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Properties

Label 36.36.1387509954...5953.1
Degree $36$
Signature $[36, 0]$
Discriminant $17^{27}\cdot 19^{32}$
Root discriminant $114.68$
Ramified primes $17, 19$
Class number Not computed
Class group Not computed
Galois group $C_{36}$ (as 36T1)

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Show commands for: Magma / SageMath / Pari/GP

magma: R<x> := PolynomialRing(Rationals()); K<a> := NumberField(R![131479, 289902, -8104196, -20290580, 113625303, 295821384, -620220074, -1656296027, 1874543316, 4933888279, -3641245978, -9032341692, 4892716648, 10966716924, -4725796398, -9231423375, 3347805950, 5531856779, -1756656704, -2395183687, 685040172, 753951297, -198208062, -172282852, 42269189, 28311871, -6560791, -3282873, 725836, 259850, -55320, -13255, 2741, 390, -79, -5, 1]);
 
sage: x = polygen(QQ); K.<a> = NumberField(x^36 - 5*x^35 - 79*x^34 + 390*x^33 + 2741*x^32 - 13255*x^31 - 55320*x^30 + 259850*x^29 + 725836*x^28 - 3282873*x^27 - 6560791*x^26 + 28311871*x^25 + 42269189*x^24 - 172282852*x^23 - 198208062*x^22 + 753951297*x^21 + 685040172*x^20 - 2395183687*x^19 - 1756656704*x^18 + 5531856779*x^17 + 3347805950*x^16 - 9231423375*x^15 - 4725796398*x^14 + 10966716924*x^13 + 4892716648*x^12 - 9032341692*x^11 - 3641245978*x^10 + 4933888279*x^9 + 1874543316*x^8 - 1656296027*x^7 - 620220074*x^6 + 295821384*x^5 + 113625303*x^4 - 20290580*x^3 - 8104196*x^2 + 289902*x + 131479)
 
gp: K = bnfinit(x^36 - 5*x^35 - 79*x^34 + 390*x^33 + 2741*x^32 - 13255*x^31 - 55320*x^30 + 259850*x^29 + 725836*x^28 - 3282873*x^27 - 6560791*x^26 + 28311871*x^25 + 42269189*x^24 - 172282852*x^23 - 198208062*x^22 + 753951297*x^21 + 685040172*x^20 - 2395183687*x^19 - 1756656704*x^18 + 5531856779*x^17 + 3347805950*x^16 - 9231423375*x^15 - 4725796398*x^14 + 10966716924*x^13 + 4892716648*x^12 - 9032341692*x^11 - 3641245978*x^10 + 4933888279*x^9 + 1874543316*x^8 - 1656296027*x^7 - 620220074*x^6 + 295821384*x^5 + 113625303*x^4 - 20290580*x^3 - 8104196*x^2 + 289902*x + 131479, 1)
 

Normalized defining polynomial

\( x^{36} - 5 x^{35} - 79 x^{34} + 390 x^{33} + 2741 x^{32} - 13255 x^{31} - 55320 x^{30} + 259850 x^{29} + 725836 x^{28} - 3282873 x^{27} - 6560791 x^{26} + 28311871 x^{25} + 42269189 x^{24} - 172282852 x^{23} - 198208062 x^{22} + 753951297 x^{21} + 685040172 x^{20} - 2395183687 x^{19} - 1756656704 x^{18} + 5531856779 x^{17} + 3347805950 x^{16} - 9231423375 x^{15} - 4725796398 x^{14} + 10966716924 x^{13} + 4892716648 x^{12} - 9032341692 x^{11} - 3641245978 x^{10} + 4933888279 x^{9} + 1874543316 x^{8} - 1656296027 x^{7} - 620220074 x^{6} + 295821384 x^{5} + 113625303 x^{4} - 20290580 x^{3} - 8104196 x^{2} + 289902 x + 131479 \)

magma: DefiningPolynomial(K);
 
sage: K.defining_polynomial()
 
gp: K.pol
 

Invariants

Degree:  $36$
magma: Degree(K);
 
sage: K.degree()
 
gp: poldegree(K.pol)
 
Signature:  $[36, 0]$
magma: Signature(K);
 
sage: K.signature()
 
gp: K.sign
 
Discriminant:  \(138750995485716909371262412964988528335755201772779980362581466025765915953=17^{27}\cdot 19^{32}\)
magma: Discriminant(Integers(K));
 
sage: K.disc()
 
gp: K.disc
 
Root discriminant:  $114.68$
magma: Abs(Discriminant(Integers(K)))^(1/Degree(K));
 
sage: (K.disc().abs())^(1./K.degree())
 
gp: abs(K.disc)^(1/poldegree(K.pol))
 
Ramified primes:  $17, 19$
magma: PrimeDivisors(Discriminant(Integers(K)));
 
sage: K.disc().support()
 
gp: factor(abs(K.disc))[,1]~
 
This field is Galois and abelian over $\Q$.
Conductor:  \(323=17\cdot 19\)
Dirichlet character group:    $\lbrace$$\chi_{323}(256,·)$, $\chi_{323}(1,·)$, $\chi_{323}(4,·)$, $\chi_{323}(137,·)$, $\chi_{323}(140,·)$, $\chi_{323}(271,·)$, $\chi_{323}(16,·)$, $\chi_{323}(273,·)$, $\chi_{323}(149,·)$, $\chi_{323}(157,·)$, $\chi_{323}(30,·)$, $\chi_{323}(290,·)$, $\chi_{323}(35,·)$, $\chi_{323}(169,·)$, $\chi_{323}(302,·)$, $\chi_{323}(47,·)$, $\chi_{323}(305,·)$, $\chi_{323}(310,·)$, $\chi_{323}(55,·)$, $\chi_{323}(188,·)$, $\chi_{323}(191,·)$, $\chi_{323}(64,·)$, $\chi_{323}(81,·)$, $\chi_{323}(220,·)$, $\chi_{323}(225,·)$, $\chi_{323}(123,·)$, $\chi_{323}(101,·)$, $\chi_{323}(106,·)$, $\chi_{323}(237,·)$, $\chi_{323}(239,·)$, $\chi_{323}(115,·)$, $\chi_{323}(118,·)$, $\chi_{323}(120,·)$, $\chi_{323}(251,·)$, $\chi_{323}(234,·)$, $\chi_{323}(254,·)$$\rbrace$
This is not a CM field.

Integral basis (with respect to field generator \(a\))

$1$, $a$, $a^{2}$, $a^{3}$, $a^{4}$, $a^{5}$, $a^{6}$, $a^{7}$, $a^{8}$, $a^{9}$, $a^{10}$, $a^{11}$, $a^{12}$, $a^{13}$, $a^{14}$, $a^{15}$, $a^{16}$, $a^{17}$, $a^{18}$, $a^{19}$, $a^{20}$, $a^{21}$, $a^{22}$, $a^{23}$, $a^{24}$, $a^{25}$, $a^{26}$, $\frac{1}{2} a^{27} - \frac{1}{2} a^{26} - \frac{1}{2} a^{25} - \frac{1}{2} a^{24} - \frac{1}{2} a^{23} - \frac{1}{2} a^{21} - \frac{1}{2} a^{17} - \frac{1}{2} a^{16} - \frac{1}{2} a^{15} - \frac{1}{2} a^{14} - \frac{1}{2} a^{13} - \frac{1}{2} a^{12} - \frac{1}{2} a^{11} - \frac{1}{2} a^{10} - \frac{1}{2} a^{9} - \frac{1}{2} a^{8} - \frac{1}{2} a^{6} - \frac{1}{2} a^{4} - \frac{1}{2} a^{3} - \frac{1}{2} a - \frac{1}{2}$, $\frac{1}{2} a^{28} - \frac{1}{2} a^{23} - \frac{1}{2} a^{22} - \frac{1}{2} a^{21} - \frac{1}{2} a^{18} - \frac{1}{2} a^{8} - \frac{1}{2} a^{7} - \frac{1}{2} a^{6} - \frac{1}{2} a^{5} - \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2}$, $\frac{1}{2} a^{29} - \frac{1}{2} a^{24} - \frac{1}{2} a^{23} - \frac{1}{2} a^{22} - \frac{1}{2} a^{19} - \frac{1}{2} a^{9} - \frac{1}{2} a^{8} - \frac{1}{2} a^{7} - \frac{1}{2} a^{6} - \frac{1}{2} a^{4} - \frac{1}{2} a^{3} - \frac{1}{2} a$, $\frac{1}{2} a^{30} - \frac{1}{2} a^{25} - \frac{1}{2} a^{24} - \frac{1}{2} a^{23} - \frac{1}{2} a^{20} - \frac{1}{2} a^{10} - \frac{1}{2} a^{9} - \frac{1}{2} a^{8} - \frac{1}{2} a^{7} - \frac{1}{2} a^{5} - \frac{1}{2} a^{4} - \frac{1}{2} a^{2}$, $\frac{1}{382} a^{31} + \frac{6}{191} a^{30} - \frac{7}{191} a^{29} - \frac{35}{191} a^{28} + \frac{8}{191} a^{27} + \frac{147}{382} a^{26} + \frac{177}{382} a^{25} - \frac{167}{382} a^{24} - \frac{65}{191} a^{23} + \frac{10}{191} a^{22} - \frac{13}{382} a^{21} + \frac{62}{191} a^{20} + \frac{17}{191} a^{19} - \frac{65}{191} a^{18} + \frac{25}{191} a^{17} + \frac{62}{191} a^{16} + \frac{79}{191} a^{15} + \frac{90}{191} a^{14} - \frac{48}{191} a^{13} + \frac{94}{191} a^{12} - \frac{61}{382} a^{11} - \frac{171}{382} a^{10} - \frac{75}{382} a^{9} + \frac{179}{382} a^{8} - \frac{8}{191} a^{7} - \frac{175}{382} a^{6} - \frac{181}{382} a^{5} - \frac{44}{191} a^{4} - \frac{179}{382} a^{3} + \frac{93}{191} a^{2} + \frac{7}{191} a + \frac{90}{191}$, $\frac{1}{382} a^{32} + \frac{33}{382} a^{30} - \frac{93}{382} a^{29} + \frac{46}{191} a^{28} - \frac{45}{382} a^{27} - \frac{59}{382} a^{26} - \frac{95}{191} a^{25} - \frac{18}{191} a^{24} + \frac{26}{191} a^{23} - \frac{31}{191} a^{22} - \frac{51}{191} a^{21} - \frac{117}{382} a^{20} + \frac{35}{382} a^{19} + \frac{41}{191} a^{18} - \frac{47}{191} a^{17} - \frac{92}{191} a^{16} - \frac{94}{191} a^{15} + \frac{18}{191} a^{14} - \frac{94}{191} a^{13} - \frac{25}{382} a^{12} + \frac{179}{382} a^{11} - \frac{62}{191} a^{10} - \frac{67}{382} a^{9} + \frac{64}{191} a^{8} + \frac{17}{382} a^{7} - \frac{91}{191} a^{6} - \frac{17}{382} a^{5} + \frac{113}{382} a^{4} - \frac{149}{382} a^{3} - \frac{117}{382} a^{2} - \frac{179}{382} a + \frac{66}{191}$, $\frac{1}{382} a^{33} + \frac{42}{191} a^{30} - \frac{19}{382} a^{29} - \frac{27}{382} a^{28} - \frac{7}{191} a^{27} + \frac{58}{191} a^{26} - \frac{147}{382} a^{25} + \frac{12}{191} a^{24} - \frac{165}{382} a^{23} - \frac{189}{382} a^{22} + \frac{121}{382} a^{21} - \frac{23}{191} a^{20} - \frac{85}{382} a^{19} - \frac{3}{191} a^{18} - \frac{115}{382} a^{17} + \frac{113}{382} a^{16} - \frac{21}{382} a^{15} + \frac{175}{382} a^{14} - \frac{52}{191} a^{13} - \frac{52}{191} a^{12} + \frac{85}{191} a^{11} - \frac{77}{191} a^{10} + \frac{60}{191} a^{9} + \frac{31}{382} a^{8} - \frac{18}{191} a^{7} + \frac{14}{191} a^{6} + \frac{165}{382} a^{5} - \frac{55}{191} a^{4} + \frac{30}{191} a^{3} - \frac{7}{191} a^{2} + \frac{26}{191} a - \frac{19}{382}$, $\frac{1}{1347985174} a^{34} - \frac{793785}{1347985174} a^{33} + \frac{1158397}{1347985174} a^{32} - \frac{731793}{673992587} a^{31} + \frac{132859629}{673992587} a^{30} - \frac{135944800}{673992587} a^{29} - \frac{287636973}{1347985174} a^{28} + \frac{16162892}{673992587} a^{27} + \frac{600662911}{1347985174} a^{26} - \frac{135489548}{673992587} a^{25} + \frac{316158339}{1347985174} a^{24} + \frac{74219715}{673992587} a^{23} - \frac{270709511}{1347985174} a^{22} - \frac{301734078}{673992587} a^{21} + \frac{157539561}{673992587} a^{20} + \frac{567176637}{1347985174} a^{19} + \frac{507390069}{1347985174} a^{18} - \frac{201617281}{1347985174} a^{17} + \frac{565607291}{1347985174} a^{16} - \frac{613879765}{1347985174} a^{15} + \frac{111209012}{673992587} a^{14} - \frac{83962305}{1347985174} a^{13} - \frac{312474774}{673992587} a^{12} + \frac{19376848}{673992587} a^{11} + \frac{627411043}{1347985174} a^{10} - \frac{147960068}{673992587} a^{9} + \frac{156991659}{1347985174} a^{8} - \frac{304843108}{673992587} a^{7} + \frac{413840565}{1347985174} a^{6} + \frac{109312699}{673992587} a^{5} - \frac{136703403}{1347985174} a^{4} - \frac{544161655}{1347985174} a^{3} - \frac{482450441}{1347985174} a^{2} - \frac{137836100}{673992587} a + \frac{146655969}{673992587}$, $\frac{1}{6090026173840654386622070022661166681208230391556732632746721266852361178309633221671326156131010321177595015397118} a^{35} - \frac{639890037625034733487767030790189369317563758854575423274168605729417015822693726764281236635725594663246}{3045013086920327193311035011330583340604115195778366316373360633426180589154816610835663078065505160588797507698559} a^{34} + \frac{687775353151431798144498390434328179477897247055011143425548579916715451897396374303778732353843784468247005766}{3045013086920327193311035011330583340604115195778366316373360633426180589154816610835663078065505160588797507698559} a^{33} - \frac{1158507037175517267179496914762513472909757062995498761957319718984066577266951980089843963727423065013535808491}{3045013086920327193311035011330583340604115195778366316373360633426180589154816610835663078065505160588797507698559} a^{32} - \frac{1451155288992376257799392199710583285858020877603674976710314088970997696115590494717306616248875668448574682171}{3045013086920327193311035011330583340604115195778366316373360633426180589154816610835663078065505160588797507698559} a^{31} + \frac{277393791944218849290796438793391558241666565441170775921004662424766833586512212130057338312213844458830326499481}{3045013086920327193311035011330583340604115195778366316373360633426180589154816610835663078065505160588797507698559} a^{30} + \frac{1075452331506547783074444390381110714283918513573140229322237084828853719238513821864210240753342310615319356405265}{6090026173840654386622070022661166681208230391556732632746721266852361178309633221671326156131010321177595015397118} a^{29} + \frac{45814993594538189140579984703134906622095289290678946318661736965138641331398263023724578032985491531758834333157}{6090026173840654386622070022661166681208230391556732632746721266852361178309633221671326156131010321177595015397118} a^{28} - \frac{373543304584207565608141549422773736124707569982906707940944219484069359645256338684202036127492028947567271746339}{3045013086920327193311035011330583340604115195778366316373360633426180589154816610835663078065505160588797507698559} a^{27} - \frac{1396593621264450815559790084741390292068121230910134378282924729268765757231733428888902469650654614846625359847390}{3045013086920327193311035011330583340604115195778366316373360633426180589154816610835663078065505160588797507698559} a^{26} - \frac{193342031234067614028151022802574798602434436791418069461446941512374642092703528784547604962164036191287236965935}{3045013086920327193311035011330583340604115195778366316373360633426180589154816610835663078065505160588797507698559} a^{25} - \frac{219123890430764990373215136248092728030116313164525637439743193186556889526398606081448921629860843261100528558753}{6090026173840654386622070022661166681208230391556732632746721266852361178309633221671326156131010321177595015397118} a^{24} + \frac{1024795541181601101495858826561465263950118835824050818081374618702050303326436253631652668689570820328790213032685}{6090026173840654386622070022661166681208230391556732632746721266852361178309633221671326156131010321177595015397118} a^{23} - \frac{409433869821425328055543673255382263970794875244206193474775394980005431366893366743173989320042418732382481785626}{3045013086920327193311035011330583340604115195778366316373360633426180589154816610835663078065505160588797507698559} a^{22} + \frac{1473726538773266774681621748530448146098404471381506665193351638379012992173166628613792175243902882624745025049745}{3045013086920327193311035011330583340604115195778366316373360633426180589154816610835663078065505160588797507698559} a^{21} + \frac{597230298178591251021299740498267287198757290022009997315811129774394431144729399447282971068958134043518292698341}{6090026173840654386622070022661166681208230391556732632746721266852361178309633221671326156131010321177595015397118} a^{20} + \frac{13140442381733786812755474660137784212879061619611708137622206559930032422734811135710131002915211878745944326951}{3045013086920327193311035011330583340604115195778366316373360633426180589154816610835663078065505160588797507698559} a^{19} - \frac{290711845416281952940599364473957091415911566376682167471362831446006462360728492716702775414382194270413394936451}{3045013086920327193311035011330583340604115195778366316373360633426180589154816610835663078065505160588797507698559} a^{18} - \frac{972815496842944154583984687403589080176379468885486784241028812364049577501329472162094100437867828478190434726175}{3045013086920327193311035011330583340604115195778366316373360633426180589154816610835663078065505160588797507698559} a^{17} + \frac{419174603968017723738283816539699408274631896306428035233468939012578056964035357933850999863729059819748020477758}{3045013086920327193311035011330583340604115195778366316373360633426180589154816610835663078065505160588797507698559} a^{16} + \frac{582546642310061491479627050576694471823080555614393769659284474113930935139834963453565660904388483580671669480025}{6090026173840654386622070022661166681208230391556732632746721266852361178309633221671326156131010321177595015397118} a^{15} - \frac{1528281639608707355006223330968505057052309866151234999126790006179268154028447786777252425984729085322621719052687}{6090026173840654386622070022661166681208230391556732632746721266852361178309633221671326156131010321177595015397118} a^{14} - \frac{2951507799626711203873346537299789607800024035080195526047605614419245276221689376324756308344016109435126704421351}{6090026173840654386622070022661166681208230391556732632746721266852361178309633221671326156131010321177595015397118} a^{13} - \frac{849911329406796944413750476208204016947129128953382731020533630670381381426537627213787274522883600031106352408967}{6090026173840654386622070022661166681208230391556732632746721266852361178309633221671326156131010321177595015397118} a^{12} + \frac{809349665439412320157633644360056275525820273989277088102360813756702573512523789416648526178120586824757607647388}{3045013086920327193311035011330583340604115195778366316373360633426180589154816610835663078065505160588797507698559} a^{11} - \frac{444790636471584303420709589769632815330282489925894122057434569417631467580060305341866416830894023171997759590892}{3045013086920327193311035011330583340604115195778366316373360633426180589154816610835663078065505160588797507698559} a^{10} - \frac{997206024875290871833023799264243316950104277069979393767208400291476410618791094229767513947410636409349360132503}{3045013086920327193311035011330583340604115195778366316373360633426180589154816610835663078065505160588797507698559} a^{9} - \frac{639305319026205289174295287197806862290129404040250118089287038297756288034881137671508692867938887500820274682967}{6090026173840654386622070022661166681208230391556732632746721266852361178309633221671326156131010321177595015397118} a^{8} - \frac{6047988545286781356290149726540765766307969975657715341848892380798789517053363421652720866357189856400762997289}{3045013086920327193311035011330583340604115195778366316373360633426180589154816610835663078065505160588797507698559} a^{7} + \frac{527099779225730550674048369955838804639044364970660572918244519604165115515486117427396528893054438237207570465108}{3045013086920327193311035011330583340604115195778366316373360633426180589154816610835663078065505160588797507698559} a^{6} + \frac{2255489136566815422571246372204837047297581020934873013386035906806947954671099025865928425620066837015721229151943}{6090026173840654386622070022661166681208230391556732632746721266852361178309633221671326156131010321177595015397118} a^{5} - \frac{2534451079648900960262625714878471468442099644235657800262840739088382075565004908173488237866027065601756530819079}{6090026173840654386622070022661166681208230391556732632746721266852361178309633221671326156131010321177595015397118} a^{4} - \frac{612094911130913755922950653699641783716724187463438303621370643740910527948799292436135935264597449871289699577595}{3045013086920327193311035011330583340604115195778366316373360633426180589154816610835663078065505160588797507698559} a^{3} + \frac{2296524175619526012367727097730141322576573608366531075875364513246281821928432068134041058847464601486317993561997}{6090026173840654386622070022661166681208230391556732632746721266852361178309633221671326156131010321177595015397118} a^{2} + \frac{868393483315063362990301708328335007775969177669569660411243085873692982387796355739626441784897091302980471125214}{3045013086920327193311035011330583340604115195778366316373360633426180589154816610835663078065505160588797507698559} a + \frac{402197182752830419355067521356798682438577231005974069718880760582666516845215051760012737222273229428085000345204}{3045013086920327193311035011330583340604115195778366316373360633426180589154816610835663078065505160588797507698559}$

magma: IntegralBasis(K);
 
sage: K.integral_basis()
 
gp: K.zk
 

Class group and class number

Not computed

magma: ClassGroup(K);
 
sage: K.class_group().invariants()
 
gp: K.clgp
 

Unit group

magma: UK, f := UnitGroup(K);
 
sage: UK = K.unit_group()
 
Rank:  $35$
magma: UnitRank(K);
 
sage: UK.rank()
 
gp: K.fu
 
Torsion generator:  \( -1 \) (order $2$)
magma: K!f(TU.1) where TU,f is TorsionUnitGroup(K);
 
sage: UK.torsion_generator()
 
gp: K.tu[2]
 
Fundamental units:  Not computed
magma: [K!f(g): g in Generators(UK)];
 
sage: UK.fundamental_units()
 
gp: K.fu
 
Regulator:  Not computed
magma: Regulator(K);
 
sage: K.regulator()
 
gp: K.reg
 

Galois group

$C_{36}$ (as 36T1):

magma: GaloisGroup(K);
 
sage: K.galois_group(type='pari')
 
gp: polgalois(K.pol)
 
A cyclic group of order 36
The 36 conjugacy class representatives for $C_{36}$
Character table for $C_{36}$ is not computed

Intermediate fields

\(\Q(\sqrt{17}) \), 3.3.361.1, 4.4.4913.1, 6.6.640267073.1, \(\Q(\zeta_{19})^+\), 12.12.2014044676385121747377.1, 18.18.34205654728777159191037355893457.1

Fields in the database are given up to isomorphism. Isomorphic intermediate fields are shown with their multiplicities.

Frobenius cycle types

$p$ 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59
Cycle type $18^{2}$ $36$ $36$ ${\href{/LocalNumberField/7.12.0.1}{12} }^{3}$ ${\href{/LocalNumberField/11.12.0.1}{12} }^{3}$ ${\href{/LocalNumberField/13.9.0.1}{9} }^{4}$ R R $36$ $36$ ${\href{/LocalNumberField/31.12.0.1}{12} }^{3}$ ${\href{/LocalNumberField/37.4.0.1}{4} }^{9}$ $36$ $18^{2}$ ${\href{/LocalNumberField/47.9.0.1}{9} }^{4}$ $18^{2}$ $18^{2}$

In the table, R denotes a ramified prime. Cycle lengths which are repeated in a cycle type are indicated by exponents.

magma: p := 7; // to obtain a list of $[e_i,f_i]$ for the factorization of the ideal $p\mathcal{O}_K$:
 
magma: idealfactors := Factorization(p*Integers(K)); // get the data
 
magma: [<primefactor[2], Valuation(Norm(primefactor[1]), p)> : primefactor in idealfactors];
 
sage: p = 7; # to obtain a list of $[e_i,f_i]$ for the factorization of the ideal $p\mathcal{O}_K$:
 
sage: [(e, pr.norm().valuation(p)) for pr,e in K.factor(p)]
 
gp: p = 7; \\ to obtain a list of $[e_i,f_i]$ for the factorization of the ideal $p\mathcal{O}_K$:
 
gp: idealfactors = idealprimedec(K, p); \\ get the data
 
gp: vector(length(idealfactors), j, [idealfactors[j][3], idealfactors[j][4]])
 

Local algebras for ramified primes

$p$LabelPolynomial $e$ $f$ $c$ Galois group Slope content
17Data not computed
19Data not computed