Atkin-Lehner |
2+ 7+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
39872i |
Isogeny class |
Conductor |
39872 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
4976640 |
Modular degree for the optimal curve |
Δ |
8607840730087424 = 224 · 78 · 89 |
Discriminant |
Eigenvalues |
2+ -2 -2 7+ 0 -4 2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-684089889,-6887034378689] |
[a1,a2,a3,a4,a6] |
j |
135058930188560270934200713/32836306496 |
j-invariant |
L |
0.53136600579608 |
L(r)(E,1)/r! |
Ω |
0.02952033365067 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
39872bl1 1246b1 |
Quadratic twists by: -4 8 |