Atkin-Lehner |
2+ 3+ 5+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
33840a |
Isogeny class |
Conductor |
33840 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
333312 |
Modular degree for the optimal curve |
Δ |
-74008080000000 = -1 · 210 · 39 · 57 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 1 6 1 -5 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1377243,-622105542] |
[a1,a2,a3,a4,a6] |
Generators |
[15077540557833:-239493678546474:10232446211] |
Generators of the group modulo torsion |
j |
-14333893854522732/3671875 |
j-invariant |
L |
5.7692123931277 |
L(r)(E,1)/r! |
Ω |
0.069681406614238 |
Real period |
R |
20.698535927477 |
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 |
16920i1 33840e1 |
Quadratic twists by: -4 -3 |