Atkin-Lehner |
2+ 3- 5- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
87840o |
Isogeny class |
Conductor |
87840 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
131072 |
Modular degree for the optimal curve |
Δ |
10005525000000 = 26 · 38 · 58 · 61 |
Discriminant |
Eigenvalues |
2+ 3- 5- 2 0 2 4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-6357,-122056] |
[a1,a2,a3,a4,a6] |
Generators |
[-47:270:1] |
Generators of the group modulo torsion |
j |
608937674176/214453125 |
j-invariant |
L |
8.5524310219167 |
L(r)(E,1)/r! |
Ω |
0.55016885588061 |
Real period |
R |
0.97156888006456 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999946769 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
87840s1 29280q1 |
Quadratic twists by: -4 -3 |