Atkin-Lehner |
2- 3+ 11- 47- |
Signs for the Atkin-Lehner involutions |
Class |
68244d |
Isogeny class |
Conductor |
68244 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
1382400 |
Modular degree for the optimal curve |
Δ |
-186140993441432832 = -1 · 28 · 38 · 119 · 47 |
Discriminant |
Eigenvalues |
2- 3+ 2 1 11- -1 0 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-5170612,-4523766872] |
[a1,a2,a3,a4,a6] |
j |
-33709597668821968/410436477 |
j-invariant |
L |
1.201420356084 |
L(r)(E,1)/r! |
Ω |
0.050059181842579 |
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 |
6204b1 |
Quadratic twists by: -11 |