Atkin-Lehner |
3- 5- 7+ 13+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
69615r |
Isogeny class |
Conductor |
69615 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
2661120 |
Modular degree for the optimal curve |
Δ |
-1.4799268424875E+20 |
Discriminant |
Eigenvalues |
-2 3- 5- 7+ 2 13+ 17+ 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,477933,571316382] |
[a1,a2,a3,a4,a6] |
Generators |
[-73:23152:1] |
Generators of the group modulo torsion |
j |
16561407340532658176/203007797323387875 |
j-invariant |
L |
3.3922015596543 |
L(r)(E,1)/r! |
Ω |
0.13526974595225 |
Real period |
R |
2.089775960316 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001962 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23205j1 |
Quadratic twists by: -3 |