Atkin-Lehner |
3- 17+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
77163d |
Isogeny class |
Conductor |
77163 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
3649536 |
Modular degree for the optimal curve |
Δ |
684774901335165273 = 36 · 179 · 892 |
Discriminant |
Eigenvalues |
1 3- 2 4 -2 2 17+ 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-21555505,-38521697977] |
[a1,a2,a3,a4,a6] |
Generators |
[-116993621060407:52432013229595:43651389761] |
Generators of the group modulo torsion |
j |
45888594979016241577/28369671417 |
j-invariant |
L |
13.063442923971 |
L(r)(E,1)/r! |
Ω |
0.070066435273206 |
Real period |
R |
15.536972006349 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002202 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
4539c1 |
Quadratic twists by: 17 |