Atkin-Lehner |
2+ 3- 7- 13+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
82992u |
Isogeny class |
Conductor |
82992 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
70656 |
Modular degree for the optimal curve |
Δ |
-14432391792 = -1 · 24 · 32 · 74 · 133 · 19 |
Discriminant |
Eigenvalues |
2+ 3- 0 7- 0 13+ 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3648,83799] |
[a1,a2,a3,a4,a6] |
Generators |
[33:21:1] |
Generators of the group modulo torsion |
j |
-335650472608000/902024487 |
j-invariant |
L |
8.9122233346356 |
L(r)(E,1)/r! |
Ω |
1.2540555183253 |
Real period |
R |
0.88834018971168 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999979481 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
41496q1 |
Quadratic twists by: -4 |