Atkin-Lehner |
2- 3+ 7- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
12768n |
Isogeny class |
Conductor |
12768 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
Δ |
-1211832377021952 = -1 · 29 · 32 · 712 · 19 |
Discriminant |
Eigenvalues |
2- 3+ 2 7- 0 -2 -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-37392,3260628] |
[a1,a2,a3,a4,a6] |
Generators |
[-164:2226:1] |
Generators of the group modulo torsion |
j |
-11292795168713864/2366860111371 |
j-invariant |
L |
4.5437988246743 |
L(r)(E,1)/r! |
Ω |
0.46517408970811 |
Real period |
R |
3.2559844620219 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
12768z4 25536do3 38304r2 89376cx2 |
Quadratic twists by: -4 8 -3 -7 |