Atkin-Lehner |
3- 5+ 7- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
69825bk |
Isogeny class |
Conductor |
69825 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
16416 |
Modular degree for the optimal curve |
Δ |
-11940075 = -1 · 33 · 52 · 72 · 192 |
Discriminant |
Eigenvalues |
0 3- 5+ 7- 0 2 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-513,-4651] |
[a1,a2,a3,a4,a6] |
Generators |
[69:541:1] |
Generators of the group modulo torsion |
j |
-12211978240/9747 |
j-invariant |
L |
6.6409838857426 |
L(r)(E,1)/r! |
Ω |
0.50147455890201 |
Real period |
R |
2.2071521435837 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999914 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69825bd1 69825e1 |
Quadratic twists by: 5 -7 |