Atkin-Lehner |
2- 3+ 11+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
9768n |
Isogeny class |
Conductor |
9768 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
142496209152 = 28 · 33 · 11 · 374 |
Discriminant |
Eigenvalues |
2- 3+ -2 4 11+ -2 -6 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1924,-26300] |
[a1,a2,a3,a4,a6] |
Generators |
[4026:89873:8] |
Generators of the group modulo torsion |
j |
3078397198672/556625817 |
j-invariant |
L |
3.6096771518593 |
L(r)(E,1)/r! |
Ω |
0.7297897288182 |
Real period |
R |
4.9461879351259 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
19536p1 78144bk1 29304f1 107448e1 |
Quadratic twists by: -4 8 -3 -11 |