Atkin-Lehner |
2- 7+ 13- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
68432h |
Isogeny class |
Conductor |
68432 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
8128512 |
Modular degree for the optimal curve |
Δ |
-1.0628732704252E+24 |
Discriminant |
Eigenvalues |
2- -1 -3 7+ 3 13- 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-3635112,49674856816] |
[a1,a2,a3,a4,a6] |
Generators |
[950506:926683018:1] |
Generators of the group modulo torsion |
j |
-1296932198474723107753/259490544537392378756 |
j-invariant |
L |
3.7291967209278 |
L(r)(E,1)/r! |
Ω |
0.071309911148383 |
Real period |
R |
13.07390747677 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999967964 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8554i1 |
Quadratic twists by: -4 |