Atkin-Lehner |
3+ 5- 11- 71- |
Signs for the Atkin-Lehner involutions |
Class |
128865l |
Isogeny class |
Conductor |
128865 |
Conductor |
∏ cp |
96 |
Product of Tamagawa factors cp |
deg |
1105920 |
Modular degree for the optimal curve |
Δ |
-557101994675007375 = -1 · 32 · 53 · 117 · 714 |
Discriminant |
Eigenvalues |
-1 3+ 5- 0 11- -2 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-172125,45150810] |
[a1,a2,a3,a4,a6] |
Generators |
[-486:4025:1] [-227:8633:1] |
Generators of the group modulo torsion |
j |
-318346162232041/314469552375 |
j-invariant |
L |
7.2852987690766 |
L(r)(E,1)/r! |
Ω |
0.26562032232365 |
Real period |
R |
4.5712483555493 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999990964 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
11715d1 |
Quadratic twists by: -11 |