Atkin-Lehner |
2- 5+ 29- 47- |
Signs for the Atkin-Lehner involutions |
Class |
68150v |
Isogeny class |
Conductor |
68150 |
Conductor |
∏ cp |
128 |
Product of Tamagawa factors cp |
deg |
10321920 |
Modular degree for the optimal curve |
Δ |
3162160000000000000 = 216 · 513 · 292 · 47 |
Discriminant |
Eigenvalues |
2- 1 5+ -3 1 -5 -6 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-263126588,1642817867792] |
[a1,a2,a3,a4,a6] |
Generators |
[-1768:1450884:1] [9368:-4220:1] |
Generators of the group modulo torsion |
j |
128943035183824533700326649/202378240000000 |
j-invariant |
L |
15.715381882449 |
L(r)(E,1)/r! |
Ω |
0.16215561971517 |
Real period |
R |
0.75715180992893 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999301 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
13630a1 |
Quadratic twists by: 5 |