Atkin-Lehner |
2+ 3+ 67+ |
Signs for the Atkin-Lehner involutions |
Class |
12864c |
Isogeny class |
Conductor |
12864 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
27648 |
Modular degree for the optimal curve |
Δ |
-5531284537344 = -1 · 222 · 39 · 67 |
Discriminant |
Eigenvalues |
2+ 3+ 3 -1 0 4 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-9249,363681] |
[a1,a2,a3,a4,a6] |
Generators |
[25:384:1] |
Generators of the group modulo torsion |
j |
-333822098953/21100176 |
j-invariant |
L |
4.7600001055242 |
L(r)(E,1)/r! |
Ω |
0.74992833563873 |
Real period |
R |
1.5868183262705 |
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 |
12864bn1 402d1 38592r1 |
Quadratic twists by: -4 8 -3 |