Atkin-Lehner |
2+ 3+ 11- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
128832f |
Isogeny class |
Conductor |
128832 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1022976 |
Modular degree for the optimal curve |
Δ |
-13694898360287232 = -1 · 236 · 33 · 112 · 61 |
Discriminant |
Eigenvalues |
2+ 3+ 0 -4 11- -2 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-117953,16617153] |
[a1,a2,a3,a4,a6] |
j |
-692332063944625/52241891328 |
j-invariant |
L |
0.77937187452142 |
L(r)(E,1)/r! |
Ω |
0.38968612283427 |
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 |
128832bi1 4026i1 |
Quadratic twists by: -4 8 |