Atkin-Lehner |
2- 3+ 7- 59- |
Signs for the Atkin-Lehner involutions |
Class |
69384w |
Isogeny class |
Conductor |
69384 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
67584 |
Modular degree for the optimal curve |
Δ |
-48977749296 = -1 · 24 · 32 · 78 · 59 |
Discriminant |
Eigenvalues |
2- 3+ -2 7- 6 0 -2 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,621,-9036] |
[a1,a2,a3,a4,a6] |
j |
14047232/26019 |
j-invariant |
L |
2.3639725341429 |
L(r)(E,1)/r! |
Ω |
0.59099313669005 |
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 |
9912l1 |
Quadratic twists by: -7 |