Atkin-Lehner |
3+ 7+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
33033g |
Isogeny class |
Conductor |
33033 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
691200 |
Modular degree for the optimal curve |
Δ |
-6069928288905343863 = -1 · 310 · 74 · 117 · 133 |
Discriminant |
Eigenvalues |
-1 3+ 0 7+ 11- 13- 0 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-419328,-158206872] |
[a1,a2,a3,a4,a6] |
Generators |
[2974:156341:1] |
Generators of the group modulo torsion |
j |
-4602875775513625/3426316276383 |
j-invariant |
L |
2.9326544148175 |
L(r)(E,1)/r! |
Ω |
0.090860208901419 |
Real period |
R |
5.3794256222023 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999993 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
99099be1 3003d1 |
Quadratic twists by: -3 -11 |