Atkin-Lehner |
2- 13+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
13936b |
Isogeny class |
Conductor |
13936 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
8064 |
Modular degree for the optimal curve |
Δ |
-13012210432 = -1 · 28 · 132 · 673 |
Discriminant |
Eigenvalues |
2- 0 2 -4 2 13+ 3 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1544,-23988] |
[a1,a2,a3,a4,a6] |
Generators |
[66:402:1] |
Generators of the group modulo torsion |
j |
-1590104383488/50828947 |
j-invariant |
L |
4.5167983977142 |
L(r)(E,1)/r! |
Ω |
0.38009411056165 |
Real period |
R |
0.99028071211099 |
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 |
3484a1 55744i1 125424w1 |
Quadratic twists by: -4 8 -3 |