Atkin-Lehner |
2+ 3- 13- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
47424bo |
Isogeny class |
Conductor |
47424 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
921600 |
Modular degree for the optimal curve |
Δ |
672109908081251328 = 210 · 318 · 13 · 194 |
Discriminant |
Eigenvalues |
2+ 3- 0 4 2 13- -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-2232653,1282694259] |
[a1,a2,a3,a4,a6] |
Generators |
[3547:194940:1] |
Generators of the group modulo torsion |
j |
1201953427358681344000/656357332110597 |
j-invariant |
L |
8.7781451993957 |
L(r)(E,1)/r! |
Ω |
0.28346336208104 |
Real period |
R |
1.7204153994361 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999921 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
47424cm1 5928a1 |
Quadratic twists by: -4 8 |