Atkin-Lehner |
3+ 5- 11+ 67+ |
Signs for the Atkin-Lehner involutions |
Class |
33165f |
Isogeny class |
Conductor |
33165 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
8960 |
Modular degree for the optimal curve |
Δ |
33330825 = 33 · 52 · 11 · 672 |
Discriminant |
Eigenvalues |
1 3+ 5- -2 11+ 4 6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-84,-85] |
[a1,a2,a3,a4,a6] |
j |
2444008923/1234475 |
j-invariant |
L |
3.3243661032866 |
L(r)(E,1)/r! |
Ω |
1.6621830516425 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
33165d1 |
Quadratic twists by: -3 |