Atkin-Lehner |
2- 3+ 13+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
69966w |
Isogeny class |
Conductor |
69966 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
18432 |
Modular degree for the optimal curve |
Δ |
-26866944 = -1 · 28 · 33 · 132 · 23 |
Discriminant |
Eigenvalues |
2- 3+ 3 0 -4 13+ -2 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-71,-321] |
[a1,a2,a3,a4,a6] |
Generators |
[11:6:1] |
Generators of the group modulo torsion |
j |
-8560539/5888 |
j-invariant |
L |
11.867082369891 |
L(r)(E,1)/r! |
Ω |
0.79887422004803 |
Real period |
R |
0.92842230914428 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000342 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69966b1 69966c1 |
Quadratic twists by: -3 13 |