↑

Properties

Label 36.0.29411719834...3125.1
Degree $36$
Signature $[0, 18]$
Discriminant $5^{18}\cdot 37^{35}$
Root discriminant $74.84$
Ramified primes $5, 37$
Class number Not computed
Class group Not computed
Galois group $C_{36}$ (as 36T1)

Related objects

Downloads

Learn more about

Show commands for: Magma / SageMath / Pari/GP

magma: R<x> := PolynomialRing(Rationals()); K<a> := NumberField(R![54018521, -54018484, 54018484, -54016375, 54016375, -53980522, 53980522, -53693698, 53693698, -52379088, 52379088, -48530866, 48530866, -40834422, 40834422, -29839502, 29839502, -18278667, 18278667, -9151692, 9151692, -3675507, 3675507, -1164687, 1164687, -285900, 285900, -53059, 53059, -7179, 7179, -667, 667, -38, 38, -1, 1]);
 
sage: x = polygen(QQ); K.<a> = NumberField(x^36 - x^35 + 38*x^34 - 38*x^33 + 667*x^32 - 667*x^31 + 7179*x^30 - 7179*x^29 + 53059*x^28 - 53059*x^27 + 285900*x^26 - 285900*x^25 + 1164687*x^24 - 1164687*x^23 + 3675507*x^22 - 3675507*x^21 + 9151692*x^20 - 9151692*x^19 + 18278667*x^18 - 18278667*x^17 + 29839502*x^16 - 29839502*x^15 + 40834422*x^14 - 40834422*x^13 + 48530866*x^12 - 48530866*x^11 + 52379088*x^10 - 52379088*x^9 + 53693698*x^8 - 53693698*x^7 + 53980522*x^6 - 53980522*x^5 + 54016375*x^4 - 54016375*x^3 + 54018484*x^2 - 54018484*x + 54018521)
 
gp: K = bnfinit(x^36 - x^35 + 38*x^34 - 38*x^33 + 667*x^32 - 667*x^31 + 7179*x^30 - 7179*x^29 + 53059*x^28 - 53059*x^27 + 285900*x^26 - 285900*x^25 + 1164687*x^24 - 1164687*x^23 + 3675507*x^22 - 3675507*x^21 + 9151692*x^20 - 9151692*x^19 + 18278667*x^18 - 18278667*x^17 + 29839502*x^16 - 29839502*x^15 + 40834422*x^14 - 40834422*x^13 + 48530866*x^12 - 48530866*x^11 + 52379088*x^10 - 52379088*x^9 + 53693698*x^8 - 53693698*x^7 + 53980522*x^6 - 53980522*x^5 + 54016375*x^4 - 54016375*x^3 + 54018484*x^2 - 54018484*x + 54018521, 1)
 

Normalized defining polynomial

\( x^{36} - x^{35} + 38 x^{34} - 38 x^{33} + 667 x^{32} - 667 x^{31} + 7179 x^{30} - 7179 x^{29} + 53059 x^{28} - 53059 x^{27} + 285900 x^{26} - 285900 x^{25} + 1164687 x^{24} - 1164687 x^{23} + 3675507 x^{22} - 3675507 x^{21} + 9151692 x^{20} - 9151692 x^{19} + 18278667 x^{18} - 18278667 x^{17} + 29839502 x^{16} - 29839502 x^{15} + 40834422 x^{14} - 40834422 x^{13} + 48530866 x^{12} - 48530866 x^{11} + 52379088 x^{10} - 52379088 x^{9} + 53693698 x^{8} - 53693698 x^{7} + 53980522 x^{6} - 53980522 x^{5} + 54016375 x^{4} - 54016375 x^{3} + 54018484 x^{2} - 54018484 x + 54018521 \)

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

Invariants

Degree:  $36$
magma: Degree(K);
 
sage: K.degree()
 
gp: poldegree(K.pol)
 
Signature:  $[0, 18]$
magma: Signature(K);
 
sage: K.signature()
 
gp: K.sign
 
Discriminant:  \(29411719834995153896864925426307140281034671856927417346954345703125=5^{18}\cdot 37^{35}\)
magma: Discriminant(Integers(K));
 
sage: K.disc()
 
gp: K.disc
 
Root discriminant:  $74.84$
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:  $5, 37$
magma: PrimeDivisors(Discriminant(Integers(K)));
 
sage: K.disc().support()
 
gp: factor(abs(K.disc))[,1]~
 
This field is Galois and abelian over $\Q$.
Conductor:  \(185=5\cdot 37\)
Dirichlet character group:    $\lbrace$$\chi_{185}(1,·)$, $\chi_{185}(134,·)$, $\chi_{185}(129,·)$, $\chi_{185}(136,·)$, $\chi_{185}(11,·)$, $\chi_{185}(141,·)$, $\chi_{185}(14,·)$, $\chi_{185}(16,·)$, $\chi_{185}(19,·)$, $\chi_{185}(21,·)$, $\chi_{185}(151,·)$, $\chi_{185}(24,·)$, $\chi_{185}(26,·)$, $\chi_{185}(154,·)$, $\chi_{185}(36,·)$, $\chi_{185}(39,·)$, $\chi_{185}(41,·)$, $\chi_{185}(46,·)$, $\chi_{185}(29,·)$, $\chi_{185}(176,·)$, $\chi_{185}(179,·)$, $\chi_{185}(181,·)$, $\chi_{185}(54,·)$, $\chi_{185}(59,·)$, $\chi_{185}(69,·)$, $\chi_{185}(71,·)$, $\chi_{185}(79,·)$, $\chi_{185}(81,·)$, $\chi_{185}(86,·)$, $\chi_{185}(89,·)$, $\chi_{185}(94,·)$, $\chi_{185}(101,·)$, $\chi_{185}(109,·)$, $\chi_{185}(119,·)$, $\chi_{185}(121,·)$, $\chi_{185}(124,·)$$\rbrace$
This is a CM field.

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

$1$, $a$, $a^{2}$, $a^{3}$, $a^{4}$, $a^{5}$, $a^{6}$, $a^{7}$, $a^{8}$, $a^{9}$, $a^{10}$, $a^{11}$, $a^{12}$, $a^{13}$, $a^{14}$, $a^{15}$, $a^{16}$, $a^{17}$, $a^{18}$, $\frac{1}{24157817} a^{19} - \frac{9227465}{24157817} a^{18} + \frac{19}{24157817} a^{17} + \frac{3010349}{24157817} a^{16} + \frac{152}{24157817} a^{15} + \frac{10498709}{24157817} a^{14} + \frac{665}{24157817} a^{13} + \frac{10787863}{24157817} a^{12} + \frac{1729}{24157817} a^{11} + \frac{9898509}{24157817} a^{10} + \frac{2717}{24157817} a^{9} + \frac{8130747}{24157817} a^{8} + \frac{2508}{24157817} a^{7} - \frac{9781297}{24157817} a^{6} + \frac{1254}{24157817} a^{5} - \frac{6320798}{24157817} a^{4} + \frac{285}{24157817} a^{3} + \frac{1467662}{24157817} a^{2} + \frac{19}{24157817} a + \frac{5702887}{24157817}$, $\frac{1}{24157817} a^{20} + \frac{20}{24157817} a^{18} + \frac{9227465}{24157817} a^{17} + \frac{170}{24157817} a^{16} + \frac{11920003}{24157817} a^{15} + \frac{800}{24157817} a^{14} + \frac{10966570}{24157817} a^{13} + \frac{2275}{24157817} a^{12} - \frac{4131543}{24157817} a^{11} + \frac{4004}{24157817} a^{10} + \frac{3339106}{24157817} a^{9} + \frac{4290}{24157817} a^{8} - \frac{10487763}{24157817} a^{7} + \frac{2640}{24157817} a^{6} - \frac{6674031}{24157817} a^{5} + \frac{825}{24157817} a^{4} - \frac{1906866}{24157817} a^{3} + \frac{100}{24157817} a^{2} + \frac{11920003}{24157817} a + \frac{2}{24157817}$, $\frac{1}{24157817} a^{21} + \frac{514229}{24157817} a^{18} - \frac{210}{24157817} a^{17} + \frac{28657}{24157817} a^{16} - \frac{2240}{24157817} a^{15} - \frac{5745074}{24157817} a^{14} - \frac{11025}{24157817} a^{13} - \frac{2468450}{24157817} a^{12} - \frac{30576}{24157817} a^{11} - \frac{1368538}{24157817} a^{10} - \frac{50050}{24157817} a^{9} - \frac{3997984}{24157817} a^{8} - \frac{47520}{24157817} a^{7} - \frac{4310627}{24157817} a^{6} - \frac{24255}{24157817} a^{5} + \frac{3720009}{24157817} a^{4} - \frac{5600}{24157817} a^{3} + \frac{6724580}{24157817} a^{2} - \frac{378}{24157817} a + \frac{6731345}{24157817}$, $\frac{1}{24157817} a^{22} - \frac{231}{24157817} a^{18} - \frac{9741694}{24157817} a^{17} - \frac{2618}{24157817} a^{16} - \frac{11434431}{24157817} a^{15} - \frac{13860}{24157817} a^{14} - \frac{6221297}{24157817} a^{13} - \frac{42042}{24157817} a^{12} + \frac{3368750}{24157817} a^{11} - \frac{77077}{24157817} a^{10} - \frac{4791}{24157817} a^{9} - \frac{84942}{24157817} a^{8} + \frac{10525159}{24157817} a^{7} - \frac{53361}{24157817} a^{6} + \frac{152574}{330929} a^{5} - \frac{16940}{24157817} a^{4} + \frac{5116217}{24157817} a^{3} - \frac{2079}{24157817} a^{2} - \frac{3039006}{24157817} a - \frac{42}{24157817}$, $\frac{1}{24157817} a^{23} + \frac{8759604}{24157817} a^{18} + \frac{1771}{24157817} a^{17} + \frac{7537312}{24157817} a^{16} + \frac{21252}{24157817} a^{15} + \frac{3198782}{24157817} a^{14} + \frac{111573}{24157817} a^{13} + \frac{7109952}{24157817} a^{12} + \frac{322322}{24157817} a^{11} - \frac{8441827}{24157817} a^{10} + \frac{542685}{24157817} a^{9} + \frac{4417990}{24157817} a^{8} + \frac{525987}{24157817} a^{7} - \frac{1664724}{24157817} a^{6} + \frac{272734}{24157817} a^{5} - \frac{5519101}{24157817} a^{4} + \frac{63756}{24157817} a^{3} - \frac{2218522}{24157817} a^{2} + \frac{4347}{24157817} a - \frac{11313038}{24157817}$, $\frac{1}{24157817} a^{24} + \frac{2024}{24157817} a^{18} + \frac{10209555}{24157817} a^{17} + \frac{25806}{24157817} a^{16} + \frac{418909}{24157817} a^{15} + \frac{145728}{24157817} a^{14} + \frac{54893}{330929} a^{13} + \frac{460460}{24157817} a^{12} - \frac{6845884}{24157817} a^{11} + \frac{868296}{24157817} a^{10} + \frac{23667}{24157817} a^{9} + \frac{976833}{24157817} a^{8} - \frac{11295903}{24157817} a^{7} + \frac{623392}{24157817} a^{6} + \frac{1744218}{24157817} a^{5} + \frac{200376}{24157817} a^{4} - \frac{10450511}{24157817} a^{3} + \frac{24840}{24157817} a^{2} - \frac{8640795}{24157817} a + \frac{506}{24157817}$, $\frac{1}{24157817} a^{25} - \frac{11551643}{24157817} a^{18} - \frac{12650}{24157817} a^{17} - \frac{4757583}{24157817} a^{16} - \frac{161920}{24157817} a^{15} - \frac{10658684}{24157817} a^{14} - \frac{885500}{24157817} a^{13} - \frac{2814028}{24157817} a^{12} - \frac{2631200}{24157817} a^{11} - \frac{7728256}{24157817} a^{10} - \frac{4522375}{24157817} a^{9} + \frac{7703363}{24157817} a^{8} - \frac{4452800}{24157817} a^{7} - \frac{141378}{330929} a^{6} - \frac{2337720}{24157817} a^{5} + \frac{3359448}{24157817} a^{4} - \frac{552000}{24157817} a^{3} - \frac{7777192}{24157817} a^{2} - \frac{37950}{24157817} a + \frac{4793238}{24157817}$, $\frac{1}{24157817} a^{26} - \frac{14950}{24157817} a^{18} - \frac{2696719}{24157817} a^{17} - \frac{203320}{24157817} a^{16} + \frac{5828228}{24157817} a^{15} - \frac{1196000}{24157817} a^{14} - \frac{3157239}{24157817} a^{13} - \frac{3887000}{24157817} a^{12} + \frac{10705649}{24157817} a^{11} - \frac{7482475}{24157817} a^{10} - \frac{11644706}{24157817} a^{9} - \frac{8551400}{24157817} a^{8} - \frac{4022533}{24157817} a^{7} - \frac{5525520}{24157817} a^{6} - \frac{5570430}{24157817} a^{5} - \frac{1794000}{24157817} a^{4} - \frac{1022049}{24157817} a^{3} - \frac{224250}{24157817} a^{2} + \frac{6854102}{24157817} a - \frac{4600}{24157817}$, $\frac{1}{24157817} a^{27} + \frac{11994418}{24157817} a^{18} + \frac{80730}{24157817} a^{17} + \frac{4532707}{24157817} a^{16} + \frac{1076400}{24157817} a^{15} - \frac{794738}{24157817} a^{14} + \frac{6054750}{24157817} a^{13} + \frac{11671207}{24157817} a^{12} - \frac{5791742}{24157817} a^{11} + \frac{4435719}{24157817} a^{10} + \frac{7909933}{24157817} a^{9} - \frac{11490027}{24157817} a^{8} + \frac{7811263}{24157817} a^{7} - \frac{8694279}{24157817} a^{6} - \frac{7204517}{24157817} a^{5} + \frac{8427955}{24157817} a^{4} + \frac{4036500}{24157817} a^{3} - \frac{11054651}{24157817} a^{2} + \frac{279450}{24157817} a + \frac{5224457}{24157817}$, $\frac{1}{24157817} a^{28} + \frac{98280}{24157817} a^{18} - \frac{5940882}{24157817} a^{17} + \frac{1392300}{24157817} a^{16} + \frac{12047818}{24157817} a^{15} + \frac{8424000}{24157817} a^{14} + \frac{7462847}{24157817} a^{13} + \frac{3790558}{24157817} a^{12} - \frac{6506017}{24157817} a^{11} + \frac{6338966}{24157817} a^{10} - \frac{11428600}{24157817} a^{9} - \frac{9230271}{24157817} a^{8} + \frac{9945359}{24157817} a^{7} - \frac{7038034}{24157817} a^{6} - \frac{6410043}{24157817} a^{5} - \frac{10644317}{24157817} a^{4} + \frac{946233}{24157817} a^{3} + \frac{1701000}{24157817} a^{2} - \frac{5249132}{24157817} a + \frac{35100}{24157817}$, $\frac{1}{24157817} a^{29} + \frac{9026955}{24157817} a^{18} - \frac{475020}{24157817} a^{17} - \frac{8424920}{24157817} a^{16} - \frac{6514560}{24157817} a^{15} - \frac{1135786}{24157817} a^{14} + \frac{10907809}{24157817} a^{13} + \frac{590839}{24157817} a^{12} + \frac{5517565}{24157817} a^{11} - \frac{1602530}{24157817} a^{10} - \frac{10521044}{24157817} a^{9} - \frac{11756892}{24157817} a^{8} - \frac{11946104}{24157817} a^{7} + \frac{11605053}{24157817} a^{6} + \frac{11059465}{24157817} a^{5} - \frac{9290482}{24157817} a^{4} - \frac{2150983}{24157817} a^{3} - \frac{745185}{24157817} a^{2} - \frac{1832220}{24157817} a + \frac{5777857}{24157817}$, $\frac{1}{24157817} a^{30} - \frac{593775}{24157817} a^{18} - \frac{10832346}{24157817} a^{17} - \frac{8652150}{24157817} a^{16} + \frac{3762623}{24157817} a^{15} - \frac{5124116}{24157817} a^{14} - \frac{11195620}{24157817} a^{13} - \frac{11007031}{24157817} a^{12} - \frac{3257943}{24157817} a^{11} + \frac{5745990}{24157817} a^{10} + \frac{86965}{330929} a^{9} - \frac{6147161}{24157817} a^{8} + \frac{7876442}{24157817} a^{7} - \frac{8588063}{24157817} a^{6} + \frac{924121}{24157817} a^{5} + \frac{6194768}{24157817} a^{4} + \frac{11459059}{24157817} a^{3} - \frac{11451375}{24157817} a^{2} + \frac{3370431}{24157817} a - \frac{237510}{24157817}$, $\frac{1}{24157817} a^{31} - \frac{7651487}{24157817} a^{18} + \frac{2629575}{24157817} a^{17} - \frac{11455366}{24157817} a^{16} - \frac{11501584}{24157817} a^{15} + \frac{7537456}{24157817} a^{14} - \frac{2671728}{24157817} a^{13} - \frac{5871753}{24157817} a^{12} - \frac{6403166}{24157817} a^{11} - \frac{6714912}{24157817} a^{10} - \frac{11434225}{24157817} a^{9} - \frac{919815}{24157817} a^{8} + \frac{6972800}{24157817} a^{7} - \frac{11285816}{24157817} a^{6} + \frac{1896291}{24157817} a^{5} - \frac{10239905}{24157817} a^{4} - \frac{11330219}{24157817} a^{3} - \frac{4715977}{24157817} a^{2} + \frac{11044215}{24157817} a + \frac{6361718}{24157817}$, $\frac{1}{24157817} a^{32} + \frac{3365856}{24157817} a^{18} - \frac{11024015}{24157817} a^{17} + \frac{1751474}{24157817} a^{16} + \frac{10988264}{24157817} a^{15} + \frac{94939}{24157817} a^{14} + \frac{9225532}{24157817} a^{13} + \frac{9081188}{24157817} a^{12} + \frac{8380212}{24157817} a^{11} - \frac{5995441}{24157817} a^{10} - \frac{11710073}{24157817} a^{9} - \frac{9654393}{24157817} a^{8} - \frac{2663118}{24157817} a^{7} + \frac{7753443}{24157817} a^{6} - \frac{5928556}{24157817} a^{5} - \frac{263551}{24157817} a^{4} + \frac{1754288}{24157817} a^{3} - \frac{1790475}{24157817} a^{2} + \frac{6793069}{24157817} a + \frac{1472562}{24157817}$, $\frac{1}{24157817} a^{33} + \frac{3247511}{24157817} a^{18} + \frac{10273661}{24157817} a^{17} + \frac{2139745}{24157817} a^{16} - \frac{4201016}{24157817} a^{15} + \frac{3256182}{24157817} a^{14} - \frac{6693888}{24157817} a^{13} - \frac{2341483}{24157817} a^{12} - \frac{3526568}{24157817} a^{11} - \frac{4197031}{24157817} a^{10} + \frac{1127498}{24157817} a^{9} - \frac{8985087}{24157817} a^{8} - \frac{2735272}{24157817} a^{7} - \frac{10845643}{24157817} a^{6} + \frac{6571000}{24157817} a^{5} + \frac{2034705}{24157817} a^{4} + \frac{5253245}{24157817} a^{3} + \frac{3211459}{24157817} a^{2} + \frac{9994749}{24157817} a + \frac{4385235}{24157817}$, $\frac{1}{24157817} a^{34} + \frac{6001613}{24157817} a^{18} - \frac{11247330}{24157817} a^{17} - \frac{8624429}{24157817} a^{16} - \frac{7209150}{24157817} a^{15} - \frac{3632760}{24157817} a^{14} - \frac{11890585}{24157817} a^{13} + \frac{7243473}{24157817} a^{12} + \frac{9627811}{24157817} a^{11} + \frac{10983998}{24157817} a^{10} + \frac{9288548}{24157817} a^{9} - \frac{5812453}{24157817} a^{8} + \frac{9738915}{24157817} a^{7} + \frac{4177637}{24157817} a^{6} - \frac{11830833}{24157817} a^{5} - \frac{6660060}{24157817} a^{4} - \frac{4332130}{24157817} a^{3} + \frac{2168299}{24157817} a^{2} - \frac{9001840}{24157817} a - \frac{8544096}{24157817}$, $\frac{1}{24157817} a^{35} - \frac{6930889}{24157817} a^{18} - \frac{1865991}{24157817} a^{17} - \frac{1986663}{24157817} a^{16} + \frac{2119110}{24157817} a^{15} - \frac{8958658}{24157817} a^{14} + \frac{2210633}{24157817} a^{13} - \frac{1061469}{24157817} a^{12} - \frac{2101386}{24157817} a^{11} + \frac{8250205}{24157817} a^{10} - \frac{5668499}{24157817} a^{9} - \frac{4706846}{24157817} a^{8} + \frac{2452224}{24157817} a^{7} + \frac{3775594}{24157817} a^{6} + \frac{4556142}{24157817} a^{5} + \frac{7395578}{24157817} a^{4} + \frac{6913601}{24157817} a^{3} + \frac{2420443}{24157817} a^{2} - \frac{1785658}{24157817} a + \frac{8632882}{24157817}$

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:  $17$
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

\(\Q(\sqrt{37}) \), 3.3.1369.1, 4.0.1266325.1, 6.6.69343957.1, 9.9.3512479453921.1, 12.0.2779962840304068953125.1, \(\Q(\zeta_{37})^+\)

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 $36$ ${\href{/LocalNumberField/3.9.0.1}{9} }^{4}$ R $18^{2}$ ${\href{/LocalNumberField/11.6.0.1}{6} }^{6}$ $36$ $36$ $36$ ${\href{/LocalNumberField/23.12.0.1}{12} }^{3}$ ${\href{/LocalNumberField/29.12.0.1}{12} }^{3}$ ${\href{/LocalNumberField/31.4.0.1}{4} }^{9}$ R $18^{2}$ ${\href{/LocalNumberField/43.4.0.1}{4} }^{9}$ ${\href{/LocalNumberField/47.6.0.1}{6} }^{6}$ $18^{2}$ $36$

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
5Data not computed
37Data not computed