Atkin-Lehner |
2- 3+ 5- 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68970bt |
Isogeny class |
Conductor |
68970 |
Conductor |
∏ cp |
128 |
Product of Tamagawa factors cp |
deg |
184320 |
Modular degree for the optimal curve |
Δ |
33323062410000 = 24 · 32 · 54 · 117 · 19 |
Discriminant |
Eigenvalues |
2- 3+ 5- 0 11- 6 2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-8775,147885] |
[a1,a2,a3,a4,a6] |
j |
42180533641/18810000 |
j-invariant |
L |
4.7132934684841 |
L(r)(E,1)/r! |
Ω |
0.58916168453208 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
6270c1 |
Quadratic twists by: -11 |