Atkin-Lehner |
2+ 3+ 11+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
21648a |
Isogeny class |
Conductor |
21648 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
129024 |
Modular degree for the optimal curve |
Δ |
-7424324303616 = -1 · 28 · 312 · 113 · 41 |
Discriminant |
Eigenvalues |
2+ 3+ -3 5 11+ -6 -1 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-49772,-4259376] |
[a1,a2,a3,a4,a6] |
Generators |
[88844:137052:343] |
Generators of the group modulo torsion |
j |
-53265713623008208/29001266811 |
j-invariant |
L |
3.7476254208136 |
L(r)(E,1)/r! |
Ω |
0.15981162818566 |
Real period |
R |
5.8625668597467 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10824j1 86592dj1 64944x1 |
Quadratic twists by: -4 8 -3 |