Atkin-Lehner |
3- 7+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
33033u |
Isogeny class |
Conductor |
33033 |
Conductor |
∏ cp |
28 |
Product of Tamagawa factors cp |
deg |
87360 |
Modular degree for the optimal curve |
Δ |
-3878278310907 = -1 · 37 · 7 · 117 · 13 |
Discriminant |
Eigenvalues |
-2 3- 0 7+ 11- 13+ -6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-11898,504488] |
[a1,a2,a3,a4,a6] |
Generators |
[51:-182:1] |
Generators of the group modulo torsion |
j |
-105154048000/2189187 |
j-invariant |
L |
2.8119492678499 |
L(r)(E,1)/r! |
Ω |
0.7843915024169 |
Real period |
R |
0.12803142213629 |
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 |
99099u1 3003i1 |
Quadratic twists by: -3 -11 |