Atkin-Lehner |
2+ 7- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
128576x |
Isogeny class |
Conductor |
128576 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
79030009856 = 214 · 76 · 41 |
Discriminant |
Eigenvalues |
2+ 2 2 7- -2 6 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-2417,-42895] |
[a1,a2,a3,a4,a6] |
j |
810448/41 |
j-invariant |
L |
5.4640919353682 |
L(r)(E,1)/r! |
Ω |
0.68301151999435 |
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 |
128576cl1 16072c1 2624c1 |
Quadratic twists by: -4 8 -7 |