 47^{47}$	$2$	$92.6238779755$			✓	$F_{47}$ (as 47T4)	not computed	$2$	$23$	$$
47.1.277...320.1	x^47 + 2x - 2	$47$	[1,23]	$-\,2^{46}\cdot 5\cdot 13\cdot 17\cdot 89\cdot 361179289\cdot 582997712425903553\cdot 19\!\cdots\!87$	$8$	$92.6548218769$			✓	$S_{47}$ (as 47T6)	not computed	$2$	$23$	$$
47.3.815...889.1	x^47 - 3x - 1	$47$	[3,22]	$45361\cdot 5090740900405619\cdot 35\!\cdots\!71$	$3$	$127.204144117$			✓	$S_{47}$ (as 47T6)	not computed	$2$	$24$	$$
47.1.815...784.1	x^47 + 3x - 2	$47$	[1,23]	$-\,2^{47}\cdot 151\cdot 4406810867\cdot 798813369105083\cdot 10\!\cdots\!23$	$5$	$127.204145023$			✓	$S_{47}$ (as 47T6)	not computed	$2$	$23$	$$
47.1.343...439.1	x^47 - 2x - 3	$47$	[1,23]	$-\,13\cdot 19051\cdot 13\!\cdots\!53$	$3$	$137.742384398$			✓	$S_{47}$ (as 47T6)	not computed	$2$	$23$	$$
47.1.343...727.1	x^47 - 3	$47$	[1,23]	$-\,3^{46}\cdot 47^{47}$	$2$	$137.742384399$			✓	$F_{47}$ (as 47T4)	not computed	$2$	$23$	$$
47.1.351...479.1	x^47 + 3x - 3	$47$	[1,23]	$-\,3^{46}\cdot 19\cdot 41\cdot 2593\cdot 95957\cdot 371957\cdot 523877\cdot 221163397457\cdot 47\!\cdots\!53$	$9$	$137.81114769$			✓	$S_{47}$ (as 47T6)	not computed	$2$	$23$	$$
47.1.607...327.1	x^47 + 4x - 1	$47$	[1,23]	$-\,3\cdot 161387\cdot 659693\cdot 1442983\cdot 48897948557\cdot 5667513832583\cdot 47737985627803\cdot 1031694803012501\cdot 1239335306776487\cdot 77947030248288422983$	$10$	$169.60552549$			✓	$S_{47}$ (as 47T6)	not computed	$2$	$23$	$$
47.1.480...384.1	x^47 + 2x - 4	$47$	[1,23]	$-\,2^{90}\cdot 7\cdot 11\cdot 1983262109989\cdot 9629954559409\cdot 26\!\cdots\!33$	$6$	$177.230423466$			not computed	$S_{47}$ (as 47T6)	not computed	$2$	$23$	$$
47.1.192...496.1	x^47 - 3x - 4	$47$	[1,23]	$-\,2^{46}\cdot 503\cdot 12399061109599\cdot 43\!\cdots\!37$	$4$	$182.535803478$			✓	$S_{47}$ (as 47T6)	not computed	$2$	$23$	$$
47.1.192...944.1	x^47 + x - 4	$47$	[1,23]	$-\,2^{46}\cdot 3\cdot 90\!\cdots\!07$	$3$	$182.535803643$			✓	$S_{47}$ (as 47T6)	not computed	$2$	$23$	$$
47.1.588...375.1	x^47 - 5x - 5	$47$	[1,23]	$-\,5^{46}\cdot 101\cdot 40\!\cdots\!87$	$3$	$216.531047325$			not computed	$S_{47}$ (as 47T6)	not computed	$2$	$23$	$$
47.1.551...911.1	x^47 - 4x - 5	$47$	[1,23]	$-\,11\cdot 887\cdot 56\!\cdots\!23$	$3$	$227.089027186$			✓	$S_{47}$ (as 47T6)	not computed	$2$	$23$	$$
47.1.551...375.1	x^47 - 5	$47$	[1,23]	$-\,5^{46}\cdot 47^{47}$	$2$	$227.089032514$			✓	$F_{47}$ (as 47T4)	not computed	$2$	$23$	$$
47.1.551...663.1	x^47 + 2x - 5	$47$	[1,23]	$-\,19\cdot 43\cdot 97694879\cdot 33279582301451\cdot 20\!\cdots\!91$	$5$	$227.089032514$			✓	$S_{47}$ (as 47T6)	not computed	$2$	$23$	$$
47.1.551...127.1	x^47 + 3x - 5	$47$	[1,23]	$-\,769\cdot 204367\cdot 1847903553389\cdot 18\!\cdots\!41$	$4$	$227.089032514$			✓	$S_{47}$ (as 47T6)	not computed	$2$	$23$	$$
47.47.605...769.1	x^47 - x^46 - 138x^45 + 315x^44 + 8338x^43 - 29804x^42 - 276833x^41 + 1433626x^40 + 5033859x^39 - 41190458x^38 - 30657314x^37 + 748097961x^36 - 742659788x^35 - 8506344013x^34 + 21519259357x^33 + 52948548811x^32 - 268879641855x^31 - 30332528938x^30 + 1920252236103x^29 - 2430736233424x^28 - 7367030656288x^27 + 21401598866455x^26 + 5373046913681x^25 - 89240242581627x^24 + 85735098102709x^23 + 174332690558567x^22 - 418760640969237x^21 + 24016008538438x^20 + 845143941649693x^19 - 850093833789498x^18 - 563502754038610x^17 + 1652337279635119x^16 - 688139958495907x^15 - 1132046847057208x^14 + 1399925903803443x^13 - 129366579867529x^12 - 739733924950208x^11 + 464611724348759x^10 + 61382685657965x^9 - 169596960618209x^8 + 46703998783537x^7 + 17972540150505x^6 - 11555848466611x^5 + 591153994800x^4 + 757301830397x^3 - 134933083169x^2 - 1756074840x + 132954859	$47$	[47,0]	$283^{46}$	$1$	$250.969396701$		✓		$C_{47}$ (as 47T1)	not computed	$2$	$46$	$$
47.47.466...641.1	x^47 - x^46 - 322x^45 + 257x^44 + 46168x^43 - 32856x^42 - 3928972x^41 + 2800261x^40 + 223114373x^39 - 173143135x^38 - 9003548066x^37 + 7929128719x^36 + 268197678343x^35 - 271080896060x^34 - 6041385515832x^33 + 6979624724342x^32 + 104494842005772x^31 - 136657122243604x^30 - 1400247413062994x^29 + 2052225750352966x^28 + 14591458839594017x^27 - 23782847219941819x^26 - 118118630838181495x^25 + 213321125182479282x^24 + 738128822260196887x^23 - 1480085655858130569x^22 - 3514638820507932409x^21 + 7908202660646656434x^20 + 12455131093399060106x^19 - 32248927636656562527x^18 - 31433221457470396690x^17 + 98930979031819081241x^16 + 51111011671312688653x^15 - 223422112969694652903x^14 - 36045180999704955067x^13 + 359687682365174498379x^12 - 43326797472112521543x^11 - 392741974421328427418x^10 + 139313975200941570964x^9 + 266729246622027266884x^8 - 153819291119830123270x^7 - 92300136797476126809x^6 + 82337017997204992796x^5 + 4438182302442319866x^4 - 17703030829530739458x^3 + 4375073965542285492x^2 - 7552331260195558x - 66410957360928749	$47$	[47,0]	$659^{46}$	$1$	$573.996347907$		✓		$C_{47}$ (as 47T1)	not computed	$2$	$46$	$$
47.47.609...241.1	x^47 - x^46 - 460x^45 + 327x^44 + 94524x^43 - 38110x^42 - 11539413x^41 + 809932x^40 + 937957195x^39 + 272017844x^38 - 53844657814x^37 - 36415505127x^36 + 2255802403789x^35 + 2452634499322x^34 - 70139481731357x^33 - 106937338241973x^32 + 1626084100876542x^31 + 3250400054052522x^30 - 27906088812601386x^29 - 70884683396944095x^28 + 346512540625848199x^27 + 1118163243198969746x^26 - 2955220812359278078x^25 - 12685164476223506555x^24 + 15046746180109293999x^23 + 101582059147167915284x^22 - 18312922973366227046x^21 - 554548726919125907181x^20 - 318711846399705268031x^19 + 1938753789920516494271x^18 + 2414984135254760303399x^17 - 3792697335240007382545x^16 - 8178953624841789295386x^15 + 2279595290530927592625x^14 + 14681478777833447802999x^13 + 5435523725560836559149x^12 - 12942546360599189199808x^11 - 11501227765200381452105x^10 + 3183515530405052075328x^9 + 7591082677180116655272x^8 + 2077754691851067407232x^7 - 1323128253866746375290x^6 - 896927209808036028574x^5 - 132715131473527952574x^4 + 23448602689225942698x^3 + 8115247135424866684x^2 + 574328145019154892x - 1980612833005069	$47$	[47,0]	$941^{46}$	$1$	$813.432947308$		✓		$C_{47}$ (as 47T1)	not computed	$2$	$46$	$$
47.47.680...841.1	x^47 - 1081x^45 - 705x^44 + 534061x^43 + 683944x^42 - 160057842x^41 - 299647654x^40 + 32561335719x^39 + 78763416061x^38 - 4767066709455x^37 - 13908937919967x^36 + 519679734845940x^35 + 1750397799006104x^34 - 43074182887990763x^33 - 162478138072805487x^32 + 2749329116777664352x^31 + 11358660939804373275x^30 - 136126237738133225032x^29 - 605463962245369166572x^28 + 5246767648352840100798x^27 + 24765274103500484906219x^26 - 157566416740809178648611x^25 - 778707155396426126313230x^24 + 3684240622296757942862071x^23 + 18785271879388363208006658x^22 - 66986754039408931327563467x^21 - 345795459416186142486923619x^20 + 946170254872545787018973465x^19 + 4814104180441102948763936108x^18 - 10375613255284454207094751556x^17 - 50032174963571133079560800941x^16 + 88105844627120217056303008521x^15 + 380945711116472915778482842595x^14 - 573465045108814971325177493888x^13 - 2067158816911927150047646995633x^12 + 2787145282695598886975483579427x^11 + 7670341992113409376277564204296x^10 - 9619799236229244848389374409877x^9 - 18271828994795512973409030766888x^8 + 21757031287162404406727090902813x^7 + 25318069661907634555608128065064x^6 - 28749901083465227418574423514388x^5 - 17172272828610619745842195295332x^4 + 19384902113022958413624018194070x^3 + 2828656546972432377231017394241x^2 - 5355885371863393108886638462583x + 1052824394331287344099620777449	$47$	[47,0]	$47^{92}$	$1$	$1875.1785026$		✓		$C_{47}$ (as 47T1)	not computed	$2$	$46$	$$