Atkin-Lehner |
3- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
69a |
Isogeny class |
Conductor |
69 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
2 |
Modular degree for the optimal curve |
Δ |
-207 = -1 · 32 · 23 |
Discriminant |
Eigenvalues |
1 3- 0 -2 4 -6 4 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-1,-1] |
[a1,a2,a3,a4,a6] |
j |
-15625/207 |
j-invariant |
L |
1.2029319337805 |
L(r)(E,1)/r! |
Ω |
2.405863867561 |
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 |
1104f1 4416c1 207a1 1725f1 |
Quadratic twists by: -4 8 -3 5 |