Atkin-Lehner |
2+ 3+ 7- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
68208i |
Isogeny class |
Conductor |
68208 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
98304 |
Modular degree for the optimal curve |
Δ |
-128393647872 = -1 · 28 · 3 · 78 · 29 |
Discriminant |
Eigenvalues |
2+ 3+ 4 7- 4 -2 2 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,964,-13152] |
[a1,a2,a3,a4,a6] |
j |
3286064/4263 |
j-invariant |
L |
4.4515614355859 |
L(r)(E,1)/r! |
Ω |
0.55644517920596 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
34104r1 9744f1 |
Quadratic twists by: -4 -7 |