| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 15.3.114...000.1 |
$x^{15} - 3 x^{14} + 6 x^{13} - 4 x^{12} + 60 x^{11} - 228 x^{10} + 328 x^{9} - 234 x^{8} - 81 x^{7} + 651 x^{6} - 954 x^{5} + 258 x^{3} + 270 x^{2} - 396 x - 24$ |
$15$ |
[3,6] |
$2^{16}\cdot 3^{28}\cdot 5^{6}\cdot 7^{2}$ |
$4$ |
$40.1784098506$ |
|
|
|
? |
$A_{15}$ (as 15T103) |
trivial |
$2$ |
$8$ |
$20248897.1734$ |
| 15.3.165...000.1 |
$x^{15} - 42 x^{13} - 232 x^{12} - 342 x^{11} + 864 x^{10} + 3052 x^{9} - 7704 x^{8} - 42786 x^{7} - 3072 x^{6} + 330672 x^{5} + 360336 x^{4} - 505624 x^{3} - 727680 x^{2} - 218688 x - 265728$ |
$15$ |
[3,6] |
$2^{30}\cdot 3^{20}\cdot 5^{6}\cdot 7^{10}$ |
$4$ |
$120.561421335$ |
$4296.823103962565$ |
|
|
|
$A_{15}$ (as 15T103) |
trivial |
$2$ |
$8$ |
$220936418447$ |
| 15.7.239...000.1 |
$x^{15} - 6 x^{14} - 35 x^{13} + 155 x^{12} + 90 x^{11} - 2999 x^{10} - 6401 x^{9} + 63495 x^{8} - 44745 x^{7} + 79390 x^{6} + 4121184 x^{5} + 1379896 x^{4} + 1819820 x^{3} + 92482920 x^{2} + 167327200 x + 68779600$ |
$15$ |
[7,4] |
$2^{14}\cdot 3^{14}\cdot 5^{14}\cdot 7^{10}\cdot 11^{6}$ |
$5$ |
$228.350660331$ |
$5661.013417208126$ |
|
|
|
$A_{15}$ (as 15T103) |
trivial |
$2$ |
$10$ |
$67854593545900$ |
| 15.15.261...400.1 |
$x^{15} - 7 x^{14} - 7359928431352125900718990 x^{13} + 1146457846473474900984125591032014636 x^{12} + 19416023607681635771974377467999027201012470447336 x^{11} - 4851441635553959977410832765485972884294052691589377374372104 x^{10} - 24112141174821303187004606425942845234248871089681871165011461250635692496 x^{9} + 7525619576196337038633314245779978268926520611790180372053298333899736463357803938528 x^{8} + 14831714078915979721371947057780505772689617125060296449666823575343124172731731023953452534616512 x^{7} - 5256932037437038243776691960971134474163890327375515560268021053433747350168623150274653781603424258659192064 x^{6} - 4187440903299802988131602439725223670111389325383345006067783417457128080730177931291623405329927138776601510804218358016 x^{5} + 1636289240075960072632144299035232342883646538534039778167325700212172858442261459632125257443454155238866530126648359882779165933056 x^{4} + 383494372081854656235932138604055828450497422037577510303835612027653867214885179476035568117107343912098335867193187164865789498037634655836160 x^{3} - 186190519991829328117093062073654072984048894439789642881671127020544062770027703363859101244685185827323447461850817494168568946387320074577080553170765824 x^{2} + 13508930687881199540651510080488415574271789490099733587937952758668580093635509254682839181235154905691209505141762824480586168456201619647093939738893681190016425984 x + 507411620437731696863219371714152920724096317226541786887422139156853975207125192962971274329824077544411017905137335814893509681760672329266984926805264627052495547140209049600$ |
$15$ |
[15,0] |
$2^{6}\cdot 5^{2}\cdot 40\!\cdots\!13^{2}$ |
$3$ |
$1.44939966195e+24$ |
$3.458842446111571e+120$ |
|
|
|
$A_{15}$ (as 15T103) |
not computed |
$2$ |
$14$ |
|
| 15.15.431...656.1 |
$x^{15} - 5 x^{14} - 221584162646793998513255353501399 x^{13} + 1838670156860300310069312728919884823738949256286 x^{12} - 3507023244192976964558416481099406573730496697448620459346328930 x^{11} - 14362008159569853844540720730083793432812116474852958151205155011697664776172820 x^{10} + 64602056789898574256926262206136858080967125931084643922590575676076508148167756527778331169331 x^{9} - 33697709243721905054152252591855334721489853448734037787055716415386872089045941472773485428938880790887566657 x^{8} - 199381466159240057619705724838804936403878218727037546105365546281797527608452154038159494907307983910975648507019999418706044 x^{7} + 326683869846098044978092609526116450102068872868419127712422323820121517610943957757948356312839662926743742685869776163380748480058707484531 x^{6} - 38578699046534874013040340436824895294135877847715385855724581279195106788112634318355399287835903754765629284615351410300699246590743479564498441342192476 x^{5} - 185939728326540812216443307316257995548796349515614730102904984029787308882837162776107862941289526967590997258789803550527271245670461242543150905101802499111703704829969 x^{4} + 48289058906863954886809276340245314233430190534546012632817767554693810252556657379376803536031751623918227207510936156431241415033549082989120174149268391864347529638405486389804966075 x^{3} + 31992975519327851261488244855753113589281871346020951017875261661894469373179907643763080708058286539443485194979412502463061900571306134152629483321798484323534654221589039563992238039205359337537566 x^{2} - 358331498044011683369137838394734568793729144619439502957388771960860030308117563213045826031148746131597994434418962819750273523632124215559085747527434382566893137231273783971944896294857796980202840024296104890 x - 1862350565305131754269801165431480203311311924697970220537624869577538866666332472102888016379856454708485963606152069180692473824996257515779272821974830524382348895683501928468108135725683587089319830991007586025083385087714$ |
$15$ |
[15,0] |
$2^{10}\cdot 3^{2}\cdot 7^{2}\cdot 97\!\cdots\!03^{2}$ |
$4$ |
$3.76415587973e+31$ |
$2.8029550233745125e+157$ |
|
|
? |
$A_{15}$ (as 15T103) |
not computed |
$2$ |
$14$ |
|
