Atkin-Lehner |
2+ 3- 7- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
67536x |
Isogeny class |
Conductor |
67536 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
145152 |
Modular degree for the optimal curve |
Δ |
268050384 = 24 · 36 · 73 · 67 |
Discriminant |
Eigenvalues |
2+ 3- -3 7- -4 1 4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-86274,-9753669] |
[a1,a2,a3,a4,a6] |
Generators |
[-1163123:854:6859] |
Generators of the group modulo torsion |
j |
6088579813251072/22981 |
j-invariant |
L |
4.7084630814005 |
L(r)(E,1)/r! |
Ω |
0.27856693850544 |
Real period |
R |
5.6341492001197 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000255 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33768s1 7504j1 |
Quadratic twists by: -4 -3 |