Atkin-Lehner |
2- 11- 47- |
Signs for the Atkin-Lehner involutions |
Class |
33088bh |
Isogeny class |
Conductor |
33088 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-33882112 = -1 · 216 · 11 · 47 |
Discriminant |
Eigenvalues |
2- 0 4 1 11- 7 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,52,-240] |
[a1,a2,a3,a4,a6] |
j |
237276/517 |
j-invariant |
L |
4.3011360057776 |
L(r)(E,1)/r! |
Ω |
1.0752840014444 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33088b1 8272a1 |
Quadratic twists by: -4 8 |