Atkin-Lehner |
2+ 3- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368r |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
Δ |
797937134911488 = 214 · 39 · 114 · 132 |
Discriminant |
Eigenvalues |
2+ 3- 0 -2 11+ 13+ 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-24060,-465104] |
[a1,a2,a3,a4,a6] |
Generators |
[-136:540:1] [-78:968:1] |
Generators of the group modulo torsion |
j |
128962402000/66806883 |
j-invariant |
L |
10.352175451383 |
L(r)(E,1)/r! |
Ω |
0.40560449917785 |
Real period |
R |
1.5951769939092 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999512 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368el2 5148f2 27456bd2 |
Quadratic twists by: -4 8 -3 |