Atkin-Lehner |
2- 3- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
33708c |
Isogeny class |
Conductor |
33708 |
Conductor |
∏ cp |
39 |
Product of Tamagawa factors cp |
deg |
21060 |
Modular degree for the optimal curve |
Δ |
-71655252912 = -1 · 24 · 313 · 532 |
Discriminant |
Eigenvalues |
2- 3- 0 -1 4 -2 -4 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-353,-13248] |
[a1,a2,a3,a4,a6] |
Generators |
[31:81:1] |
Generators of the group modulo torsion |
j |
-108544000/1594323 |
j-invariant |
L |
6.8594149339211 |
L(r)(E,1)/r! |
Ω |
0.46852880714971 |
Real period |
R |
0.3753929993613 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
101124j1 33708a1 |
Quadratic twists by: -3 53 |