Atkin-Lehner |
2- 3+ 7+ 71+ |
Signs for the Atkin-Lehner involutions |
Class |
47712m |
Isogeny class |
Conductor |
47712 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
Δ |
-45265401925632 = -1 · 212 · 33 · 78 · 71 |
Discriminant |
Eigenvalues |
2- 3+ 2 7+ 0 -6 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,7023,228897] |
[a1,a2,a3,a4,a6] |
j |
9351255626432/11051123517 |
j-invariant |
L |
0.85383609225182 |
L(r)(E,1)/r! |
Ω |
0.4269180461904 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
47712k2 95424r1 |
Quadratic twists by: -4 8 |