Atkin-Lehner |
2- 5- 7+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
69440dd |
Isogeny class |
Conductor |
69440 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
568852480 = 219 · 5 · 7 · 31 |
Discriminant |
Eigenvalues |
2- 1 5- 7+ 3 -5 -6 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-37665,-2826145] |
[a1,a2,a3,a4,a6] |
Generators |
[-770963:2336:6859] |
Generators of the group modulo torsion |
j |
22542871522249/2170 |
j-invariant |
L |
6.9554889686202 |
L(r)(E,1)/r! |
Ω |
0.34269999916968 |
Real period |
R |
5.0740363180587 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000974 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69440bx1 17360q1 |
Quadratic twists by: -4 8 |