Atkin-Lehner |
2- 3- 5- 7- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
129360hr |
Isogeny class |
Conductor |
129360 |
Conductor |
∏ cp |
128 |
Product of Tamagawa factors cp |
deg |
442368 |
Modular degree for the optimal curve |
Δ |
-61198663680000 = -1 · 218 · 32 · 54 · 73 · 112 |
Discriminant |
Eigenvalues |
2- 3- 5- 7- 11+ -4 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,9840,-19692] |
[a1,a2,a3,a4,a6] |
Generators |
[66:-960:1] |
Generators of the group modulo torsion |
j |
74991286313/43560000 |
j-invariant |
L |
8.9588465053223 |
L(r)(E,1)/r! |
Ω |
0.36922079469621 |
Real period |
R |
0.7582561952809 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999387914 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
16170bu1 129360dz1 |
Quadratic twists by: -4 -7 |