Atkin-Lehner |
3- 5+ 13+ 73+ |
Signs for the Atkin-Lehner involutions |
Class |
42705c |
Isogeny class |
Conductor |
42705 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
944640 |
Modular degree for the optimal curve |
Δ |
-90582736105528875 = -1 · 321 · 53 · 13 · 732 |
Discriminant |
Eigenvalues |
-2 3- 5+ 1 5 13+ -7 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-710103,-230773946] |
[a1,a2,a3,a4,a6] |
j |
-54320058140180893696/124256153779875 |
j-invariant |
L |
0.32888168814023 |
L(r)(E,1)/r! |
Ω |
0.082220422064997 |
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 |
14235f1 |
Quadratic twists by: -3 |