Atkin-Lehner |
2+ 5+ 11+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
78320a |
Isogeny class |
Conductor |
78320 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
5879808 |
Modular degree for the optimal curve |
Δ |
-4.0217784881592E+23 |
Discriminant |
Eigenvalues |
2+ 0 5+ 2 11+ 0 -4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-12761758,-35197727793] |
[a1,a2,a3,a4,a6] |
Generators |
[67724978390066699120940618688894131417651467319153721077829252614745412862341333201959:1515351689593088976265126363946799834220045460246100050233788786567664509722834812247094:14261482900077114999545127654110210865415129475734054660784576673478143240290403377] |
Generators of the group modulo torsion |
j |
-14365979557640915085010944/25136115550994873046875 |
j-invariant |
L |
5.090843036949 |
L(r)(E,1)/r! |
Ω |
0.037711763219464 |
Real period |
R |
134.99350341491 |
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 |
39160d1 |
Quadratic twists by: -4 |