Atkin-Lehner |
2+ 3- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
6768b |
Isogeny class |
Conductor |
6768 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
7680 |
Modular degree for the optimal curve |
Δ |
4708334843136 = 28 · 311 · 473 |
Discriminant |
Eigenvalues |
2+ 3- -1 -3 1 -2 -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-8868,-304004] |
[a1,a2,a3,a4,a6] |
j |
413269421056/25228989 |
j-invariant |
L |
0.9877094032612 |
L(r)(E,1)/r! |
Ω |
0.4938547016306 |
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 |
3384e1 27072bz1 2256g1 |
Quadratic twists by: -4 8 -3 |