Atkin-Lehner |
3+ 29- 31- |
Signs for the Atkin-Lehner involutions |
Class |
78213d |
Isogeny class |
Conductor |
78213 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
3273984 |
Modular degree for the optimal curve |
Δ |
36427443545407059 = 34 · 299 · 31 |
Discriminant |
Eigenvalues |
1 3+ 1 2 0 2 5 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-78242452,-266418845903] |
[a1,a2,a3,a4,a6] |
Generators |
[-1901535789791171041070748308392:955434396166869586332887132753:372312594094686440047445683] |
Generators of the group modulo torsion |
j |
3651481427900669/2511 |
j-invariant |
L |
8.0729490341048 |
L(r)(E,1)/r! |
Ω |
0.050762025267366 |
Real period |
R |
39.758800952011 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
78213i1 |
Quadratic twists by: 29 |