Atkin-Lehner |
2- 3- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
6864t |
Isogeny class |
Conductor |
6864 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
3456 |
Modular degree for the optimal curve |
Δ |
-2699034624 = -1 · 221 · 32 · 11 · 13 |
Discriminant |
Eigenvalues |
2- 3- -1 3 11+ 13+ -4 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-736,-8332] |
[a1,a2,a3,a4,a6] |
Generators |
[58:384:1] |
Generators of the group modulo torsion |
j |
-10779215329/658944 |
j-invariant |
L |
4.9695086072095 |
L(r)(E,1)/r! |
Ω |
0.45663195216562 |
Real period |
R |
1.3603703660139 |
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 |
858g1 27456bv1 20592bm1 75504cw1 |
Quadratic twists by: -4 8 -3 -11 |