Atkin-Lehner |
2+ 3- 47- |
Signs for the Atkin-Lehner involutions |
Class |
6768d |
Isogeny class |
Conductor |
6768 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
2560 |
Modular degree for the optimal curve |
Δ |
2131432704 = 28 · 311 · 47 |
Discriminant |
Eigenvalues |
2+ 3- 1 1 -1 -4 4 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-732,7292] |
[a1,a2,a3,a4,a6] |
Generators |
[1:81:1] |
Generators of the group modulo torsion |
j |
232428544/11421 |
j-invariant |
L |
4.4548886930065 |
L(r)(E,1)/r! |
Ω |
1.4481329610301 |
Real period |
R |
0.76907452783853 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
3384g1 27072cl1 2256a1 |
Quadratic twists by: -4 8 -3 |