Atkin-Lehner |
2- 3- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
51264be |
Isogeny class |
Conductor |
51264 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
274176 |
Modular degree for the optimal curve |
Δ |
-536239546598592 = -1 · 26 · 323 · 89 |
Discriminant |
Eigenvalues |
2- 3- 4 2 -2 -6 -4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-15888,1354790] |
[a1,a2,a3,a4,a6] |
Generators |
[20455:221389:125] |
Generators of the group modulo torsion |
j |
-9506571157504/11493474507 |
j-invariant |
L |
8.0836672870485 |
L(r)(E,1)/r! |
Ω |
0.47070006128152 |
Real period |
R |
8.5868559959395 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000049 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51264p1 12816j1 17088j1 |
Quadratic twists by: -4 8 -3 |