Atkin-Lehner |
2+ 3+ 7+ 67+ |
Signs for the Atkin-Lehner involutions |
Class |
67536c |
Isogeny class |
Conductor |
67536 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
25738240 |
Modular degree for the optimal curve |
Δ |
1.7213191396443E+19 |
Discriminant |
Eigenvalues |
2+ 3+ 2 7+ -6 6 6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1977322254,-33842644730725] |
[a1,a2,a3,a4,a6] |
Generators |
[1215846822701196346640213785994892556725423851657050973746485412858531629062874654321213006866069200004833295072738260330937765278879790857340818976978154869237969396677731824576416047941467122069197023013:-459768556302442550392355110606074001138816933005187557833395435695609666983115635015661309546240679946017905875194053073882577281010683975141662294984552659554272643751574968502788810240073269605380118215610:7745938273273006904214278899864416565786955080269982283362606098748753790765320006446957570118277095077090122816138825253733493788358026148159243185238533721166136965892751797321510233824819004201631] |
Generators of the group modulo torsion |
j |
1979120912964331319793367824384/39845350454728903 |
j-invariant |
L |
7.0912850082447 |
L(r)(E,1)/r! |
Ω |
0.022640196460549 |
Real period |
R |
313.21658452044 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
33768n1 67536f1 |
Quadratic twists by: -4 -3 |