Atkin-Lehner |
3- 7- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
33033x |
Isogeny class |
Conductor |
33033 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
5760 |
Modular degree for the optimal curve |
Δ |
-7630623 = -1 · 32 · 72 · 113 · 13 |
Discriminant |
Eigenvalues |
-1 3- -2 7- 11+ 13+ 0 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-74,-285] |
[a1,a2,a3,a4,a6] |
Generators |
[13:25:1] |
Generators of the group modulo torsion |
j |
-33698267/5733 |
j-invariant |
L |
3.7924856738419 |
L(r)(E,1)/r! |
Ω |
0.80632540435491 |
Real period |
R |
2.3517091569722 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
99099bl1 33033q1 |
Quadratic twists by: -3 -11 |