Atkin-Lehner |
2+ 11+ 13+ 41- |
Signs for the Atkin-Lehner involutions |
Class |
128986c |
Isogeny class |
Conductor |
128986 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
3514368 |
Modular degree for the optimal curve |
Δ |
-706856730651824896 = -1 · 28 · 119 · 134 · 41 |
Discriminant |
Eigenvalues |
2+ -2 1 5 11+ 13+ -3 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,222637,-1140306] |
[a1,a2,a3,a4,a6] |
j |
517588208389/299776256 |
j-invariant |
L |
1.3604379009724 |
L(r)(E,1)/r! |
Ω |
0.17005455592942 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
128986r1 |
Quadratic twists by: -11 |