Atkin-Lehner |
2+ 11- 67- |
Signs for the Atkin-Lehner involutions |
Class |
64856d |
Isogeny class |
Conductor |
64856 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
102432 |
Modular degree for the optimal curve |
Δ |
-3676683526912 = -1 · 28 · 118 · 67 |
Discriminant |
Eigenvalues |
2+ 0 2 -4 11- -4 -5 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-5324,-175692] |
[a1,a2,a3,a4,a6] |
Generators |
[86:50:1] |
Generators of the group modulo torsion |
j |
-304128/67 |
j-invariant |
L |
4.4181013107024 |
L(r)(E,1)/r! |
Ω |
0.27620725263327 |
Real period |
R |
3.9989005246145 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001974 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
129712c1 64856j1 |
Quadratic twists by: -4 -11 |