Atkin-Lehner |
2- 7- 13+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
68432r |
Isogeny class |
Conductor |
68432 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
337920 |
Modular degree for the optimal curve |
Δ |
-238804476624896 = -1 · 232 · 7 · 132 · 47 |
Discriminant |
Eigenvalues |
2- 1 -3 7- 3 13+ -4 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-70112,-7207564] |
[a1,a2,a3,a4,a6] |
j |
-9305656686742753/58301874176 |
j-invariant |
L |
2.3462718092518 |
L(r)(E,1)/r! |
Ω |
0.14664198837612 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8554l1 |
Quadratic twists by: -4 |