Atkin-Lehner |
2+ 3- 7- 13- 61- |
Signs for the Atkin-Lehner involutions |
Class |
33306k |
Isogeny class |
Conductor |
33306 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
36864 |
Modular degree for the optimal curve |
Δ |
65264838912 = 28 · 38 · 72 · 13 · 61 |
Discriminant |
Eigenvalues |
2+ 3- -2 7- -4 13- 2 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-1242,11404] |
[a1,a2,a3,a4,a6] |
Generators |
[-19:177:1] |
Generators of the group modulo torsion |
j |
211634149400857/65264838912 |
j-invariant |
L |
4.4415369172051 |
L(r)(E,1)/r! |
Ω |
1.0210114803328 |
Real period |
R |
0.54376676986005 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
99918bh1 |
Quadratic twists by: -3 |