Atkin-Lehner |
2+ 3+ 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
6864a |
Isogeny class |
Conductor |
6864 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
10752 |
Modular degree for the optimal curve |
Δ |
-21186486427392 = -1 · 28 · 314 · 113 · 13 |
Discriminant |
Eigenvalues |
2+ 3+ 0 0 11+ 13+ -4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,2852,212608] |
[a1,a2,a3,a4,a6] |
Generators |
[399:13708:27] |
Generators of the group modulo torsion |
j |
10017976862000/82759712607 |
j-invariant |
L |
3.3804752610105 |
L(r)(E,1)/r! |
Ω |
0.49762077658408 |
Real period |
R |
6.7932759645121 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
3432c1 27456ci1 20592g1 75504e1 |
Quadratic twists by: -4 8 -3 -11 |