Atkin-Lehner |
2- 17- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
72896r |
Isogeny class |
Conductor |
72896 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-19827712 = -1 · 210 · 172 · 67 |
Discriminant |
Eigenvalues |
2- 2 0 -2 -2 6 17- 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,67,-67] |
[a1,a2,a3,a4,a6] |
Generators |
[8139:141128:27] |
Generators of the group modulo torsion |
j |
32000000/19363 |
j-invariant |
L |
9.0857343376149 |
L(r)(E,1)/r! |
Ω |
1.2577238535531 |
Real period |
R |
7.223950084044 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000039 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
72896k1 18224e1 |
Quadratic twists by: -4 8 |