Atkin-Lehner |
2+ 3- 5+ 11- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
19470m |
Isogeny class |
Conductor |
19470 |
Conductor |
∏ cp |
108 |
Product of Tamagawa factors cp |
deg |
134784 |
Modular degree for the optimal curve |
Δ |
-4114616949234000 = -1 · 24 · 39 · 53 · 116 · 59 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -1 11- 5 3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-69879,7745002] |
[a1,a2,a3,a4,a6] |
Generators |
[-217:3672:1] |
Generators of the group modulo torsion |
j |
-37735909554597608809/4114616949234000 |
j-invariant |
L |
4.5475093343483 |
L(r)(E,1)/r! |
Ω |
0.42731738236677 |
Real period |
R |
0.88683289478365 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
58410bi1 97350bt1 |
Quadratic twists by: -3 5 |