Atkin-Lehner |
3+ 5+ 7- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
8715b |
Isogeny class |
Conductor |
8715 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
6720 |
Modular degree for the optimal curve |
Δ |
-194567821875 = -1 · 37 · 55 · 73 · 83 |
Discriminant |
Eigenvalues |
0 3+ 5+ 7- 2 -2 6 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-201,-21184] |
[a1,a2,a3,a4,a6] |
j |
-902548946944/194567821875 |
j-invariant |
L |
1.3473888074937 |
L(r)(E,1)/r! |
Ω |
0.44912960249791 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
26145s1 43575o1 61005ba1 |
Quadratic twists by: -3 5 -7 |