Atkin-Lehner |
2+ 11- 47- |
Signs for the Atkin-Lehner involutions |
Class |
33088p |
Isogeny class |
Conductor |
33088 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
-879435628544 = -1 · 214 · 11 · 474 |
Discriminant |
Eigenvalues |
2+ -1 -1 -2 11- 0 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,2379,5677] |
[a1,a2,a3,a4,a6] |
Generators |
[52:517:1] |
Generators of the group modulo torsion |
j |
90845732864/53676491 |
j-invariant |
L |
3.3638542058564 |
L(r)(E,1)/r! |
Ω |
0.54028220758934 |
Real period |
R |
1.556526459045 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33088x1 2068a1 |
Quadratic twists by: -4 8 |